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IV Brazilian Conference on Rheology – Rio de Janeiro, Brazil, July 02-04, 2008

METHODS OF ASSAYS FOR DEFINITION OF THE COMPOSITION OF THE PASTE IN SELF-COMPACTING CONCRETE (SCC)

SANTOS, Liane Ferreira/Graduate - Master of Science in Mechanical Engineering at FEIS – UNESP

[email protected]

Mônica Pinto Barbosa/Professor at the Civil Engineering Department at FEIS

– UNESP, Ilha Solteira, [email protected]

Geraldo de Freitas Maciel/Professor at the Civil Engineering Department at FEIS – UNESP, Ilha Solteira, Brazil.

[email protected]

SALLES, Flávio Moreira/Engineer CESP Laboratory –Ilha Solteira – SP

[email protected]

ABSTRACTThis paper describes the methodology used for the

paste flow and mortar funnel test of the paste in self-compacting concrete (SCC), for the method of Okamura et. al. and makes an analogy with the classic rheology, collating these test with test of characterization of the rheological parameters in rheometer R/S Brookfield. The influence of the ratio water/cement, percentage of limestone filler and the dosage of superplasticizer assumes decisive role in the workability of this cementitious materials. The cement paste show a not-Newtonian behavior, and the traditional tests allow measurements of viscosity for one determined shear stress, already with rheometer is possible, for the same sample, to carry through measurements of viscosity for a widely gamma of shear stress.

INTRODUCTIONThe self-compacting of fresh concrete is

characterized as the ability for its easiness of launching, moving itself and filling entirely the existing spaces between the armors, without influence of additional energy of compacting, being subject only to the action of the gravity. This concrete has the total volume of bigger paste when compared with the volume of paste of a conventional concrete, being imperative the study of the pastes for the paste flow and mortar funnel traditional test. However, the study the rheological parameters of cement pastes and additions come if becoming each more important time in the dosage of concrete with superplasticizer, in the behavior of the additions, the workability and its stability. In this way, the rheological study of the pastes it assumes basic role, making an analogy with the traditional tests of characterization and making possible one better agreement of the behavior of the results gotten in the tests.

METHODOLOGYPaste

The self-compacting concrete paste is composed of cementitious materials, limestone filer and water. This mixture makes possible stability and improvement in the workability of this cement based materials, a time that cause one better wrapping up of particles. Of this form

the program of tests developed encloses a study of the paste of the SCC, appealing to the paste flow and mortar funnel conventional test, and more complex tests for characterization of rheologicals parameters. In paragraphs subsequent the tests will be presented and will be clarified its importance.Paste flow test

The use of the cement substitution for limestone filler in the SCC has as purpose the reduction of the water required of the powder, being the excellent text of substitution determined for the paste flow test. This test is made using one form trunk conical for mixtures with different water/powder reasons volumetric, without use of superplasticizer, determining itself the average diameter of flow test. As result, water/powder volume versus relative area of flow test was represented a linear straight line of behavior of the mixture with relation and was verified the excellent text of substitution of limestone filler for the cement, scrumbling itself it necessity of the water of powder, since the main characteristic of particles of the cement is to possess high specific surfaces, thus causing, in a capacity of catch water approximately equivalent to the proper volume.Mortar funnel test

In this test the necessary time of flowability of a certain volume of paste through the inside orifice of the cone of Marsh for dosages of paste with different superplasticizer additive texts was determined. As result determined it dosage of saturation, represented for the mixture where the flowability time became constant.Rheological test

The described tests previously, enclose a small gamma of results, how much to the behavior of viscosity of the material, mentioning themselves only to one determined shear stress. The use of rheometer allows to the determination of viscosity for a vast interval of shears stress, making possible one better distinction of the behavior of the pastes. The rheological behavior of pastes with the same relation was determined water/powder and different texts of cement substitution for limestone filler, getting graphics of behavior and making possible to evaluate the behavior of the viscosity of the pastes with the text increment of filer. Also pastes with different dosages of superplasticizer had been made, verifying

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mailto:[email protected]




IV Brazilian Conference on Rheology – Rio de Janeiro, Brazil, July 02-04, 2008themselves the behavior of viscosity with the superplasticizer increment, and determining it dosage of saturation for one given dosage of stress.

ACKNOWLEDGMENTSThis study was carried out in the framework of the

UNESP – São Paulo State University, supported by the LABCESP – Laboratory of Engineering of the Company of Energy of São Paulo. Research as part of a special study dealing with the stability of cementitious materials.

REFERENCESSKARENDAHL, A.; PETERSSON, O.Self-compacting concrete, State-of-the-artreport of RILEM Committee 74-SCC,Report 23, RILEM Publications, 154 p.,2001.EFNARC, Specification and Guidelines for Self-compacting Concrete, 32 p., 2002.OKAMURA et al. Self-compacting concrete. Structural Concrete, pp. 3-17, 2000.NUNES, S. Betão Auto-Compactável: Tecnologia e Propriedades. Tese de Mestrado, Faculdade de Engenharia da Universidade do Porto (FEUP), Dep. Eng. Civil, 2001.NUNES, S.; COUTINHO, J. S.;FIGUEIRAS, J. Tecnologia do Betão Auto-compactável. V Simpósio EPSUP sobre Estruturas de Concreto, 2003.

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THE RHEOLOGICAL AND MECHANICAL BEHAVIOR OF THE DIFFERENT BRAZILIAN GROUTS

Felipe Sakae Bertolucci/Master-degree student at FEIS – UNESP, Ilha

Solteira, Brazil.

Mônica Pinto Barbosa/Professor at the Civil Engineering Department at FEIS

– UNESP, Ilha Solteira, Brazil.

Geraldo de Freitas Maciel/Professor at the Civil Engineering Department at FEIS – UNESP, Ilha Solteira, Brazil.

Marcelo de Araújo Ferreira/ Professor at the Building Civil Engineering

Department - Federal University of São Carlos –UFSCar, Brasil.

ABSTRACTGrout is a mortar of high resistance and compensated

retraction that has amongst its functions to fill the spaces between structural elements - beam and pillar. It is a product in dust ready for the use, to the cement base portland, natural and additive aggregates, that develops high mechanical resistances without retraction, being indicated, in general, for grouting services or as a mortar of repairs, presenting fluidity for a long period.

Through rheometrical assays, using rheometer R/S Brookfield, it was made the characterization of the material and, in the sequence the assays of mechanical properties such as axial compressive strength, diametrical compression, modulus of elasticity for different grouts existing in the market, with ages of rupture of 3 and 7 days.

The rheologic inquiry of grout has as one of its objectives the elaboration of a product with same rheological and mechanical characteristics, however without the addition of aggregates, and with bigger fluidity to be used in the fulfilling of meetings and niches of the industry of construction of concrete structures.

INTRODUCTIONThe rheology, as a science, explain the behavior of

“complex” materials that doesn’t fit in the simple classification of solid, liquid or gas, TARTTERSSALL [1976].

In a general way, suspensions are mixtures of the solid/liquid kind made by a group of particles distributed in a relatively uniform way through a liquid field, without the dissolution of the particled material in function of time, STEIN [1986].

In cases where the concentration of solids is very reduced (<5% of volume) and the frequency of collisions is relatively low, the suspension viscosity is usually constant in function of the shear rate and the suspension still behaves as a Newtonian fluid, where the shear tension is directly proportional to the deformation rate.

In this case the main factors that affects the suspension viscosity is the volumetric concentration of solids and the liquid field characteristics (density, for example); and temperature. However, as the solids concentration increases and the particles start to interact, the suspension’s rheological behavior deviates of the

Newtonian model and start to depend not only on the above mentioned factors, but other variables as well, among them, the particles physical characteristics (granulemetric distribution, shape, specific superficial area, superficial rugosity, density, among other); and the type of interaction between them (attraction, repulsion).

The rheological behavior of suspensions becomes even more complex when some molecules (dispersers) are added to the liquid field to adsorb the particles surface, in a way to impede the formation of agglomerates. In this case, other variables show as interest, as the liquid field disperser molecules concentration, molecular weight, and spatial disperser molecule conformation.

Grout is a fluid and self-compacting material in the just mixed state, made to fill sockets (small spaces between the blocks of foundations and the base of the equipment) and subsequently to become adherent, resistant and without retraction in the hard state. The mixture must present cohesion and must have fluidity enough to fill the emptinesses.

METHODOLOGYThe experimental procedure was made with assays

in the cool and in the hardened state for the grouts existing on the market.

For the accomplishment of these assays, the product was mixed in a mortar mixer of a 20-liter-capacity, per 1 minute in low speed, and 3 minutes in high speed.

The rheological assays of simple shear (shear stress x shear rate) had been carried through with samples soon after its preparation, under controlled tension. For the determination of the rheological parameters the methodology used was of the Vane Test type.

With the results, it was verified that the rheologic model of Hershel-Bulkley was what better adapted to the behavior presented by the grouts for one determined deformation band.

Concomitantly to the rheometrical assays, it was carried through, tests of slump flow, inferring on the workability of the grout.

The dosage of each grout analyzed was made in accordance with the data supplied for its respective manufacturer, with the objective of getting the maximum workability of the product. For this matter, it was used

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IV Brazilian Conference on Rheology – Rio de Janeiro, Brazil, July 02-04, 2008the maximum amount of water suggested by the manufacturer.

With this, some grouts presented an average scattering higher at 300 mm without having the necessity of applying blows in the consistency table. However for some samples it was necessary to apply 30 blows to get an opening higher than 240 mm. One of the assayed samples presented a fast setting time, beyond having presented expansion during the cure period.

In the sequence, it was started the molding of the cylindrical bodies of test with 10x20 cm for the accomplishment of the assays of mechanical properties. Assays of axial compressive strength, diametrical compression, modulus of elasticity for the rupture ages of 3 and 7 days was carried through. For the assays of retraction by drying, prismatic bodies of test with 25x25x285mm were made. The majority of the analyzed products had presented average retraction of 0.1%.

The inquiry will continue with a more detailed evaluation of its rheological behavior, from the restriction of the number of selected samples.

ACKNOWLEDGMENTSI thank the sponsors who had supplied grouts for the

development of the research: BASF, Vedacit, Sika and MC Bauchemie and Capes for the Master of Science grant.

REFERENCESABNT NORMAS, METHOD OF TESTS AND PROCEDURING: NBR 5738: Molding and curing of concrete cylindrical or prismatic test specimens - Procedure; NBR 5739: Concrete - Compression test of cylindric specimens - Method of test; NBR 7215: Portland cement - Determination of compressive strength.BARBOSA et al. “A Influência da Adição de Finos Basálticos nas Características Reológicas e Mecânicas dos Concretos Auto-Adensáveis (CAA)”. 46º Brazilian Concrete Congress, Florianópolis – SC, September 2004.BARBOSA et al, ““Rheological and Mechanical Evaluation of the cement paste manufactured with micro-cements of the type MC-20 and MC-30””. 47º Brazilian Concrete Congress, IBRACON, CDROM, Recife-PE, 2005.BERTOLUCCI, F.S., BARBOSA, M.P., SANTOS, F.L.,SALLES, F.M.,” The Superplasticizers Influence on the Rheological Properties of Cemented Paste”, in 49° Brazilian Concrete Congress, 2007, Bento Gonçalves RS.BERTOLUCCI, F.S., BARBOSA, M.P., SANTOS, F.L., MACIEL, G.F., SALLES, F.M., “The Influence of The Mixing in the Rheological Behavior of Cement Pastes.” In: V INTERNATIONAL ACI/CANMET CONFERENCE, 2008, MANAUS. ANAIS DO V INTERNATIONAL ACI/CANMET CONFERENCE, 2008. v. 1. p. 1-21. (Paper accepted by the Scientific Committee to plublication in the ACI Special Publication SP of V Internacional ACI/CANMET).STEIN, H.N., Rheological behavior of suspensions. In: CHEREMISINOFF, N. P. (Ed.) Encyclopedia of fluid

mechanic: slurry flow technology. Houston: Gulf Publishing, 1986, v.5, p. 3 -47.TARTTERSALL, G.H., “The Workability of Concrete”, SLOUGH, Viewpoint Publication, 1976

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ROLL WAVES IN HYPERCONCENTRATED FLOWS WITH FREE SURFACE

F. O. Ferreira1

Master of Science-Mechanics Engineering-PPGEM/UNESP, Ilha

Solteira-SP, Brasil

G. F. Maciel2

Professor-Department of Civil Engineering – College of Engineering

of Ilha Solteira – São Paulo State University- PPGEM – Mechanical Engineering Graduate Program.

A. S. Vieira3


Solteira-SP, Brasil

L.O. B. Leite4


Solteira-SP, Brasil

ABSTRACTThe proposal of this work is to conduct a global

analysis of the roll waves phenomenon in hyperconcentrated flows whit free surface, applying the Herschel-Bulkley rheologic model, as it is a representative and “more generalized” model of hyper concentrated fluid, hence enabling to resort to other rheologic proposals, such as the power law, the Binghamian and Newtonian models.

INTRODUCTIONFree surface flows have numerous practical

applications. However, the flows occurring in sloping canals may develop instabilities in the form of hydraulic jumps or bore waves. These instabilities are called “roll waves”.

It is not uncommon to find them in mudflows or in debris flows. This phenomenon can be perceived in oceans (Swaters, 2003) and lakes (Fer et al, 2003), moreover, these waves can take place in shallow waters, in roof drainpipes and street gutters on raing days.

