Wall Slippage · Rheology · Silicone Investigation of Wall Slippage … · 2018-06-19 · In an...

PRÜFEN UND MESSEN TESTING AND MEASURING

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Wall Slippage · Rheology · Silicone Rubber · Capillary Rheometer

Compared to organic rubber, silicone rubbers have a lower viscosity and a stronger structural viscosity. Further-more, silicone rubber tends to wall slip even at very low wall shear stresses, which can lead to a reduction in extru-date quality due to stick-slip, especially in extrusion at high throughputs. To characterize the wall slippage behavior of silicones, rheometric analyses are performed with a high-pressure capilla-ry rheometer to evaluate the pressure drop in the capillary. A rectangular slit capillary with a total of three equidis-tant pressure measurement positions along the flow path is used. The so-called critical shear stress is used as an evaluation criterion for wall-slippage. If it is exceeded, a non-linear pressure drop due to the wall-slippage can be detected.

Untersuchung zum Wand- gleiten von Silikonkautschuk im Hochdruck-Kapillarrheometer Wandgleiten · Rheologie · Silikonkaut-schuk · Kapillarrheometer

Im Vergleich zu organischen Kautschu-ken sind Siliconkautschuke niedrigvis-koser und weisen ein stärkeres struk-turviskoses Verhalten auf. Weiterhin neigt Siliconkautschuk bereits bei sehr geringeren Wandschubspannungen zu Wandgleiten was besonders in der Ext-rusion bei hohen Durchsätzen zu einer Minderung der Extrudatqualität durch stick-slip führen kann. Zur Charakteri-sierung des Wandgleitverhaltens von Siliconen werden rheometrische Analy-sen mit einem Hochdruck-Kapillarrheo-meter durchgeführt, um den Druckab-fall in der Kapillare zu bewerten. Ver-wendet wird eine rechteckige Schlitzka-pillardüse mit insgesamt drei äquidistanten Druckmesspositionen entlang des Fließwegs. Als Bewertungs-kriterium wird die sogenannte kritische Schubspannung herangezogen, bei de-ren Überschreitung ein nichtlinearer Druckabfall aufgrund des Wandgleitens erkennbar ist.

Figures and Tables:By a kind approval of the authors.

IntroductionWall slippage is a significant rheological phenomenon of some materials and is one of the greatest challenges when it comes to the extrusion of rubber, since the effect of wall slip will reduce the pressurization efficiencies of the extrud-er by reducing the shear rate near the wall and will also affect the stability of the extrusion process [1]. However, cur-rently in the processing of elastomeric materials, wall adhesion (in which the melt is always sticking to the wall and moves with the same velocity with the wall along the flow-path) is the prevalent approach in extrusion design due to its simplicity. In return, the consideration of wall slippage would lead to a more so-phisticated model of flow behavior [2]. Some of the major disadvantages of the assumption of no-slip boundary condi-tion are: the failure of true-shear rate calculation, while if wall slippage ap-pears, the required shear rate in the pro-cessing will be reduced [3]; and wall-slip will also reduce the throughput rate of the process [4]. In contrast, wall slip can also lead to an advantage, such as in re-ducing the energy requirement for the process [5]. Therefore, there is an urgent need to take this phenomenon into con-sideration, which should not be dis-counted in the analysis as it usually is.

Given the limitations of the wall ad-hesion assumption all along the flow path, it is therefore critical to describe the phenomenon of wall slippage. Only by investigating this complex flow anomaly, the rheological behavior of the material will be better analyzed. Conse-quently, one will be able to determine the suitable parameter for processing. Two models have been developed to il-lustrate the wall slippage behavior [6, 7]. The first model is Coulomb’s friction model that describes the wall slippage as a function of inadequate adhesion be-tween the wall and the fluid, in which the wall shear stress is a function of pres-sure. On the other hand, the thin slip layer model from Girard describes the

wall slippage as the presence of a thin slip layer between the wall and the fluid, where the wall shear stress is a function of the velocity. Bingham [8] reported that thin layer (between the wall and the main flow of the compound) is as a result of inadequate adhesion between the material and the shearing surface.