With regards to generating Roll Waves in newtonian and in non-newtonian fluids (hyperconcentrated fluids), previous studies have been conducted seeking an explanation for such phenomenon, may appear both in laminares flow as a turbulent flow. The detailed observations were presented by (Cornish, 1910).

In 1925, studying turbulent flows, Jeffreys was the first to establish a criterion on the formation of roll waves. He deduced from an analysis of linear stability that the flow became instable if the Froude number was greater than 2. Dressler (Dressler, 1949), tried to deliniate the profile of the surface and confirmed the formation of roll waves, describing the incidence as a series of well-defined wavelengths, separated by discontinuity on the free and unimpeded surface.

As regards the roll waves formation in hyperconcentrated flows and laminars, several studies were done, although what appears more often in the literature is the study of roll waves generated in

Bingham’s fluids (Liu and Mei, 1994), (Maciel, 1998), (Noble, 2004).

Roll waves formation was undertaken by (Ng and Mei, 1994), starting from a rheological proposal of fluids with pseudoplastic behavior (power law), carry out an analytical investigation by seeking roll waves solutions characterized as periodic shocks connected by smoothly increasing depth profiles. Pascal (2006) investigate the generation and structure of roll waves developing on the surface of a power-law fluid layer flowing down a porous incline.

Through laboratory studies carried out by the research group of Unesp-Ilha Solteira, such instabilities were observed in hyper concentrated fluid (water+clay, water+water+fine sand) flowing in a sloped canal. The formation of these waves can bring about significant variations in the depth of the flow, hence provoking “overflow” and undermining the canal banks. Therefore, the present work presents a mathematical model capable of reproducing roll waves in hyperconcentrated flows.

Figure 1 illustrates the development of roll waves generated in mud on the torrential lava ramps of UNESP - Ilha Solteira.

Fig 1: View of Roll Waves on the torrential lava ramps of UNESP - Ilha Solteira

METHODOLOGYThis work, in the theoretical plan, a general

mathematical model is determined, on the basis of the integrated Navier-Stokes equation in the vertical, of tensor tensions the rheology of Herschel-Bulkley is

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IV Brazilian Conference on Rheology – Rio de Janeiro, Brazil, July 02-04, 2008introduced.

The average velocity of the flows is determined taking itself in consideration that the flows presents a parabolic profile of speed in the shear region (near of the floor of canal) connected to a linear profile in the region not shear (condition of plug), categorized as flows of mudflows and debris flows. From the system of equations (conservation of the mass and equation of the momentum) in nondimensional variables, an analysis of linear stability is carried through, placing the conditions of formation of these instabilities, as much in hyperconcentrated fluid as in Newtonian fluid. With the conditions of formation of instabilities established, an analytical theory of permanent Roll Waves is employed and a mathematical model for generation of such stabilities it’s determined. Thus, the equation of the roll waves is given by:

( ) ( ) 22

2

11

U hU hzh

αα β

− ∂ − − + = ∂

( ) ( )( ) ( )( )

** *

*

1 1 11

U h Ch C C

h C

+ − − − − − × × −

( )( )

*

*

11

nn nC

n h nC

+ + × + +

(1)

*

0

cCh g sen

τρ θ

= (2)

( )( )

( ) ( )

( ) ( )

2 *

22 * 2 *

2 1 4 32 13 2 1 2( 1)

n h C n nnn n h n nC n C h

α + + ++ = ×

+ + + + +

(3)

where: cτ is the critical tension, n is the flow index of the fluid and U represents a constant velocity of propagation (celerity).

In the numerical plan, using the computational consol Python, the validity of model is checked, considering of this waves are adjusted by shocks devided by the singularities existents in the model. With the determination of conditions of shock and the velocity of propagation of wave in a critical point; we can observe the formation of Roll Waves such in fluids non-Newtonians (Herschel-Bulkley, Bingham, Power law) as Newtonian fluids.

Figure 8 illustrates the profile of the roll waves for 1Fr = (nº de Froude), 0.1C ∗ = and 0.4n = .

Fig 8: Profile of the roll waves for 1Fr = .

REFERENCESCornish, V. 1910. Ocean Waves and Kindred Geophysical Phenomena. Cambridge University Press.Dressler, R.F 1949. Mathematical solution of the problem of roll waves in inclined open channels Communs pure appl. Math, vol 2, p 149 –194.Fer, I., Lemmin, U. and Thorpe, S.A. 2003. Winter cascading of cold water in lake geneva. J. Geophys, vol.107 (C6), nº 3060.Liu, K. and Mei, C.C. 1994. Roll waves on a layer of a muddy fluid flowing down a gentle slope – A Bingham model. Phys Fluids, vol. 6, p. 2577-2590.Maciel, G.F. 2001. Roll waves evoluindo em canais de forte declividade: Uma abordagem matemática com aproximação numérica. Ilha Solteira, Tese (Livre Docência em Roll Waves) – Faculdade de Engenharia, Universidade Estadual Paulista.Jeffreys, H. 1925. The flow of Water in na Inclined Channel of Rectangular section. Phil Magazine, vol 49, p. 793-807.Noble P. 2004. Existence et Stabilité de Roll-Waves pour les Équations de Saint Venant, C.R. Acad. Sci. Paris, Ser. 1338, p.819-824.Ng, C.O. and Mei, C.C. 1994. Roll waves on a layer of fluid mud modelled as a power law fluid, J. Fluid Mech, vol. 263, p. 151-183.Pascal, J.P. 2006. Instability of Power-Law Fluid Down a Porous Incline, J. Non-Newtonian Fluid Mech, vol 133, p. 109-120.Swaters, G.E. 2003, Baroclinic characteristics of frictionally destabilized abyssal overflows. J. Fluid Mech, vol. 489, p. 349-379.

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MECHANICAL PROPERTIES OF ASPHALT BINDERS

Leni F. M. Leite Petrobras Research Center [email protected]

Luis Alberto H. NascimentoPetrobras Research Center

[email protected]

Margareth C. CravoPetrobras Research Center

[email protected]

ABSTRACTThe effect of modification and aging of asphalt

binders was studied through rheological study using dynamic shear rheometers - DSR. Asphalt cement and polymer modified asphalts were submitted to laboratory aging and hot mixing process at asphalt plant. The recovered, aged and virgin samples were tested in an oscillatory test (frequency sweep) at different temperatures. The asphalt binders’ results were plotted on Black diagrams. The polymer addition improved the phase angle at high and intermediate temperatures but the aging of the polymer modified samples seemed to break the polymeric chains, causing a phase angle increase.

INTRODUCTIONAs the traffic volume and loads have increased, it

has been found that unmodified asphalt cement has been less capable to be flexible, cohesive and adhesive enough to support the traffic stresses and also have a broad inservice temperature range. Elastomers modifiers are by far the most common in today’s market. Elastomeric polymers are typified by their rubber-like properties, ability to stretch and recover. Polymer modification stiffens the asphalt cement at high temperatures and depending upon the type of modifier can also alter the phase angle (1).

Before progressing to the concepts that characterize the mechanical properties of asphalt binders, the nature of these properties should be appreciated. First of all they change significantly as they age. Any form of handling which requires heating (mixing and compaction) or inservice exposure affects these properties. The two most important mechanisms involved in ageing of asphalt binder are loss of volatile components and chemical reaction with oxygen. Both of these process lead to an increase in complex modulus. The most common method for determining the ageing characteristics is the rolling thin film oven test – RTFOT that simulates the ageing during hot mixing with aggregates (2).

Moreover, the mechanical properties depend upon the rate or time of loading. They become stiffer as the test temperature is lowered, the rate of loading is increased, or the loading time is decreased. This interchangeability of the effects of time and temperature is the basis of time temperature superposition.

In a dynamic shear rheometer, a determined oscillatory stress or strain is applied to the sample with the temperature controlled. The rate of displacement of one plate relative to the other is measured. The resulting shear strain or stress is measured. The data obtained is used to plot a Black diagram that helps to the

understanding of asphalt binder rheological behavior.The interpretation of mechanical properties of

asphalt binders related to polymer modification and aging was the aim of this study. Black diagrams were plotted from modified, unmodified, virgin and aged samples (RTFOT aged and recovered from field).

METHODOLOGYThree asphalt binder samples were tested: asphalt

cement penetration 30/45, SBS polymer modified asphalt and asphalt rubber modified asphalt. The aging was done in two ways: RTFOT aging test at laboratory and inservice aging followed by recovery and extraction of asphalt binder from hot mixtures. The virgin and aged samples were submitted to DSR tests. The measurement of the complex modulus and phase angle in a dynamic shear rheometer was done in the range of the linear viscoelasticity. The experiments were done at temperature range of 5 to 65ºC submitted to frequency sweep in the range of 0.01 to 100 Hz. Test specimens, nominally 8 mm or 25 mm in diameter are used in the plate-plate geometry, depending on the temperature of the test (3).

RESULTSThe results obtained are shown in the figures below.

The Figure 1 presents the aging effect on 30/45 penetration grade asphalt cement. The aging causes a phase angle decrease for the same modulus value. The curve for RTFOT aged is almost the same as the recovered and extracted sample. It seems that RTFOT aging is more severe than the in-service sample because the phase angle at low modulus region is lower and the modulus is higher at high modulus region. The Figures 2 and 3 present the modified asphalts aging behaviours.

The aging causes an increase in phase angle at low modulus region and more significant increase in complex modulus in the high modulus region. The phase angle increase can be associated to small molecular breakage at aging temperatures of the butadiene double bonds that leads to molecular weight loss, reducing the complex modulus. Even though the remained phase angle continues to be much lower than the value of the traditional asphalt cement that means elasticity enhancement. The Figure 4 compares the SBS and tire rubber effect on the asphalt binder. The Figure 5 shows the effect of SBS addition on the asphalt cement. The performance of modified asphalts is almost the same, the phase angle increase with the decrease of modulus, then reach a maximum and after decrease whereas in the asphalt cement, the phase angle increases with the

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IV Brazilian Conference on Rheology – Rio de Janeiro, Brazil, July 02-04, 2008decrease of modulus.

Figure 1: 30/45 aging

Figure 2: Asphalt rubber aging

Figure 3: SBS modified asphalt aging

It seems that at high and intermediate temperatures or low and intermediate modulus region, the modified asphalts will increase its elasticity, improving the rutting and fatigue cracking resistance. Ramond observed the same effect on Black diagram with polymer modification (4, 5). The advantage of Black diagram is the use of all the results of phase angle and complex modulus obtained experimentally without the superposition or other calculation.

Figure 4: Modified asphalts

Figure 5: Improvement caused by polymers addition

CONCLUSIONSThe polymer modification and aging effects on

asphalt cement can be seen through phase angle and complex modulus determination. The increase of phase angle at low and intermediate modulus for polymer modified asphalts showed the enhancement of rutting and fatigue resistance. The aging of polymer asphalts cement revealed a breaking in the molecular chain due the fact of phase angle decrease at low modulus region and modulus decrease at high modulus region.

ACKNOWLEDGMENTSThe authors are very thankful to Diego F.

Assumpção, Ulisses S. Figueiredo, Luis Rosa da Silva, Priscila A. Pinto for their assistance with respect to the operational and analytical research.

REFERENCES(1) Hunter R. Asphalt in road construction Thomas Telford, London 2000(2) Asphalt Institute Asphalt binder Testing - Technician’s Manual for Specification Testing of Asphalt Binders MS25 2007(3) IP CM 02 Determination of the complex shear modulus and phase angle of bituminous binders DSR method(4) Ramond G., Such C. Le module complexe dês liants bitumineux - Études et recherches des laboratoires des ponts et chaussées Routes CR32 Fevrier 2003(5) Corté J.F. & Benedetto H. Matériaux routiers bitumineux 1 – description et propriétés des constituants Lavoisier 2005.

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RHEOLOGY EVALUATION OF MUCOADHESIVE DRUG DELIVERY SYSTEMS

Flávia Chiva CarvalhoPharmaceutical Sciences School

of UNESP Araraquara, Brazil

Victor Hugo Vitorino SarmentoInstitute of Chemistry, UNESP

Araraquara, Brazil

Mariana da Silva BarbiPharmaceutical Sciences School of

UNESP Araraquara, Brazil

Maria Palmira Daflon Gremião Pharmaceutical Sciences School

of UNESP Araraquara, Brazilpgremiã[email protected]

ABSTRACTMucoadhesive drug delivery systems have been

developed to improve increasing drug time residence in mucous membrane. Some gel-like systems presents this capacity through increase viscosity after mucus contact. In order to analyze this behavior, it is proposed the study of oscillatory rheology. For this propose, it is obtained the viscosity and elastic modulus measurements from the formulation and mucus mixture. Systems that show greater elastic modulus after mucus contact can predict mucoadhesion [1].

INTRODUCTIONNasal route for drug delivery provides an alternative

route for drug ineffective by oral route due to their metabolism in the gastrointestinal tract or by first-pass effect, like zidovudine (AZT). Its limitation is the rapid mucociliary clearance that removes the formulation from local action [2]. Mucoadhesive systems have been developed to improve increasing time residence drug in mucous membrane [3]. Some colloidal systems, like microemulsions (ME) and lyotropic liquid crystalline mesophases (CLs), are known by mucoadhesion ability, which can result of the increase of viscosity with the in situ water absorption [4]. The aim of this study is to develop a microemulsion of adequate viscosity for intranasal administration of the AZT, that when entering in contact with physiological fluids in the nasal cavity, increases its viscosity, due its reestruturation in liquid crystalline mesophases. For this, the effect of the increase of the water phase in stabilized colloidal systems with propoxyl 5 OP ethoxyl 20 OE cethyl alcohol (PPG-5-CETETH-20), oleic acid as oil phase and AZT as drug was analyzed through the rheologic behavior.

METHODOLOGY• Preparation of formulations.

A ternary phase diagram was constructed by the titration method and the different regions obtained were delimited by visual inspection. An excess of AZT was put in the chosen samples and maintained constant agitation during 48hs. After centrifugation, the supernatant was quantified by spectroscopy.

• Polarized light microscopy Polarized light microscopy (PLM) was employed to

examine the phases and isotropic/anisotropic behavior of samples at ambient temperature.

• Rheological Characterization of FormulationsOscillatory analysis of each formulation under examination was performed after determination of its linear viscoelastic region. Frequency sweep analysis was performed following application of a constant stress. In continuous shear analysis, flow curves for each formulation were measured over shear rates ranged from 10 to 2000 s-1. All the assays had been carried through at temperatures of 25ºC and 32ºC.

RESULTSThe results show that with the variation of the

constituent s proportion, it was possible to obtain systems with different aggregation forms dependents on the ratio water/surfactant/oil like emulsion (E)- opalescent, ME -transparent and liquid, lyotropic crystalline mesophases (CL) -transparent and viscous systems, and phase separation (SF) (Figure 1). The chosen formulations meet in the ME region due to adjusted administration viscosity, indicated in Figure 1 and 2.

Figure 1: Phase diagram of PPG-5-CETETH-20 as surfactant (T), oleic acid as oily phase (O) and water (A).

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Figure 2: Photomicrographs obtained from PLM of chosen formulations

The F1, F2 and F3 presented Newtonian behavior, characteristic of microemulsion structure, and F4 pseudoplastic one, indicating a transition to a lamellar phase. It was added 5, 10, 30, 50 and 100% of water in relation to the initial weight of formulations, and was observed that the contact of water changed the rheological behavior: the viscosity and storage modulus (G') increase. These results can be evidenced by oscillatory assay, images of PLM and photograph of F3 added 5, 10, 30, 50 and 100% of water, showed in Figure 3 and 4. The results show the strong influence of the water in the rheologic properties of the systems.

Figure 3: Images and PLM photomicrographs of F3 added 5, 10, 30, 50 and 100% of water.

CONCLUSIONSThe studied systems have the capacity to increase

viscosity with the water addition, and can be powerfulmucoadesives systems of nasal release of the zidovudina.

ACKNOWLEDGMENTSCAPES, FURP, IQ/UNESP.

REFERENCES[ 1] C. Callens; J. Ceulemans; A. Ludwig; P. Foreman; J. P. Remon. Eur. J. Pharm. Biopharm. 55 323-328 (2003). [2] R. M. Mainardes; M. C. C. Urban; P. O. Cinto; M. V. Chaud; R. C. Evangelista; M. P. D. Gremião Current Drug Del. 3 275-285 (2006).[3] A. Ahuja; R. K. Khar; J. Ali Drug Dev. Ind. Pharm. 23 (5) 489-515 (1997).[4] J. C. Shah; Y. Sadhale; D. M. Chilukuri Adv. Del. Rev. 47 229-250 (2001).

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ELASTICITY IN PETROLEUM PITCHES

Alessandra Maciel dos Santos - M.Sc.Centro Tecnológico do Exército

Av. das Américas, 28705 - [email protected]

Luiz Depine de Castro - PhDCentro Tecnológico do Exército


Carlos H. M. de Castro Dutra - M.Sc.Centro Tecnológico do Exército


ABSTRACTThe objective of this work was to provide a

comprehensive rheological study of mesophase pitch produced at different heat treatments. Oscillatory and creep and recovery analysis were carried out at 350 ºC at various values of stress within linear viscoelasticity region to aim its viscoelastic behavior.

INTRODUCTIONMesophase pitch is a high molecular weight material

(typically, MW ≅ 1000) composed of planar aromatic molecules. It is used in the production of mesophase pitch-based carbon fibers, carbon foams and carbon-carbon composites. In each of these applications, mesophase offers distinct advantages (Cato, Edie and Harrison, 2005).

The chemical and physical properties of pitch precursors, especially their rheological behavior, are critical in their processing to carbon material. In the case of mesophase pitch, its rheological behavior is known to be more complex than that of isotropic pitches (Daji, Rand and Turpin, 1998).

METHODOLOGYThe petroleum pitches samples were analyzed in a

rotational rheometer HAAKE, model Rheo-Stress 1 (RS-1) using a double plate cell of 35 mm in diameter and programmed to operate with controlled stress mode.

Two samples of pitches produced at different heat treatments were studied.

The Table 1 shows the physic-chemical properties of the samples and its respective softening points.

Table 1 – Specification of the Pitches AnalyzedSamp

le Pitch

Softening Point ( °C )

Mesophase (%)

Toluene Insoluble

(%)

Quinoline Insoluble

(%)

Coking Value (%)

A 200,6 31,4 49,2 31,2 77B 324,1 100 69,9 72,7 89

The softening point, from the samples was measured according to criterion mentioned by Py, et. al, (Py, et. al 1997). The authors have been argued that the softening point is approximately a temperature at which the viscosity is equal to 1000 Pa.s.

In order to obtain the linear viscoelasticity region, oscillatory tests, with controlled stress, were performed at 350 ºC and 1 Hz.

After this experiment, using values of stress within the linear viscoelasticity region, creep and recovery tests were done to provide a measurement of pitch elasticity.

Figure 1 and 2 show the results obtained for the pitches in oscillatory test. The viscous modulus (G” ) remain higher than elastic modulus (G’ ) during the stress sweep in linear viscoelastic range for the pitch A. This graphic illustrates that this sample has viscous behavior. However, for the pitch B, G’ is higher than G”, thus the present pitch has elastic behavior. For the sample A, the linear viscoelasticity region is between 0,1 – 50 Pa and the sample B, 10 – 800 Pa.

1 10 100 10000,1

1

10

100

1000

G' G'' |η *|

τ (Pa)

G',

G''

(Pa)

0,1

1

10

100

|η∗| (P

a.s)

Figure 1 – Dynamic stress sweep test for the pitch A.

1 10 100 100010

100

1000

10000

100000

1000000

G' G'' | η * |

τ (Pa)

G',

G''

(Pa)

100

1000

10000

100000

| η*| (Pa.s)

Figure 2 – Dynamic stress sweep test for the pitch B.

The curves obtained in creep and recovery tests for both pitches can be seen in Figures 3, 4, 5 and 6, respectively. Table 2 shows the values of recovery for each stress applied.

The analyzes of these graphics, for different values of stress within linear viscoelasticity region, shows that both pitches exhibit the same behavior, which went from an elastic solid to a viscous liquid when the stresses increased.

4


IV Brazilian Conference on Rheology – Rio de Janeiro, Brazil, July 02-04, 2008The elastic solid behavior appeared at low stresses

while the liquid viscous behavior occurred at high stresses, for both pitches. However, elasticity of pitch A, with low mesophase contents, is much smaller than the one of pitch B, which is a 100% anisotropic material, for the same stress level (Table 2).

Although it is not clear, yet, why pitches exhibit elastic behavior, once their molecules are too small to promote entanglements such as polymers, there is a possibility that a tridimensional network, like a sol-gel, can be developed inside the material, during heat treatment. In this case, the increase of the stress would break the network and would explain both increase of the strain and the reduction of the elastic behavior. It is necessary to investigate more deeply why and how pitches develop elastic behavior and if the elasticity is related or not with the softening point or with the mesophase contents.

0 100 200 300 400 500 6000

10

20

30

40

τ = 10 Pa τ =30 Pa γ ( τ =10 Pa) γ ( τ =30 Pa)

t (s)

τ (P

a)

0,0

0,2

0,4

0,6

0,8

1,0

1,2

γ

Figure 3 – Creep and recovery test for the pitch A at τ = 10, and 30 Pa

.

0 100 200 300 400 500 6000

10

20

30

40

50

60

τ = 50 Pa γ (τ = 50 Pa)

t (s)

τ (P

a)

0

20000

40000

60000

80000

100000

120000

γ

Figure 4 – Creep and recovery test for the pitch A at τ = 50 Pa.

ACKNOWLEDGMENTSThe authors thank PETROBRAS for the financial

support and raw material supply.

0 100 200 300 400 500 6000

50

100

150

200

250

300

350

τ = 30 Pa τ = 100 Pa τ = 300 Pa γ ( τ = 30 Pa ) γ ( τ = 100 Pa ) γ ( τ = 300 Pa )

t (s)

τ (P

a)

0,00

0,01

0,02

0,03

0,04

0,05

0,06

0,07

γ

Figure 5 – Creep and recovery test for the pitch B at τ = 30, 100 and 300 Pa.

0 100 200 300 400 500 6000

100

200

300

400

500

600

700

800

τ = 400 Pa τ = 500 Pa τ = 700 Pa γ ( τ = 400 Pa ) γ ( τ = 500 Pa ) γ ( τ = 700 Pa )

t (s)τ

(Pa)

0

100

200

300

400

500

600

700

800

γ

Figure 6 – Creep and recovery test for the pitch B at τ = 400, 500 and 700 Pa.

Table 2 – Recovery at Different Stress for the Pitch A and B

Stress Recovery ( % ) Pitch

A

Recovery ( % ) Pitch B

10 6,2 *30 5,4 40,550 0,2 30,9100 - 30,5300 - 33,5400 - 0500 - 0,5700 - 0

*measure with noise; - out of linear viscoelasticity region

REFERENCES-Cato, A.D.; Edie, D.D.; Harrison, G.M., Steady State and Transient Rheological Behavior of Mesophase Pitch, Part I: Experimental – J. Rheology, 49, 2005, 161 – 174.-Daji, J.; Rand, B.; Turpin, M.; Viscoelastic Behavior of a Heat Treated Isotropic Pitch – Carbon, 36, 1998, 1406 – 1409.-Py, X.; Daguerre, E.; Spinner, B., Alfha-Relaxation of an Isotropic Petroleum Pitch: a Controlled Stress and Strain Oscillatory Rheometry Study – Carbon, 35, 1997, 1013 – 1021.

4


WALL SLIP DURING THE FLOW OF CARBOPOL SOLUTIONSTHROUGH A PARALLEL PLATE CHANNEL

Paulo R. de Souza Mendes, Renata A. B. Pereira and Jonathan PedronDept.Mechanical Engineering

Pontíficia Universidade Católica-RJRio de Janeiro, RJ 22453-900, Brazil

[email protected]

ABSTRACTExperiments were performed to investigate the

phenomenon of wall slip during the flow of aqueous solutions of carbopol through a parallel plate channel. The Reynolds number is low for all cases investigated, to ensure negligible development length. In the experiments, the pressure drop is measured for different flow rate values, and the results are presented in the form of curves of dimensionless average velocity versus dimensionless wall shear stress. We also performed experiments with glycerol, and the results agreed with the analytical solution available in the literature. Moreover, this agreement ensures the absence of wall slip for this Newtonian case. Comparisons between the experimental and numerical results show that (apparent) wall slip occurs when the wall shear stress is below a threshold stress of a few times the yield stress. Above this threshold, the numerical and experimental curves tend to merge.

INTRODUCTIONThe phenomenon of wall slip is often observed

during internal flows of viscoplastic liquids. If well understood, it could allow the reliable design of low head-loss flow systems of these high-viscosity liquids. However, its mechanisms and origins are still uncertain [1], and the prediction capability of its occurrence is presently rather poor. Wall slip is also expected to be a function of surface parameters such as roughness and wettability. This paper briefly describes a experimental and numerical study aiming at determining the amount of wall slip observed in the flow through a parallel-plate channel of a viscoplastic liquid, namely, a carbopol solution.

METHODOLOGYThe apparatus is composed of a test section (parallel-

plate channel), a pump, a reservoir and a digital manometer, as illustrated Fig. 1. The channel is 74mm wide and 150mm long, and the gap is b =1mm. The manometer is employed to measure the pressure at the plenum that precedes the channel inlet (not shown in Fig. 1). The flow outlet is at ambient pressure.

Figure 1. Schematics of the apparatus.

The flow rate is measured by collecting the outflowing liquid for a period of time and then weighing it.

Two plate materials were examined, stainless steel and teflon. The roughness e and contact angle θ to water were measured for both, yielding e = 0:05µm, θ = 860 for the steel plate and ε = 0:47µm, θ = 1150 for the teflon one.

A rotational rheometer ARES-LS is θused to obtain the viscosity function of the carbopol with a grooved Couette geometry.

NUMERICAL SOLUTIONSWe have numerically solved the motion equation in

conjunction with the generalized Newtonian fluid constitutive equation and a recently proposed viscosity function [2], given in Eq. (1). In the analysis the no-slip condition is assumed, and thus the numerical flow rate versus pressure drop curve pertains to the case of no wall slip.

The parameters that appear in this equation are: the zeroshear- rate viscosity, 0 ; the yield stress, 0 ; the consistency index, K; the behavior index, n; and the infinite-shear-rate viscosity, ∞ .

4



Figure 2. Dimensionless average velocity x Dimensionless wall shear stress

RESULTSThe results are presented in the form u*×0 curves,

where u=u /b 1 , where ≡0/K1 /n is the

dimensionless average velocity, and *≡wall /0 the dimensionless wall shear stress.