In illustrating the wall slip behavior, the term wall slippage is closely bonded by commonly named critical shear stress as the onset of wall slip. Several research-ers have studied this issue and showed that wall slippage is observed in rubber compound after the material exceeds the critical shear stress [4, 9, 10]. On the other hand, contradictory finding has been reported by Geiger [11]. With EPDM as the investigated material, it is claimed that wall-slippage is taking place before the critical shear stress, and wall-sticking is arising after the critical shear stress. Therefore, based on these contradictory results, this paper aims to call into ques-tion the slip behavior of silicone rubber compounds.

In an attempt to analyze the rheologi-cal anomaly and to determine the critical shear stress, one of the methods that is frequently adopted is the use of capillary rheometer. This instrument has been proved its ability to observe the wall slip

Investigation of Wall Slippage in Silicone Rubber Compound by means of High-pressure Capillary Rheometer

AuthorsChristian Hopmann, Michael Drach, Aachen, Germany, Michelle Limantara, Bangkok, Thailand

Corresponding AuthorMichael Drach, M.ScInstitut für KunststoffverarbeitungRWTH AachenSeffenter Weg 20152074 Aachen, GermanyE-Mail: [email protected]


92 KGK · 06 2018 www.kgk-rubberpoint.de

phenomenon in a rubber compound be-cause of its ability to reach high shear rates [12]. The wall slippage can be ob-served by examining pressure drop in-side the capillary, as it has been demon-strated as the indication of the change of condition from wall adhesion to wall slippage behavior [13]. In describing the wall slippage behavior, the Mooney method [14] has been utilized by several researchers [15, 16, 17] and is frequently used in determining the slip velocity, which is the difference between the ve-locity of the fluid and the velocity of the wall [18].

There is mounting evidence of wall slippage in elastomeric material [11, 12, 19], however, there is still an inconsider-able amount of researches that portray the behavior of silicone rubber com-pound, compared to the examinations of wall slippage in organic rubber com-pound. Therefore, this study will enhance the understanding of wall slippage be-havior in silicone rubber compound. Sili-cone rubber is selected to be the investi-gated material because of its growing importance and position in the industry, considering its excellent flexibility, ther-mal insulation, high resistance to chemi-cal influence, and stability at high tem-perature [20]. In order to achieve the de-sired results, high-pressure capillary rheometer (HCR) will be utilized in inves-tigating the silicone rubber compounds. The system is fully integrated with rec-tangular slit capillary.

Experimental Section

MaterialsSilicone rubber or silicone elastomers (scientific name: Polydimethylsiloxane) are inorganic synthetic elastomers made from cross-linked silicone-based poly-mers. They are derived from silica or quartz and have an inorganic main chain [21]. Solid silicone rubber is an elastomer with high molecular weight and rela-tively long polymer chains and referred as high-temperature-vulcanizing silicone rubber [22]. Compared to the organic rubber that has carbon to carbon back-bone, silicone rubber offers better resist-ance to UV and heat because of the ab-sence of carbon to carbon backbone in the main chain of this material. In this study, non-vulcanized solid silicone rub-ber is investigated and supplied by Wack-er-Chemie AG, Burghausen, Germany. The Mooney viscosity (ML(1+4)) is deter-mined at 25°C by a Mooney Viscometer

(MV2000) by Alpha Technologies GmbH, Heilbronn, Germany. The density of the material is determined with a pycnome-ter (AccuPyc 1330) from Micrometrics GmbH, Aachen, Germany. Further, heat capacity of the material is also deter-mined with DSC Q1000 from TA Instru-ments Inc, New Castle, USA and is carried out for two repetitions. The materials are prepared with maximum weight of 10 grams at 25°C. The following table sum-marizes the material data which are ob-tained from the apparatuses.