Figure 2 illustrates the behavior observed in the experimental and numerical investigations. It is seen that wall slip occurs when the wall shear stress is below a threshold stress of a few times the yield stress. Above this threshold, the numerical and experimental curves tend to merge. Moreover, the results for the rougher plate present less slip, as expected.

CONCLUSIONSComparisons between the experimental and

numerical results show that (apparent) wall slip occurs in the range of wall shear stress below about a threshold in the vicinity of a few times the yield stress. Above this threshold, the numerical and experimental curves tend to merge. A systematic study of the influence of the parameters that govern this flow is under way, and its results will be presented at the conference.

ACKNOWLEDGMENTSThe authors are indebted to Petrobras S.A., CNPq,

CAPES, FAPERJ, FINEP, and MCT for the financial support to the Group of Rheology at PUC-RIO.

REFERENCES[1] H. A. Barnes. A handbook of elementary rheology. University of Wales, 2000. [2] P. R. de Souza Mendes. Dimensionless non-Newtonian fluid mechanics. J. Non-Newt. Fluid Mech., 147(1- 2):109–116, 2007.

4


LIQUID-LIQUID DISPLACEMENT FLOWS IN A HELE-SHAW CELL INCLUDING VISCOPLASTIC EFFECTS

Paulo R. de Souza Mendes, Priscilla R. VargesDept. Mechanical Engineering

Pontifícia Universidade Católica-RJRio de Janeiro, RJ 22453-900, Brazil

[email protected]

ABSTRACTViscous fingering in non-Newtonian fluids in a

rectangular Hele-Shaw cell is investigated. This cell is filled with aqueous solutions of carbopol in two different concentrations. A Newtonian mineral oil is then injected into the cell and the displacement is observed. A digital camera is used to capture images of the interface between the fluids during the flow. Applications include displacement of heavy crude oil in reservoirs. The main parameters that govern this flow are the viscosity ratio, the rheological capillary number, and the (dimensionless) flow rate. The interface shape is given for different values of flow rate and viscosity ratio.

INTRODUCTIONIn surging oil wells, the secondary recovery stage

consists of injection of water or gas to displace the oil from the porous rock. The study of such displacement flows is important because the production of oil in the primary stage, obtained by the natural pressure of the reservoir, is rather limited. The displacement efficiency can be evaluated by the shape of the interface between the liquids. Injected fluids tend to flow towards the more permeable layers or zones, bypassing a large amount of oil in the unswept region [1]. This will create an early breakthrough of the injected fluid, therefore implying low oil recovering rates and eventually, an uneconomical process.

The Saffman-Taylor or viscous fingering instability occurs when, in a porous medium or low-gap rectangular channel (Hele-Shaw cell), one fluid pushes a more viscous one. The interface between the fluids may become unstable, leading to the formation of fingerlike patterns [2]. Figure 1 illustrates a schematic diagram of the displacement flow in a Hele-Shaw cell and gives the cell dimensions in millimeters. the displacement flow in a Hele-Shaw cell and gives the cell dimensions in millimeters.

The Saffman-Taylor instability has been extensively studied for Newtonian fluids [see 3]. For gas-displaced non-Newtonian liquids (zero viscosity ratio), a large number of articles is also found in the literature [e.g. 4, 5, 6, 7]. Yamamoto [6] studied the growth phenomenon of viscous fingering which repeat three patterns: spreading, splitting and shielding. Chevalier et al. [5] investigated tthe effects of inertia on the width of the viscous fingers.Amar and Poiré [4] simplified the Hele-Shaw cell into a

two-dimensional problem. Displacement flows involving two liquids of comparable viscosity, however, have received very little attention.

EXPERIMENTSVisualization experiments were performed to

investigate the phenomenon of viscous fingering during the displacement of carbopol aqueous solutions by a less viscous Newtonian oil flowing through a Hele-Shaw cell. The interface shape is recorded as it proceeds along the cell. Different flow rate values are investigated to determine the conditions under which fingering occurs. Figure 2 depicts the flow visualization apparatus. The upstream chamber and guillotines provide an initially straight interface. Two pumps are used to fill the channel, one for each liquid. The Reynolds number is kept low for all cases investigated, to ensure negligible inertia [5].

The channel is initially filled with carbopol. Then the upstream guillotine is closed, and the upstream chamber is washed out from the carbopol and filled with a mineral oil. A digital camera is used to capture images of the interface between the fluids during the flow. This allows comparing the results for different viscosity ratios and outflows. The viscosity data for these liquids are obtained with an ARES rotational rheometer at controlled strain mode, with a Couette geometry. The viscosity data for the carbopol solutions are well fitted to a recently proposed viscosity function, given by Eq. (1):

4


=1−exp−0 0 [0

K ˙n−1]∞1−exp− ∞

K n−1 (1)

The parameters that appear in this equation are: the zeroshear-rate viscosity, 0 ; the yield stress, 0 ; the consistency index, K; the behavior index, ; and the infinite-shear-rate viscosity, ∞ .

RESULTS AND DISCUSSIONThe problem is non-dimensionalized in accordance

with [8], and the main governing parameters that arise are (i) the dimensionless flow rate u*=u / 1 b (b is the gap, and =0/K1 /n ); (ii) the rheological capillary number Ca= 0b / ( is the interfacial tension); and (iii) the viscosity ratio u*=u / 1 b . Figure 3 illustrates the different observed patterns for Ca = 0:2 and four different sets ( oil /1 ; u* ), namely (a) (0:066;0:20); (b) (0:066;0:51); (c) (0:14;4:6); and (d)(0:14;6:0). Analyzing the two pictures for oil /1 = 0.066 ((a) and (b)), it is observed that there is a formation of two main fingers. They ramify and bypass a large amount of carbopol which remains in the channel. In this case, the lower flow rate case presented more branching. The two pictures for oil /1 = 0.14 ((c) and (d)) show that several wide fingers are formed and merge into a single sweeping plug. As the flow rate is increased, larger amounts of carbopol are left behind in the cell.

FINAL REMARKSA systematic study of the influence of the parameters

that govern this flow is under way, and its results will be presented at the conference. In general, it was already observed that the displacement efficiency increases with the viscosity ratio, while decreasing with the flow rate.

ACKNOWLEDGMENTSThe authors are indebted to Petrobras S.A., CNPq,

CAPES, FAPERJ, FINEP, for the financial support to the Group of Rheology at PUC-Rio.

REFERENCES[1] Moghadasi, J., M¢uller-Steinhagen, H., Jamialahmadi, M., and Sharif, A., J.Petr. Sci. Eng. 43 (2004) 163.[2] Saffman, P. G. and Taylor, G. I., Proc. R. Soc. London A 245 (1958) 312.[3] Homsy, G., Annual Review of Fluid Mechanics 19 (1987)271.[4] Amar, M. B. and Poiré, E. C., Physics of Fluids 11 (1999)1757.[5] Chevalier, C., Amar, M. B., Bonn, D., and Lindner, A., J. Fluid Mech. 552 (2006) 83.[6] Yamamoto, T., Journal of the Society of Rheology, Japan 34 (2006) 283.[7] Yamamoto, T., Kamikawa, H., Mori, N., and Nakamura, K., Journal of the Society of Rheology 30 (2002) 121.[8] de Souza Mendes, P. R., J. Non-Newt. Fluid Mech. 147 (2007) 109.

4


NUMERICAL ANALYSIS BY BREZZI'S THEOREM FOR A REGULARIZED STABILIZED MIXED FEM FORMULATION FOR VISCOPLASTIC FLUIDS

* CRISTIANE O. FARIA and J. KARAM F.Laboratório Nacional de Computação Científica,Av. Getúlio Vargas, 333, Petrópolis, RJ, Brasil,

email: [email protected] [email protected]

ABSTRACTViscoplasticity, as idealized by Bingham[1], is a

phenomenon characterized by the existence of a residual value for the shear stress, beyond which the material would present a viscous flow. He attempted to the fact that before flowing as in a Newtonian way, those material systems behaved as plastic solids and called them viscoplastic fluids. Defining τy as the residual stress, or yield stress, and µ as the plastic viscosity the first model made by Bingham for this behavior was

u=y⇔uy

u=0⇔u ≤y (1.1)

System (1.1) presents a singularity, wich was handled by Glowinski[2] to a one variable problem by using a lagrangean multiplier and solving the formulation through a regularization method. Viscoplastic flow problems of incompressible fluids can be modelled by the following system of

−div u∇ p= f in div u=0 in (1.2)

with u=u on ∂Ω and τ(u) is given by (1.1). Ω and ∂Ω are the domain and its boundary, respectively. Few numerical methods have been proposed for these problems and, in general, they transfer the instabilities to the boundaries, resulting in unstable pressure fields. Karam and Loula[3] proposed a mixed stabilized finite element formulation in velocity and discontinuous pressure variables able to handle the incompressibility constraint. Although obtaining stable results for linear case, when (1.1) is considered it is difficult to obtain theoretically the range of the stabilizing parameters. Based on both approaches, in this work we propose a mixed regularized stabilized finite element method in velocity and discontinuous pressure to wich it is possible to obtain mathematically the range of stabilizing parameters. Perturbing the classical Galerkin formulation by adding least-squares of the governing equations, stable regularized mixed finite element approximations for this problem are constructed here with descontinuous pressure interpolations as follows. Let Sk

h (Ω) be the finite element space of polynomials of degree k and class Co , and Qk

h(Ω) that of polynomials of degree l and class C− 1 . Thus we can define the approximation spaces

V h=S 0hk 2=S h

k ∩H 01⊂V , Wh = Qk

h(Ω) ⊂ L2

0(Ω). Then, the proposed formulation can be written in the following manner where the discontinuous pressure has been decomposed at the element level, to make the analysis easier, into a zero mean valued function, ph

*, and a constant by part ph , that is, ph= p h

* ph , ph*∈w h

* , ph∈ W h such that

Problem PGGh: Find uh, ph ∈ Vh x Wh, such that

Where δ1 e δ2 are positive constants to be fixed. Applying Brezzi's theorem[4] we can prove existence, uniqueness and stability of Problem PGGh[5], since we have the continuity of Ah

*uh , ph* ; v h , qh

* and b ph* , v h , the

LBB condition for b ph , vh , and the ellipticity of Ah

*uh , ph* ; v h , qh

* obtained in the following equivalent norm:

4


where ∥vh , qh∥v x w=∥v h∥v∥qh∥w and Λu + B'p* = -2 µ div ε (u) + ∇ p* . Note that in finite dimensional spaces the norms ∥v h , qh∥v x w and are equivalent. By the consistence of PGGh and using Brezzi's theorem we get the following result.Theorem: Problem PGGh has a unique solution and

with Ψh independent of h given by

where

γ1, γ2, βh, C12 come from inequality constants and n is the

space dimension.For Sk

h(Ω) and Qkh(Ω) as defined we may apply inverse

estimates and interpolation results[6] to get

with s = min k, l+1.

CONCLUSIONSThe regularized stabilized formulation in velocity

and discontinuous pressure proposed in this work allows same order interpolation and satisfies Brezzi’s theorem.Stable results have been generated for a wide

range of the stabilizing parameters for high yield stress values even for the pressure. Optimal order of convergence is obtained as proved here in the numerical analysis and confirmed by the numerical results.

ACKNOWLEDGMENTSDuring the course of this work C.O. Faria has been

supported by Faperj. J. Karam F. would like to acknowledge PRONEX/FAPERJ project no. E-26/171.199/2003.

REFERENCES[1] E. C. Bingham, Fluidicity and Plasticity, Vol.I, McGraw Hill, 215-221, 1922.[2] R. Glowinski, “Sur l’approximation d’une inéquation variationnelle elliptique de type Bingham”. R.A.I.R.O. Analyse Numérique, Vol. 10, n.12, 13-30, 1976.[3] J. Karam F. and A.F.D. Loula. “A non-stantard application of the Babu?ska-Brezzi theory to finite element analysis of Stokes problem”. Comp. App. Math., Vol.10, n.3, 243-262, 1991.[4] F. Brezzi. “On the existence, uniqueness and approximation of saddle- point problems a rising from lagrange multipliers”. Revue Française d’Automatique Informatique et Recherche Opérationnelle, Ser. Rouge Analyse. Numérique ., 8 :129–151, 1974.[5] C.O. Faria and J. Karam F., “A regularized stabilized mixed FEM formulation for Bingham fluids”, 8th. World Congress on Computational Mechanics (WCCM8), 2008.[6] P.G. Ciarlet . The Finite Element Method for Elliptic Problems. Pergamon Press, Oxford, 1959 .

4


THE FLOW OF A SPTT FLUID OVER AN OSCILLATING FLAT PLATE

F. T. Pinho*Centro de Estudos de Fenómenos de Transporte,

DEMEGI, Faculdade de Engenharia,Universidade do Porto, Rua Dr. Roberto Frias,

4200-465 Porto, Portugal, [email protected]

D. O. A. CruzDepartamento de Engenharia Mecânica,

Universidade Federal do Pará-UFPaCampus Universitário do Guamá, 66075-900,

Belém, Pará, Brasil, [email protected]

ABSTRACTThe quest for analytical solutions of the most

popular viscoelastic rheological model for simple flow situations is a matter of great importance. In recent works, some analytical expressions were obtained by the authors, for a variety of flow situations such as: the annular flow of SPTT fluids under the influence of rotation and the pipe flow of some viscoelastic liquids with a Newtonian solvent contribution. Those solutions however, do not consider the influence of unsteady effects into the flow pattern.

In this work an analytical solution for the flow of a Viscoelastic SPTT fluid over an oscillating flat plate is derived. The flow field and the stress components behavior are presented and discussed.

The solution is similar to the second Stokes Newtonian problem and represents an important addition to the existing results of unsteady flow analytical solutions.

4


NUMERICAL SOLUTION OF THE PTT CONSTITUTIVE EQUATION FOR THREE-DIMENSIONAL FREE SURFACE FLOWS

Murilo F. Tomé/Departamento de Matemática Aplicada e Estatística – ICMC – USP

Gilcilene S. de Paulo/Departamento de Matemática Aplicada e Estatística – ICMC - USP

ABSTRACTThis work is concerned with the development of a

numerical technique for simulating three-dimensional viscoelastic free surface flows using the nonlinear constitutive equation PTT (Phan-Thien-Tanner). In particular, we are interested in flows possessing moving free surfaces. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. The fluid is modelled by a Marker-and- Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are considered. The PTT equation is solved by a high order method which requires the calculation of the extra-stress tensor on the mesh contours. To validate the numerical technique developed in this work an analytic solution for fully developed flow in a tube, using Cartesian coordinates, was derived. Fully developed flow in a pipe was simulated and the numerical solutions were compared with the respective analytic solutions. Results of complex free surface flows using the PTT equation such as the transient extrudate swell problem and a jet flowing onto a rigid plate are presented. An investigation of the effects of the parameters epsilon and xi on the extrudate swell and jet buckling problems is given.

4


LIQUID-LIQUID DISPLACEMENT FLOWS IN AN ANNULARSPACE INCLUDING VISCOPLASTIC EFFECTS

Paulo R. de Souza Mendes, Jane Celnik, and Flávio H. MarchesiniDept. Mechanical Engineering

Ponfif´ıcia Universidade Católica-RJRio de Janeiro, RJ 22453-900, Brazil

[email protected]

ABSTRACTVisualization experiments were performed to

investigate the sweeping efficiency during the displacement of one fluid by another as they flow through an annular space. Applications include cementation processes of oil and gas wells. The tubes are made of transparent glass to allow flow visualization. The Reynolds number is kept low for all cases investigated, to ensure negligible inertia. The apparatus was built in such a way that the interface is flat at the startup of the flow. The orientation of the axis with respect to gravity can be varied from 0 to 90o. In the experiments, the interface shape is recorded as it proceeds along the annulus for different sets of values of the governing parameters, and the displacement efficiency is determined.

INTRODUCTIONWhile drilling, cementing and completing oil and gas

wells, a number of fluids circulate in the space between the annular space formed between the casing and the rock formation. The success of the cementing operation depends on how well the drilling mud can be washed out of the annulus, so that cement bonding is guaranteed [1]. Defective bonding may shorten significantly the useful life of the well and cause serious environmental damages. Therefore, replacement fluid operations during drilling, cementing and completion need a detailed design to ensure its effectiveness and the operational safety.

Most fluids that circulate through the annulus, such as drilling muds and cement slurries, behave like viscoplastic liquids. Viscoplastic or yield-stress liquids are materials that have an yield stress below which they behave as a high viscosity liquid, and above which they behave as a shear-thinning liquid [3]. At the yield stress, an often dramatic drop of the viscosity level is observed. A thorough understanding of the conditions for an effective displacement is essential for reliable designs of cementing operations.

THE EXPERIMENTThe experimental setup is sketched in Fig. 1. The

innertube outside diameter of the annulus is 16mm, while its gap is 7.15mm. The inner tube is filled with the displacing liquid (Liquid 1), by pressurizing its reservoir with the aid of compressed air and the valve manifolds VM1 and VM2. The annular space is then filled with the displaced liquid (Liquid 2) in a similar way. After this

loading procedure, the connection gate between them is opened, allowing contact between the two liquids and forming a flat interface. The displacement flow is then ready to start. The apparatus dimensions and the flowrate were chosen such that their dimensionless parameters match a typical real cementing operation [2]. The displacement process begins by pumping Liquid 1 through the inner tube so as to displace Liquid 2 in the annular space. Tracer particles (30µm in diameter) are mixed with Liquid 1. Two laser beams are employed to provide the visualization plane. The shape of the liquid-liquid interface front is photographed for different liquid rheologies and flow rates. The main parameters that govern this flow are the orientation angle, the viscosity ratio, the density ratio, and the dimensionless flow rate. Due to the range of large gaps examined, the capillary force is not expected to play a significant role [4].

RESULTSThe results presented here pertain to the vertical

concentric annulus case. The flow is downwards in the tube and upwards in the annular space.

The interface shape evolution for the case of one Newtonian liquid displacing another is illustrated in Fig. 2. This figure shows pictures of the interface at different times. For this case Liquid 1 is glycerol and Liquid 2 is a lower viscosity oil. The viscosity ratio Nµ = µ1=µ2 was ' 8 and the density ratio was around 1.36. It can be seen that, for this combination of parameters, the interface evolves to a fixed shape, and the displacement efficiency is nearly 100%. The cases involving viscoplastic liquids

4

IV Brazilian Conference on Rheology – Rio de Janeiro, Brazil, July 02-04, 2008employ carbopol solutions at different concentrations. Three such cases are examined, namely: (i) both Liquid 1 and 2 are viscoplastic (carbopol solutions at different concentrations); (ii) Liquid 1 is viscoplastic while Liquid 2 is Newtonian; and (iii) Liquid 1 is Newtonian while Liquid 2 is viscoplastic. Results for these cases will be presented at the conference.

FINAL REMARKSA systematic study of the influence of the various

parameters that govern this flow is under way, and its results will be presented at the conference. In general, it was already observed that the displacement efficiency increases with Nµ and with the density ratio, while decreasing with the flow rate.

ACKNOWLEDGMENTThe authors are indebted to Petrobras S.A., CNPq,

CAPES, FAPERJ, FINEP, and MCT for the financial support to the Group of Rheology at PUC-Rio.

REFERENCES[1] A. T. Bourgoyne Jr., K. K. Millheim, M. E. Chenevert, and F. S. Young Jr. Applied Drilling Engineering. SPE Textbook Series, 1991.

4


RHEOLOGICAL BEHAVIOR OF AQUEOUS DISPERSION OF HEAVY OIL

Clenilson da Silva Sousa Junior (MSc.) Department of Organic Processes, School of Chemistry,

Federal University ofRio de Janeiro, 21949900, RJ, Brazil

[email protected]

Cheila Gonçalves Mothé (DSc.)Department of Organic Processes, School of Chemistry,

Federal University ofRio de Janeiro, 21949900, RJ, Brazil

[email protected]

ABSTRACTNew draining technologies for the high viscosity

oils, the so called heavy oils, are being developed motivated by the increase of oil wells with this kind of oil and by the rising value of the barrel of the light oil worldwide. Due to its discharge viscosity, the nonconventional oil presents a great resistance to the drainage, hindering its locomotion inside the pipelines, thus requesting the use of facilitative agents for its transport. Now most of the Brazilian production of oil is transported by oil tankers, and the oil drainage just by sea becomes insufficient due to the great amount of oil to be transported. Because of this growing factor, the use of pipelines becomes essential. Natural sea water has been used to aid the transportation and to facilitate the drainage of the oil. In this work, two oils are studied, one light and another heavy, mixed with distilled water, natural sea water and synthetic sea water, in different temperatures, for the evaluation of the rheologicalbehavior.

INTRODUCTIONBeing the oil constituted by several hydrocarbons –

with different arrangements, structures and number of carbons, and substances formed by different chemical elements, among them the oxygen, the nitrogen and the sulfur – a classification that considers its density and mainly its viscosity is needed. Regarding its density, the raw oil can be: light, medium, heavy and ultraheavy.

Since the density is a property of the liquids, the industry of the oil uses the expression ºAPI (degree API), of American Petroleum Institute, as reference for the density of the oil measured in relation to the water, with the intention of identifying quickly if the oil is light, medium, heavy or ultraheavy. The higher the degree API, the lighter the oil will be, therefore more valuable in the larger market.

Usually, it is considered that the heavy oils have less than 19ºAPI, a larger density than 0,90 g/mL and a larger viscosity than 20 cP. They also are characteristically known for their high indexes of residues of carbon, resins, sulfur, nitrogen, heavy metals, composed aromatic and paraffin.

For those unfavorable characteristics, the transport of the oils is the largest difficulty found to make possible the exploration of heavy oils and ultraheavy. Among the alternatives more in use now, there is the transportation by trucks or pipelines with heating. For the efficient displacement on considerable distances, it is necessary the use of pipelines. Most of those pipelines, however,

have specifications for smaller viscosity than 100cP, which is not the reality of the nature of the heavy oils and ultraheavy, hence demanding for this pipelines a larger thickness or internal diameter to assist the specificities of the oils.

The majors transport techniques for pipelines, as well as much for oil fields offshore and onshore, are: initial heating of the oil to a temperature that allows the fluid to arrive to its destiny without the need of discharges pressures of pump isolating thermal the pipeline; heating of the oil for the injection of a warm fluid for a concentric line to the pipeline or for electric middle; generation of oil emulsions in water; reduction of the viscosity with the dilution in lighter fractions of oil; injection of water forming a ring involving the oil, known as core-flow.

METHODOLOGYThe seawater used in the preparation of the solutions

was collected in Macaé, coast north of the state of Rio de Janeiro. It was filtered in a filter paper before been used for the retreat of solids. The synthetic seawater used in the mixture of the solutions was prepared in agreement with ASTM 1141. The sample of raw oil was a light national, with degree API 28,74, collected in the basin of Santos. Another sample of raw oil was the heavy national, with degree API 18,70, collected in the platform P-38, in Campos' basin.

The rheological study was accomplished with a mixture of 50% of oil (light or heavy) and 50% of the water (distilled, natural sea or synthetic sea) in the own glass of analysis of the rheometer. The sample was placed in movement by 15 minutes before beginning the rheological measurement. The rheological rehearsals were accomplished in a rheometer model LV-DVIII, of the Brookfield, coupled to a computer and the bath of hot water, also of the Brookfield, model TC - 501. The strip of shear rate used varied from 50s-1 to 490s-1, using the spindle CP 52. All the rheological analyses were conducted at three different temperatures: 25, 35 and 45ºC.

DISCUSIONSFigures 1, 2 and 3 show the curves of viscosity of the

raw oils (light and heavy). They also show the mixtures in the proportion of 50% of oil with 50% of distilled water (DW), synthetic seawater (SW) and natural sea water (NW), using different temperatures.

According to what was presented, when the light oil was used at temperature 25oC (Figure 1), none of the

4


IV Brazilian Conference on Rheology – Rio de Janeiro, Brazil, July 02-04, 2008mixtures made with the different types of water resulted in a decrease of the viscosity of the system. However, when the rheological observation in the temperature at 35 and 45oC (Figure 2 and 3) took place, it resulted in smaller viscosity values in the shear rate strip from 50 to 500 s-1

Figure 1 - Curves of viscosity of the samples of light and heavy oil, in different solvents and temperature at 25ºC.

Figure 2 – Curves of viscosity of the samples of light and heavy oil, in different solvents and temperature at 35ºC.

According to what was presented, when the light oil was used at temperature 25oC (Figure 1), none of the mixtures made with the different types of water resulted in a decrease of the viscosity of the system. However, when the rheological observation in the temperature at 35 and 45oC (Figure 2 and 3) took place, it resulted in smaller viscosity values in the shear rate strip from 50 to 500 s-1. At the temperature 35oC, a reduction of viscosity was verified in the mixture of 50% of light oil with 50% of distilled water of around 25 mPa.s, while the light oil had its viscosity in the strip rate of 35 mPa.s. At the temperature 45oC, the mixture with distilled water had a smaller viscosity values at the strip rate than the one of the raw oil, from 27 mPa.s (raw oil) to 18 mPa.s (mixture). All those mixtures indicate a Newtonian behavior when the shear stress curves are observed. Only at temperature 45oC, the mixture of 50% of light oil with

50% synthetic seawater showed a pseudoplastic behavior in smaller shear rates, but after 150s-1, the Newtonian behavior was verified, and at this point, the viscosity of this mixture became smaller than the viscosity of the raw oil.

Figure 3 – Curves of viscosity of the samples of light andheavy oil, in different solvents and temperature at 45ºC.

Regarding the case of heavy oil there was a reduction of the viscosity when the synthetic seawater was used as a solvent, mixed at the proportion of 50% each at the temperature 35oC. As where as the temperature 45oC is concerned, the only mixture that the reduction of viscosity was verified was with natural seawater. With distilled water, the viscosity was of around 23 mPa.s, while with raw oil it was of 28 mPa.s. However, when the rate shear applied is low, the behavior of the mixture is pseudoplastic, but only after the shear rate of 80s-1, the viscosity of the system reduced, exhibiting a Newtonian characteristic.

CONCLUSIONSThe use of mixed solvent to the light oil showed a

considerable effect at the temperatures 35 and 45ºC, with viscosity decreasing when distilled water was used. When the heavy oil was mixed with the synthetic seawater, in the proportion of 50% at temperature 35oC, a reduction of viscosity was verified. At temperature 45oC, the only mixture, which a reduction of viscosity was verified, was the one with natural seawater.

ACKNOWLEDGMENTSThe authors are grateful to CNPq and

CENPES/Petrobras for their financial support.

REFERENCESSOUSA JUNIOR, C.S. Tecnologia de Óleos Pesados e Ultrapesados. 2008. Dissertação de Mestrado. EQ/UFRJ – Rio de Janeiro – RJ.CORREIA, D.Z.; GARCIA, R.B.; MOTHÉ, C.G.; DE FRANÇA, F.P. Displacement of Guar Gum in Porous Media to Control Water Mobility. Journal of Reservoir Engineering. vol. 1, no 1, 2006.

4


NUMERICAL STUDY OF CERAMIC PASTES EXTRUSION

R. B. O. Jardirm, M. S. Carvalho, M. F. NaccacheDepartment Mechanical Engineerig, PUC-Rio

RJ 22453-900, Rio de Janeiro, Brazil

S. S. X. ChiaroCENPES/Petrobras

RJ 21949-900, Rio de Janeiro, Brazil

ABSTRACTThe present work is focused in the numerical

analysis of ceramic paste extrusion process. The geometry analyzed is an abrupt axisymmetric contraction. The conservation equations were solved numerically using the finite volume method. In order to model the viscoplastic behavior of the ceramic pastes, the Generalized Newtonian Fluid constitutive equation was used. The Herschel-Bulckley model was used for the viscosity function, based on rheologycal data for the ceramic pastes. The effects of the paste rheological parameters and of the extrusion process operational parameters on flow behavior were analyzed, searching the better understanding of the process and its optimization.

INTRODUCTIONThe production of catalyst to hydrorefining process

in the petroleum industry results from the extrusion process of ceramic pastes, which presents a viscoplastic behavior. The quality of the final product is strongly affected by operational variables (flow rate, geometry) and by the ceramic paste rheology. In this work a numerical study of the flow of ceramic pastes through a 4:1 axisymmetric contraction is performed, and the influence of rheologycal parameters on the pressure drop and on the force through the contraction wall are investigated.

METHODOLOGYThe geometry analyzed is shown in Fig. 1. The fluid

is incompressible; the flow is axisymmetric, isothermal, laminar and steady.

Figure 1: The geometry The conservation equation of mass is given by:

1r rv ∂ u

∂ x=0 (1)

where x and r are the axial and radial coordinates, u and

v are the axial and radial velocity components. The conservation equations of momentum in the radial and axial directions respectively, are given by:

v ∂ v∂ r

u ∂u∂ x =[ 1

r∂∂ r

r rr−∂

r∂rx

∂ x ]−∂P∂ r (2)

v ∂ u∂ r

u ∂ v∂ x =[1

r∂∂ r

rrx ∂xx

r ]−∂P∂ x

(3)

where ρ is the density and P is the modified pressure. The stress tensor is given by the Generalized Newtonian Fluid constitutive equation: = , where τ is the extra-stress tensor, =∇ v∇ vT

is the strain rate tensor, and η is the viscosity function. The viscosity function is given by the modified bi-viscosity function (Beverly and Tanner, 1992):

Where τ0 is the yield stress, k is the consistency index, n is the power-law index and ηlarge is the low shear rate viscosity. This viscosity function was chosen based on the experimental rheological data for some ceramic pastes. The boundary conditions were: developed velocity profile at the entrance, developed flow at outlet, no slip and impermeability at the walls, and at the centerline, the radial velocity and shear stress are null. After extensive mesh tests, a mesh with 170 control volumes in the axial direction and 105 control volumes in radial direction was chosen.

After extensive mesh tests, a mesh with 170 control volumes in the axial direction and 105 control volumes in radial direction was chosen.

RESULTS AND CONCLUSIONSFirst of all, the rheological data of a typical ceramic

paste was obtained experimentally, using the capillary rheometer ACER 2000. The experimental data for the viscosity was fitted with the Herschel-Bulkley equation, and the rheological parameters are given by: τ0

=8.74x104, k=1.27x105 and n=0.28. The viscosity field and streamlines for this fluid, and for a flow rate equal to 6.5x10-6 m3/s, are shown in Fig. 2. It can be observed that lower viscosities (blue zones) are found close to the contraction, due to higher deformation rates. Close to the

4

IV Brazilian Conference on Rheology – Rio de Janeiro, Brazil, July 02-04, 2008wall matrix, there is a high viscosity zone.

Figure 2: Streamlines and velocity contours.

The effect of yield stress and the power-law index on pressure drop through the contraction can be analyzed with the aid of Figs. 3 and 4. The pressure drop is evaluated extrapolating the linear pressure drop at the developed regions for the entrance and exit tubes, to the contraction section. The pressure drop is the difference between the values Pi (obtained from the entrance tube) and Po (obtained from the exit tube). It can be observed that in the analyzed range of yield stress, it does not affect the pressure drop. Fig. 4 shows the effect of the power-law index on the pressure drop. It is noted that the pressure drop increases with n, as expected, since at the same strain rate, the viscosity is higher for larger values of n, leading to a higher pressure drop. The force over the extrusion matrix is also an important result. It can be evaluated integrating the pressure force through the contraction wall. Fig. 5 shows the effect of yield stress and power-law index on the force through the contraction wall. The yield stress does not affect the force. However, the increase in the power-law index leads to an exponential increase in the force. These results, as well as the mechanical properties of the pastes, should be taken into account for the choice of paste formulation.

Figure 3: Effect of τ0 on pressure drop

ACKNOWLEDGMENTSThis research was supported by CNPq,

FINEP/CTPETRO and Petrobras.

Figure 4: Effect of n on de pressure drop

Figura 5: Effect of n and τ0 on the force at matrix wall

REFERENCESChen Y., Burbridge A., Bridgwater J. 1997, J. of Am. Cerâmic Society 80, 1841-1850.Benbow J.J., Oxley E.W., Bridgewater J. 1987, Chemical Engineering Science 42 2151-2162.Yu A. B., Bridgwater J., Burbridge A.S., Saracevic Z. 1999, Powder Technology 103 103-109.Stedman S.J., Evans J.R.G. 1990, Journal of Materials Science 25 1833-1851.Bridgwater J., Burbridge A.S. 1995, Chemical Engineering Science 50 2531-2543.Polinski A.J., Ryan M.E., Gupta R.K. 1988, Polymer Engineering and Science 28 453-459.

4


APPLICATION OF TENSOR DECOMPOSITION THEOREMS ON DNS DATA OF VISCOELASTIC DRAG REDUCING

CHANNEL FLOW

Roney L. ThompsonGrupo de Escoamento de Fluidos Complexos - LMTA -

PGMECDepartment of Mechanical Engineering, Universidade

Federal FluminenseRua Passo da Pátria 156, Niteroi, RJ 24210-240, Brazil

Laurent Thais and Gilmar MompeanUniversité des Science et Technologies de Lille,

Polytech’LilleLaboratoire de Mécanique de Lille, UMR-CNRS 8107

Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France

ABSTRACTWhen a few parts per million of a polymeric material

of a high molecular weight is added to a Newtonian turbulent flow, in a pipe for example, the drag reduces by large amount: 40%, 50%, sometimes up to 70%. This fact was verified in a number of experimental investigations and is well documented in Virk (1975). Although this phenomenon has been observed and verified, the true mechanism that leads to the drag reduction by polymer additives is still an open question. The results indicate, however, that only liquids with elastic properties are capable of producing a reduction on the drag. From some experimental data Virk et al. (1967, 1970) divided the domain in three sub-domains. Basically the viscous sub-layer and the turbulent core remain with the same features as the Newtonian ones. The di®erence occurs, mainly, at an intermediate layer where now there is a competition (notbetween inertial and viscous e®ects, as in the Newtonian case, but one) between elastic and viscous efects.

The theories presented by Lumley (1977) and Hinch (1977) are worth noting. They correlate the drag reduction phenomenon to an important rheological property of viscoelastic fluids: its extensional-thickening behavior. The turbulent flow does not exhibits a high correlation between the rate of angular deformation and the rate of linear deformation. Therefore, most of the polymer molecules, specially when they have long chains (in opposition to branched chains), can be oriented to the same direction for a long time. This kind of exposure to the main kinematics of the flow can highly distort the conformation of the molecule, and this characterizes a strong flow. In this case, the resistance to the extensional deformation, the extensional viscosity, can increase more then 104 times. This increase of resistant forces can alter dramatically the flow structure associated to the mechanisms of production and dissipation of turbulence which, at the end, changes the drag at the wall.

Since the theories to explain the drag reduction phenomenon are not consensual, investigations employing DNS calculations can be extremely helpful to understand the turbulence of viscoelastic liquids and, therefore, bring some light to this complex subject. It is worth noticing, however, that DNS simulations for viscoelastic liquids is philosophically diferent from its Newtonian counterpart. The reason for this difference is

because the expression Newtonian liquid refers to a real fluid while the expression FENE-P liquid, for example, refers to a model of a fluid. This happens because there are liquids whose behavior, captured by measurements, adhere excellently to the hypothesis of a Newtonian constitutive model. On the other hand, there is no liquid which has an excellent degree of agreement to the hypothesis of an specific viscoelastic constitutive model.

In spite of these considerations, there has been some consistent studies using DNS simulations with viscoelastic liquids in the last decade. The works of Massah and Haratty (1997), Sureskumar et al. (1997) and Dimitropoulos et al. (1998,2001) are of particular interest. They have used FENE-P and Giesekus models in their DNS simulations and found qualitative agreement with experimental results. The recent developments in DNS of viscoelastic models allow the reduction of the numerical difusion due to formulations that are based on the evolution of the conformation tensor and, therefore higher level of Reynolds number were achieved. The investigations of Housiadas and Beris (2004a, 2004b) and Li et al. (2005) have found higher values of drag reduction, a consequence of the higher levels of Reynolds number, then the ones obtained previously.

In the present work data from a DNS calculation of a viscoelastic FENE-P material in a turbulent channel flow are used to understand some aspects of the mechanism of drag reduction. We first correlate the terms from the mean momentum equation that need closure models to

the mean kinematic quantities such as D , D2 and

D⋅W −D −W −D ⋅D , where D and W are,

respectively, the symmetric and skew-symmetric parts of

the velocity gradient and D is the spin tensor related to the rotation of the eigenvectors of D. These correlations are compared to the Newtonian case. After that, we correlate the conformation tensor (an average quantity that represents the main aspects of the configuration of a set of polymer molecules) to the anisotropic Reynolds stress and identify regions where these two tensors are in-phase and out-of-phase. The approach employed in the present work indicates a path to construct models for the turbulence of viscoelastic materials.

4


A STRONG CRITERION FOR MICRO-STRUCTURED LIQUIDS IN WHICH THE MICRO-ELEMENT CAN BE REPRESENTED BY A VECTOR

Carlos R. A. dos Reis, Monica Cristina Matos, Roney L. ThompsonGrupo de Escoamento de Fluidos Complexos - LMTA - PGMEC

Department of Mechanical Engineering, Universidade Federal FluminenseRua Passo da Pátria 156, Niteroi, RJ 24210-240, Brazil

ABSTRACTBased on the kinematic strong-weak criterion

proposed by Tanner and Huilgol (1975), Tanner (1976) has developed a strong-weak criterion for a flowing system where hookean dumbbell micro-elements are present on a Newtonian solvent. Olbrich et. al (1982) have extended this idea to more complex micro-structured liquids based not only on the kinematics of the main flow but also on micro-structure features of the micro-element and its interaction with the main flow. They could encompass, with the same theory, emulsions and polymeric liquids. The vector chosen to represent the main features of the micro-element can be a single one, as in the case of drops in a fluid, or can be an expectation value of a set of vectors, as in the case of polymer chains. The basic idea of these approaches is the identification of micro-structure-velocity-gradient, the velocity gradient experienced by the micro-element considered. After that, a Lyapunov exponent stability analysis is conducted. The problem identified with the application of this method is that the eigendirection correspondent to a positive real part of a Lyapunov exponent can be orthogonal to the orientation of the micro-element considered. Therefore, the eigendirections of the Lyapunov exponent analysis have to be filtered appropriately to exclude the plane defined by the orientation of the micro-element. Situations where the two methods do not coincide are explored to show that the filtered criterion over-performs the original one. In the same problem, an alternative approach based on the ideas developed in Thompson and Souza Mendes (2005) and Thompson (2008), is to consider the Lie product of the micro-structure-velocity-gradient and its transpose. The intensity of this quantity can be seen as a measure of how far from extension the micro-structure considered is subjected. A dimensionless quantity can be built using the intensity of the deformation-rate experienced by the micro-element Comparison of the two measures are made for some examples in order to understand their diferences and similarities.

4


An orthotropic closure approximation for the fourth order moment of a strand vector and its application on partially extending strand convection models

Roney L. ThompsonGrupo de Escoamento de Fluidos Complexos - LMTA - PGMEC

Department of Mechanical Engineering, Universidade Federal FluminenseRua Passo da Pátria 156, Niteroi, RJ 24210-240, Brazil

ABSTRACTA large variety of flowing systems of complex

microstructured fluids is described by a probability density function, ψ (R, x, t) where R is a representative vector that describes the main aspect of the microstructure, x is the position vector and t is the current time. In suspensions, R is the vector of the major axis of a given particle. In immiscible blends, R is the outwardly directed unit vector normal to the droplet surface. In dilute solutions of polymeric liquids, R is the end-to-end distance of the polymer while in melts it is the difference between two entanglements.

The molecular theories developed to understand the behavior of such fluids are, therefore, based on an evolution equation for the probability density function. The probability density function obeys the probability continuity equation of the form

DψDt

∇ R⋅J ψ =ψ p−ψ d (1)

where Jψ = ψR is the probability density flux, the operator ∇R·() is the divergence resolved in the configurational space R3 , and ψp and ψd are, respectively, the local (in the sense of the Euclidean and configurational spaces) rates of production and destruction of segments per unit mass. The calculation of the elastic stress tensor was identified as strongly related (in fact proportional in most cases) to the second moment of the probability density function. Besides that, the second moment can capture the main features of a microstructure, namely size and orientation. Hence, its evolution equation can model stretching and change on orientation. Therefore, in order to gain economy on computational calculations, a simpler approach considers the evolution equation of the second moment of the probability density function defined as

⟨RR ⟩ x,t =∫ R,x,t RR d R (2)

Γ ≡⟨ RR ⟩ represents a conformation tensor. The approach that considers its evolution (instead of considering the evolution of the probability density function) is a mesoscopic approach.

In order to compute the evolution equation for the conformation tensor ⟨ ˙RR ⟩ (suppressing the dependence on (x, t)) we have to use eqs.(1) and (2).

⟨ ˙RR ⟩=⟨ R R ⟩⟨R R ⟩=∫R3 JR=R Jd R (3)

Depending on the form of the flux Jψ and the rate of production and destruction of segments (and the interaction with the medium), different evolution equations are obtained.

In the present work, the partially extending strand convection model of ? is analyzed from the framework perspective constructed by ? and it is shown that the terms related to stretching and rotation concerning a strand vector do not originate these same phenomena as far as the second moment of the probability density function, the conformation tensor, is considered. In order to produce each of these phenomena on the mesoscopic level from the correspondent phenomena at the microscopic level, it is necessary to change the classical closure approximation for the fourth moment of the probability density function of a representative microelement vector ⟨RRRR⟩≈⟨RR⟩ ⟨RR⟩ to a special one that belongs to the class of orthotropic ones presented by ?. A decomposition theorem presented by ? is used to provide such a closure approximation which are more physically consistent in the sense stated above. The new class of models for the evolution equation of the second order conformation tensor is presented with the same framework (?). An interesting improvement is the fact that these models do not lead to 3-D instabilities in a 2-D flow. The concept of the natural convected time derivative (?) is used in order to split the general evolution equation into two parts: a stretching-evolution equation and a rotation-evolution equation. This framework gives an alternative simulation algorithm that can be coupled with the matrix-logarithm approach presented by ?.

Key words: persistence of stressing, persistence of conformation stretching, natural convected time derivative, stress history, extensional flows, coaxial tensors, Lie product, elastic response.

4


PARTICLE SEDIMENTATION IN A TIME DEPENDENT VISCOSITY FLUID

Roni Abensur Gandelman /PETROBRAS

André Leibsohn Martins /PETROBRAS

Raul Bastos / PETROBRAS

Hellen Christina de Moura Guilherme/PETROBRAS

Gustavo Henrique Pinto/PETROBRAS

ABSTRACTThis work presents an initial effort to obtain a good

comprehension about particle sedimentation in a fluid which, in static conditions, gel strength increases with time.

INTRODUCTIONOne of the main functions of drilling fluids for oil

and gas wells is to transport the solids generated by the bit from the bottom of the oilwell to the surface. The gelation phenomenon is a very important characteristic of drilling fluids. Once, it helps to keep drilled solids in suspension while the pumps are off. Gelation tendencies are normally higher at low temperatures typical of deepwater risers (Gandelman et al.1, Bjørkevoll2 and Vefring3).

A fast and non progressive gel is desired to avoid excessive pressure peaks when circulation is resumed. Important parameters governing gelation are temperature, pumps off time and drill pipe rotation. The smaller the pump off time, smaller will be the time available for heat exchange and to form a gelled structure.

However, not all particles are kept in suspension during a pumps off period. Some small particles stay in suspension when gel is built, but larger particles tend to sediment when flow rate is interrupted. The sedimentation velocity of the particles decreases as the gel becomes stronger.

It is very important understand how particles sediment, while gel strength increases with time. Particle sedimentation during pumps-off time changes the solids concentration profile in an oil well and can cause operational risks.

The problem can be treated as a particle sedimentation in a fluid which viscosity increases, due to interparticle attraction, as time passes. The terminal velocity of the particle depends on the fluid viscosity in which it sediments.

Exploratory experiments were carried out to obtain a better understanding of the gelation phenomenon and to describe the fluid viscosity (during static period) as a function of the time.

METHODOLOGYThree fluids were used at the tests: two oil based

fluids (fluid A, designed for high pressure high temperature wellbores and fluid B, designed for ultra deep water environments) and a polymeric aqueous fluid (xanthan gum + water) in two different concentrations.

A preliminary rheological investigation was carried on, according to the following steps: 1. The sample was submitted to continuous shear with

deformation rates ranging from 0.01 up to 1000s-1

2. A constant shear rate (600s-1) was applied for 1 minute (to break any possible gel built).

3. The sample was submitted to a constant low frequency oscillation (0.1Hz) which allows the estimation of viscosity evolution with time without breaking the intermolecular structure growth. Fig.1 highlights results obtained in a Haake RS 600 rheometer for fluid ª

A power law approach is proposed to explain the viscosity behavior as shown in equation 1.

bta.0 += µµ (1)

Where µ0 is the fluid viscosity right before the circulation is interrupted. “a” and “b” are parameters to be fitted.

The terminal settling velocity of a single particle in a stationary fluid (wall effects not considered) is assumed to be explained by Stokes law as shown in equation 2 (Massarani4).

µρρ

.18..).( 2

pfluidsolid Dkgv

−= (2)

Where þsolid and þfluid are the specific weights of solid and fluid. “g” is the gravity acceleration, Dp is the particle diameter and µ is given by equation 1. “k” is given by equation 3:

4


)065.0/log(.843.0 φ=k (3)

Where φ is a particle shape factor. Equation 4 describes how to obtain the position of a particle falling in a time dependent viscosity fluid:

( )bpfluidsolid

taDkg

dtdSv

..18..).(

0

2

+−

==µρρ

(4)

Rearranging Eq. 4:

( ) dtta

DkgdS b

pfluidsolid

..18..).(

0

2

+−

=µρρ

(5)

Integration of the equation above gives the position of the particle as a function of time:

0

012 ;11;1;1

18..).(

)(µ

µρρ

−+−

=

b

pfluidsolid

atbb

FDkg

tS (6)

Where F1 is a hyper geometric function given by:

( ) ...)1(!2

)1()1(!1

... 2 ++

+++= zcc

bbaazc

abzcbaFa (7)

Figure 2 shows the position of a particle in fluid with time. Figure 3 shows both viscosity evolution and particle sedimentation velocity. The particle and fluid properties considered were:

Dp = 0,15 in;ρsolid = 2,3 g/cm3;φ = 0,70;ρfluid = 1,3 g/mL; µ0 = 100,23 cP a = 100,54 cP; b = 0,095 s-1

Note: the velocity tends to a constant value as viscosity becomes constant. Viscosity will be constant when gel is completely built.

FINAL REMARKSThis study represents an initial effort to establish a

methodology to understand particle sedimentation in a gelling fluid. The problem was treated as particles sedimentation in a fluid in which the viscosity increases while gel builds. This simple methodology represents a preliminary tool for the evaluation of fluid suspension capacity when the pumps are off in drilling operations. The present analysis, however, is limited to Stokes Law, no relation between viscosity and shear rate was proposed and lacks experimental validation. Future development will contemplate these factors.

REFERENCES1. Gandelman, R.A., Leal, R.A.F, Gonçalves, J.T., Aragão, A.F.L., Lomba, R.F., and Martins, A.L., “Study on Gelation and Freezing Phenomena of Synthetic Drilling Fluids in Ultradeepwater Environments”. SPE/IADC 105881-MS, The Netherlands, 20-22 February 2007.2. Bjørkevoll, K.S., Rommetveit, R., Aas, B., Gjeraldstveit, H., Merlo, A., “Transient gel breaking model for critical wells applications with field data verification”. SPE/IADC 79843, The Netherlands, 19-21 February 2003. 3. Vefring, E.H. Bjørkevoll, K.S., Hansen, S.A., Sterri, N., Saevareid, O., Aas, B., “Optimization of Displacement Efficiency During Primary Cementing”. ”. SPE 39009, Rio de Janeiro, August 30-September 3, 1997.4. Massarani, G., “Fluidodinâmica em sistemas particulados”. Editora UFRJ, Brasil, 1997.

4


EFFECT OF POLY(ETHYLENE TEREFTALATE) OLIGOMERS ADDITION ON ASPHALT RHEOLOGY

Fábio Lima da Silva/Instituto deMacromoléculas Professora Eloísa

Mano, Universidade Federal doRio de Janeiro

Marcos Lopes Dias/Instituto deMacromoléculas Professora Eloísa

Mano, Universidade Federal do Rio deJaneiro

ABSTRACTThis work shows the relationship between

rheological properties and performance, determined by rheometry, of asphalt binders modified by styrenebutadienestyrene copolymer and a oligomers obtained by alcoholisis between poly(ethylene tereftalate) and ethylene glycol. Another aim is analyzing the influence on ageing resistance in these asphalts.

INTRODUCTION

Asphalt is a dark and very viscous organic fluid which is the main material used in road construction. Because of its inherent characteristics, it becomes soft and flows when temperature increases. This phenomenon associated with traffic causes permanent deformation of pavement, which is known as rutting. Another upset which happens during the life time of asphalt is degradation for the action of temperature, sun radiation and traffic. This degradation is know as ageing and results in asphalt hardening and cracking.

The advent of polymer modified asphalts represented a revolution on pavement design. The long molecule chains act as anchor among the organic fractions of asphalt, decreasing the temperature susceptibility that it is observed in pure asphalt. The main polymers employed as modifiers agents are polyolefins - polyethelene and polypropylene - and elastomers like styrenebutadiene rubber (SBR), Ethylenevinyl acetate (EVA) and Styrenebutadienestyrene (SBS).

The popularity of poly(ethylene tereftalate) (PET) in the last 20 years in the production of soft drink bottles for its barrier properties represented a huge increase in urban garbage. To avoid ecological impact some routes are proposed for recycling. One of them is chemical where PET reacts with glycols to produce oligomers like bis(2hydroxyethyl terephthalate) (BHET) and bis( 2hydroxypropyl terephthalate) (BHPT). These oligomers are further used in polyester resin synthesis. Recently a group of researchers from CENPES/PETROBRÁS and Macromolecules Institute (IMA/UFRJ) [1] has acquired a patent describing the use of PET oligomers as modifiers agents in asphalt binders. This fact is very important because PET was mainly used as fillers, not significantly changing binder properties. The physical mixture of BHET and BHPT into asphalt improves thermal susceptibility and, therefore, the resistance to permanent deformation.

As asphalt binders are viscoelastic it is possible to analyze their thermal susceptibility determining the

dynamic rheological parameters like elastic modulus G´ and viscous modulus G´´ at constant frequency in a range of temperatures observed in pavement service. Another useful parameter is the ratio between G´´ and G´ (tan δ), which is more sensible to temperature changes than above parameters. According to Strategic Highway research Program (SHRP) the rheological parameter G * / sin δ can express the contribution on permanent of asphalt binder [2].

METHODOLOGYTwo kind of asphalt binders were used which were

produced in two Brazilian petroleum refineries (REPAR and PAULÍNIA). These binders have the same specification based on penetration (CAP 50/70). Bottle grade pellets of green PET reacted with ethylene glycol at zinc acetate presence as catalyst. After 100 minutes of reaction the products were washed in water excess and dried during 48 hours at 50 0C. The product obtained was physically mixed with asphalt binders at 185oC during 3 hours. Four mixes were obtained with the following massic ratios (oligomer/binder): 2,5/100, 5/100, 10/100 and 20/100. These mixes were latter aged (RTFOT and PAV methods). SBS copolymer (specification number Kraton D101BM) were also used to obtain four mixes, with the same massic ratios and at the same mixing conditions, for comparing.

The dynamic rheological parameters were obtained using a parallel plates geometry (1mm gap) at a fixed frequency of 10 rad/s from 25o to 90 oC.

ACKNOWLEDGMENTSThe authors would like to thank to Ipiranga Asfaltos

and Kraton Polymer, both in Paulínia, São Paulo, for the supplying of asphalt and SBS samples, respectively, and to Petrobrás Research Center (CENPES) for the ageing of polymer modified asphalts.

REFERENCES[1] Brazilian patent PI 0601920-0 A[2] Yu, J et al. Preparation and properties of montmorillonite modified asphalts. Material Science and Engineering A (2007), n. 447, p. 233-238

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RHEOLOGY OF THIN LIQUID FILMS-–NEWTONIAN VS. NON NEWTONIAN DYNAMICS

David Barbero, Ulli SteinerCavendish Laboratory University of Cambridge Cambridge, UK

[email protected]

ABSTRACTThin liquid films are ubiquitous. The range of their

applications goes from paints and coatings to micro- and nano-fluidic devices used for medical purposes. In a series of carefully controlled experiments, we show that stresses built in a thin liquid film (~100 nm) during sample preparation can dramatically change its rheological behaviour, and lead to a strong reduction in viscosity. The results of this study will likely have important implications for the design of thin coatings and layers which are pervasive in both research and industry nowadays.

INTRODUCTIONOne recurring and still unanswered question in

polymer physics concerns the possible existence of a layer of lower viscosity at the interface between a thin polymer melt and air. Various techniques have been used

to probe the free surface of liquids but the results so far have been inconclusive. In this abstract we study for the first time the rheological behaviour of thin polystyrene (PS) films, which constitute one of the most studied systems, using electric fields.

METHODOLOGYThin films of PS of various molecular weights were

spin-coated on a silicon substrate and mounted in a capacitor plate configuration. The sample was then heated above its glass transition temperature (Tg~100°C) and a difference of voltage was applied between the top and bottom electrodes. The thin film was destabilized by the high applied electric field, and formation of small patterns was recorded in real time to study the kinetics of destabilization. The characteristic time of destabilization is measured and compared to the theoretical predictions of the linear stability analysis. A comparison between samples containing stresses built in the film by the spin- coating process and samples which have been annealed for long enough times to remove all stresses is drawn. Our results show that stresses can dramatically reduce the viscosity of the thin film, and that annealed samples on the contrary follow a Newtonian behaviour as expected from the Navier Stokes equation of motion of the film.

ACKNOWLEDGMENTSThe authors would like to acknowledge support from

a Marie Curie Fellowship (PATTERNS).

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EFFECT OF SOLID CONTENT, pH AND DEFLOCCULANT CONCENTRATION VISCOSITY OF KAOLIN SLURRIES

Carla Napoli Barbato Escola de Química - UFRJ

Centro de Tecnologia Mineral -CETEM

Silvia Cristina Alves França Centro de Tecnologia Mineral -CETEM

Márcio Nele Escola de Química - UFRJ

José Carlos PintoPrograma de Eng. Química –

COPPE/UFRJ

ABSTRACTThe influence of solid concentration, deflocculant

concentration and pH on the viscosity of kaolin suspension was investigated using a complete factorial design of experiment with stars and central points (central composite). The suspensions were prepared in the range conditions: deflocculant concentration from 6 to 8 kg/t, solids concentration from 50 to 70% (w/w) and pH from 7 to 10. It was observed that the kaolin concentration has the strongest influence in the suspension viscosity and an empirical model was built relating suspension viscosity, shear rate and preparation variables.

INTRODUCTIONThe term kaolin refers to a rock whose percentage of

the mineral kaolinite is higher than 50% in kaolin. Kaolinite is often found is association with other minerals such as quartz, feldspar and micaceus with account for the percentage of impurity and contributes to the amounts of salts and cations found in kaolinite rocks (Andreola et al., 2006).

The objective of studying the rheological properties of mineral pulps is the optimization of the shear stress necessary to pump them (Nasser and James, 2008). Suspensions rheology can be affected by the volumetric solids fractions, particle size distribution, particle shape, floc and electroviscous effects (Ortega et al., 1997).

The aim of the present work was evaluate the influence of solid concentration, deflocculant concentration and pH on the viscosity of kaolin suspensions.

METHODOLOGYThe raw material was kaolin of region Borborema –

Seridó (northeast of Brazil), which the chemical composition (% in weight) is: 39.06 Al2O3, 0.418 Fe2O3, 0.7 K2O, 0.063 P2O5, 46.91 SiO2 and 12.85 loss to the fire. The average particle size d50 = 9,267 µm (laser particle- sizer analysis).

The suspensions were prepared with distilled water and 4% (w/w) of kaolin. The measurements of zeta potential (Zeta Probe-Colloidal Dynamics) were made in the pH range 2.5 to 12. The pH was adjusted with diluted solutions of NaOH and HCl. The zeta potentials of kaolin suspensions were determined in absence and presence of

sodium hexametaphosphate.Viscosity values were obtained in a Rheo Stress

Haake Rheometer (RS1), equipped with coaxial cylinder measuring sensor (Z-20 DIN) in isothermal conditions at 25 ºC. All samples were measured using three cycle: a shear rate increase from 0 to 1,000 s-1 in 600 s, followed by 10 s at a shear rate of 0 s-1 and a shear rate decrease from 1,000 to 0 s-1.

The suspensions were prepared in the following conditions: deflocculant (sodium hexametaphosphate) concentration in the range 6 to 8 kg/t, solids concentration in the range 50 to 70% (w/w) and pH in the range 7 to 10. The designed experiments are presented in Table 1. The experiments were run in a random sequence and the viscosity was measured immediately after slurry preparation.

Table 1 – Conditions experimental according to the planning of complete factorial experiment with star plan and point central.

TestsSolids

Concentration (%)

Deflocculant Concentratio

n (kg/t)pH

1 50 6 72 50 6 103 50 8 74 50 8 105 70 6 76 70 6 107 70 8 78 70 8 109 60 7 8.510 70 7 8.511 50 7 8.512 60 6 8.513 60 8 8.514 60 7 715 60 7 10

RESULTS AND DISCUSSIONSZeta PotentialFigure 1 reports the variation of zeta potential with

the increase of pH and concentration of sodium hexametaphosphate. This behaviour can be attributed by the progressive deprotonation of surface edge sites and

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IV Brazilian Conference on Rheology – Rio de Janeiro, Brazil, July 02-04, 2008the adsorption of the sodium hexametaphosphate on kaolin.

The zeta potential becomes increasingly negative as pH increases. This behaviour can be attributed to the deprotonation of aluminol group on edge of kaolinite giving a complexed anion what contributes to the increase of the negative surface charge and, consequently, to the repulsive forces between particles.

-40

-35

-30

-25

-20

-15

-10

-5

00 4 8 12

pH

no deflocculant 4kg/t 6kg/t 10kg/t 8kg/t

Figure 1 zeta potential versus pH (4% solid and different hexametaphosphate concentration).

The sodium hexametaphosphate (NaPO3)6 used as deflocculant in the kaolin slurries is chemisorbed on the edge of kaolinite. The hexametaphosphate anions interact with the exposed atoms of aluminium, giving a complexed anion. The chemisorption produces a surface excess of negative charges and therefore an increase of the repulsion forces between the particles; as a consequence, the zeta potential values of the clay particles incre’ases (Andreola et al., 2004).

Rheological StudiesTable 2 shows the viscosity values at 200, 400, 600,

800 and 1,000 s-1.

Table 2 – Viscosity values at 200, 400, 600, 800 e 1,000 s-1.Test

sViscosity (mPa.s)

τ = 200 s-1 τ = 400 s-1 τ = 600 s-1 τ = 800 s-1 τ = 1,000 s-1

1 12.21 11.19 10.97 11.97 11.032 8.86 8.58 8.84 9.23 9.673 13 11.37 10.86 10.77 10.764 8.68 8.08 8.26 8.78 9.515 1708.00 1368.00 1002.00 771.30 647.706 912.40 789.50 627.40 509.50 437.427 1231.00 911.60 676.80 542.40 469.698 882.80 724.20 579.50 475.00 403.560 36.08 32.7 31.25 30.66 29.110 45.44 41.45 39.2 36.96 34.740 46.31 41.99 39.79 37.91 36.170 46.44 39.17 35.92 34.14 33.050 50.19 44.64 41.59 39.20 37.2010 1346.00 1068.00 830.10 672.50 567.6511 12.96 11.06 10.48 10.29 10.3112 51.90 46.69 44.97 42.82 40.4513 48.90 43.23 40.67 38.39 36.0914 46.03 40.57 38.61 36.73 34.7515 63.43 53.96 49.53 46.04 42.05

The analysis of the experimental data showed that the viscosity deviates strongly from the linear behavior and concentration of solids has the strongest influence on suspension viscosity, followed by shear stress, deflocculant concentration and pH.

An empirical model was built relating suspension viscosity, shear rate, deflocculant concentration and pH.

The solid concentration had the most significant effect on the slurry viscosity. To a solid concentration increase from 50 to 70% (w/w), the viscosity increased approximately 10 times. This change in the viscosity is due to the decrease of the layer of water among the particles, giving larger attrition and interaction among them.

The viscosity of kaolin pulps decreased with the increase of deflocculant concentration. This behavior can be attributed by the chemisorption of sodium hexametaphosphate on the edge of kaolinite. The chemisorption produces a surface excess of negative charge and therefore increase of the repulsion forces between the particles; as a showed by the zeta potential values of the clay particles (Figure 1). The effect of deflocculant concentration was stronger in the kaolin pulps with 70% of solids.

The viscosity of kaolin pulps decreased with the increase of pH. This behavior can be attributed to the reaction of deprotonation of aluminol group on edge of kaolinite giving a complexed anion what contributes to the increase of the negative load and consequently of the repulsive forces among the particles. The effect of pH was stronger in the kaolin pulps with 70% of solids.

CONCLUSIONSSolid concentration is the most important variable to

the suspension viscosity. The increase of deflocculant concentration and pH contributed to decrease of viscosity of kaolin pulps. Theses effects were stronger in the suspensions with 70% of solids.

ACKNOWLEDGMENTSThe authors are grateful to CAPES for the financial

support and to CETEM and EQ/UFRJ for the laboratorial facilities. MN and JCP wish to thank to CNPq for providing financial support.

REFERENCESAndreola, F., Castellini, E., Mqanfredini, T. e Romagnoli, M. Journal of the European Society. V.24. pp: 1213-2124. 2004.Andreola, F., Castellini, E., Olhero, S. e Romagnoli, M. Applied Clay Science. V. 31. pp: 56-64. 2006. Nasser, M. S. e James, A. E. Colloids and Surfaces A: Physicochem. Eng. Aspect. V. 317. pp:211-221. 2008.Ortega, F. S., Pandolfelli, V. C., Rodríguez, J. A., Souza, D. P. F. Cerâmica. v. 43. pp:5-10. 1997.

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IV Brazilian Conference on Rheology – Rio de Janeiro, Brazil, July 02-04, 2008Índice

Methods of assays for definition of the composition of the paste in self- Compacting concrete(CC) Liane Ferreira Santos, Mônica Pinto Barbosa, Geraldo de Freitas Maciel, Flávio Moreira Salles.........................................................................................................Bcr-01-08

The rheological and mechanical behavior of the different Brazilian grouts Felipe Sakae Bertolucci, Mônica Pinto Barbosa, Geraldo de Freitas Maciel, Marcelo de Araújo..............................................................................................Bcr-02-08.

Roll waves in Hyperconcentrated flows with free surfaceF. O. Ferreira, G. F. Maciel, A. S. Vieira, L.O. B. Leite...................Bcr-04-08.......................

Mechanical properties of asphalt bindersLeni F. M. Leite, Luis Alberto H. Nascimento, Margareth C.Cravo.....Bcr-05-08.....

Rheology evaluation of mucoadhesive drug delivery systemsFlávia Chiva Carvalho Victor, Hugo Vitorino Sarmento, Mariana da Silva Barbi, Maria Palmira Daflon Gremião ...................................Bcr-06-08.......

Elasticity in petroleum pitchesAlessandra Maciel dos Santos, Luiz Depine de Castro, Carlos H. M. de Castro Dutra..(Bcr-07-08)

Wall slip during the flow of carbopol solutions through a parallel plete channelPaulo R. de Souza Mendes, Renata A. B. Pereira and Jonathan Pedron..........Bcr-08-08..............13

Liquid-liquid displacement flows in a hele-shaw cell including viscoplastic effectsPaulo R. de Souza Mendes, Priscilla R. Varges...............................................Bcr-09-08............

Numerical analysis by Brezzi's theorem for a regularized stabilized mixed fem formulation for viscoplastic fluidsCristiane O. Faria1 and j. karam F.............................................................................................Bcr-10-08

The flow of a sptt fluid over an oscillating flat plateF. T. Pinho, D. O. A. Cruz.............................Bcr-11-08......................................................10 Numerical solution of the ptt constitutive equation for three-dimensional free surface flowsMurilo F. Tomé, Gilcilene S. de Paulo.................Bcr-12-08..................................................9

Liquid-liquid displacement flows in an annular space including viscoplastic effectsPaulo R. de Souza Mendes, Jane Celnik, and Flávio H. Marchesini...................................(Bcr-13-08)

Rheological behavior of aqueous dispersion of heavy oilClenilson da Silva Sousa JuniorCheila Gonçalves Mothé.......................................(Bcr-14-08)

Numerical study of ceramic pastes extrusionR. B. O. Jardirm, M. S. Carvalho, M. F. Naccache , S. S. X. Chiaro.............................(Bcr-15-08)

Application of tensor decomposition theorems on dns data of viscoelastic drag reducing channel flow Roney L. Thompson, Laurent Thais and Gilmar Mompean.......................Bcr-16-08

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A strong criterion for microstructured liquids in which the microelement can be represented by a vectorCarlos R. A. dos Reis, Monica Cristina Matos, Roney L. Thompson...........Bcr-18-08

An orthotropic closure approximation for the fourth order moment of a strand vector and its application on partially extending strand convection modelsRoney L. Thompson...................................................................................(Bcr-19-08)

Particle sedimentation in a time dependent viscosity fluidRoni Abensur Gandelman, Raul Bastos, Gustavo Henrique Pinto, André Leibsohn Martins, Hellen Christina de Moura Guilherme.............................................................(Bcr-20-08)

Effect of poly(ethylene tereftalate) oligomers addition on asphalt rheologyFábio Lima da Silva, Marcos Lopes Dias...............................Bcr-21-08

Rheology of thin liquid films newtonian vs. non newtonian dynamicsDavid Barbero, Ulli Steiner .........................................................................Bcr-23-08

Effect of solid content, ph and deflocculant concentration viscosity of kaolin slurriesMárcio Nele Silvia ,Cristina Alves França,Carla Napoli Barbato....................Bcr-24-08.....

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