High-pressure capillary rheometer (HCR) test A high-pressure capillary rheometer (Rheograph 2002), manufactured by Göttfert Werkstoff-Prüfmaschinen Gm-bH, Buchen, Germany, is utilized in the experiments in order to generate a pres-sure-driven flow. The instrument is

mounted with a die with rectangular slit cross section (5 mm2). A piston with a diameter of 15 mm is used to push the test silicone rubber compound through the capillary and to generate different shear rates with various piston velocities. Three pressure transducers are mounted along the slit cross section in order to measure the pressure level in the capil-lary for determining the viscosity and to observe the wall slippage. The experi-ments are carried out at temperatures of 25°C and 45°C. The width, height, and length of the rectangular capillary are 10 mm, 0.5 mm, and 100 mm respec-tively. The material is observed under shear rates ranging from 5 s-1 to 260 s-1. The experiments are repeated three times to ensure the reproducibility of the data obtained and the standard devia-tion is being monitored. The experimen-tal setup in HCR is illustrated in Figure 1.

Fig. 1: Experimental setup of high-pressure capillary rheometer test

1

Fig. 2: Apparent flow curve of silicone rubber at 25°C and 45°C

2

1 Material property of silicone rubber compoundHardness [Shore A]

ML (1+4) 25°C [MU]

Density [g/cm3]

Specific Heat Capacity [J/g/°C]

60 40.15 1.174 1.315



Results and Discussion

Pseudoplastic flow behavior of silicone rubber compoundFrom the raw data obtained from the high-pressure capillary rheometer, the apparent flow curve can be determined. Apparent flow curve is used to portray the rheological properties of the materi-al and made without any capillary flow correction. With the use of volume flow rate, V·, the apparent shear rates can be determined by

�̇�𝛾𝑎𝑎𝑎𝑎𝑎𝑎 = 6 ∙ �̇�𝑉𝐵𝐵 ∙ 𝐻𝐻2 (1)

where B is the width and H is the height of the slit capillary. Consequently, from the pressure difference of each pressure transducers (Δp), cross sectional area (A) and the area of the wall of capillary rheometer (Aw), the wall shear stress can be determined by

𝜏𝜏𝑤𝑤 = Δp ∙ 𝐴𝐴𝐴𝐴𝑤𝑤

(2) The apparent viscosity is determined based on the pressure drop between the measurement point of pressure trans-ducer 1 and 3. In Figure 2, it is shown that the apparent flow curves at the two dif-ferent temperatures of the material are

both showing a pseudoplastic behavior, where it experiences a lower viscosity with increasing shear rates. Figure 2 also demonstrates that the temperature dif-ference of 20°C has not a considerable effect on the flow behavior of the mate-rial and the line of some points are in contact with one another, while they still have the identical viscosity value. How-ever, the flow curve of the material ob-served under 45°C shows that the viscos-ity at higher temperature is little lower.

From the apparent flow curve, the re-lationship between viscosity and shear rate, plotted on log-log coordinates, can be estimated with Ostwald de Waele equation and the flow behaviour index (n) that characterizes the shear-thinning behavior can be calculated. The flow be-havior index and the consistency factor (K) are determined from the point of shear rate, where wall adhesion is expec-ted to occur between the capillary wall and the melt, which is predicted on the points before the critical wall shear

stress. It should be noted that the flow behavior index will determine the pseu-doplastic behavior under no-slip bound-ary condition. Table 2 summarizes the data on the flow behavior index at both temperatures. In general, the flow beha-vior index shows that the lower its value, the higher the shear thinning experien-ces by the material. The results in Table 2 obtained from the mathematical mode-ling, with Ostwald de Waele equation written as:

𝜏𝜏𝑤𝑤 = 𝐾𝐾 ∙ �̇�𝛾𝑛𝑛 (3)

and the relationship of the apparent vis-cosity and shear rate can be written as:

𝜂𝜂 = 𝐾𝐾 ∙ (�̇�𝛾)𝑛𝑛−1 (4)

Determination of true shear rate of wall-sticking areaThe application of Weissenberg-Rabi-nowitsch correction for non-Newtonian fluid flow must be implemented to por-tray the true viscosity function of the material at wall-sticking area [11]. This correction should be performed since unlike the flow of Newtonian fluid which has the parabolic velocity profile, non-Newtonian fluid will encounter the non-parabolic velocity profile. Without this correction, error around 10-20% in viscosity will prevail in the calculation of shear rate [23] and shear rate will be underestimated. In determining the correction, a plot of 𝑙𝑙𝑛𝑛�̇�𝛾𝑎𝑎𝑎𝑎𝑎𝑎 and 𝑙𝑙𝑛𝑛𝜏𝜏𝑤𝑤 needed in determining the slope for the correction. This correction is only per-formed for the points that experience the wall-sticking behavior. Figure 3 shows the true flow curve of wall stick-ing area. It can be seen that after the correction, the true shear rate that is applied to the material will shift to higher value, compared to apparent shear rate. The equation for this correc-tion is as below [11]:

�̇�𝛾𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = �23

+13∙𝑑𝑑𝑙𝑙𝑛𝑛�̇�𝛾𝑎𝑎𝑎𝑎𝑎𝑎𝑑𝑑𝑙𝑙𝑛𝑛𝜏𝜏𝑤𝑤

� ∙ �̇�𝛾𝑎𝑎𝑎𝑎𝑎𝑎 (5)

Identification of Wall Slippage The first step of the identification of wall slip behavior can be performed with the raw data of pressure over measurement time, acquired directly from the high-pressure capillary rheom-eter, as can be seen from Figure 4. It can be observed that pressure fluctuations is occurring from the start of the meas-urement, which is from the highest ap-

Fig. 3a: Flow curves of wall-sticking area at 25°CFig. 3b: Flow curves of wall-sticking area at 45°C

3

2 Flow behavior index of silicone rubber compoundPosition along pressure transducer

Flow Behaviour Index [-]

25°C 45°C1 - 3 0.145 0.116

(a)

(b)



plied shear rate, until 330 seconds (γ· = 125 1/s). This point might be related to the critical point, where the onset of wall slip happens. This test also reveals that after this critical point the pressure fluctuation is no longer observed, which is in lower shear rate area. This pressure fluctuation might be caused by extru-date distortion [24] and may also be-come the signal of the onset of wall slip after the point of γ· = 125 1/s, as demon-strated in Figure 5.

Regarding the results in Figure 4, the existence of a critical point can be obser-ved, which might indicate the onset of wall slip. In order to justify this point, the shear stress of the material is plotted as a function of apparent shear rate as pre-sented in Figure 6. It is apparent from Fi-gure 6, that different shear rate measu-rement points will lead to different flow behavior in high pressure capillary rheo-meter experiments. It can be examined that the material is always having an in-crease in shear stress with increasing shear rate only until a certain level of shear stress, and after this peak or criti-cal point the material is not experiencing an increase in shear stress with rising shear rate. At 25°C the critical point lies at 0.13 MPa (γ· = 125 1/s). At 45 °C, the critical point lies at 0.11 MPa (γ· = 150 1/s). It is remarkable to observe, that af-ter this critical point, anomalies are ob-served, in which the value of shear stress is keep declining although there is a gro-wing value of shear rate. This anomalous flow behavior may indicate that the ma-terial is experiencing the plug flow at high shear rate region and should be as-sociated with an increase in wall slip ve-locity, where it cannot be neglected any-more. Lately, it is reported that at wall-sticking to wall-slippage change cross section, an increase of shear stress will be observed before the flow undergoes a complete slip condition, as it is the case in Figure 5 [13]. Consequently, if both re-sults of Figure 5 and Figure 6 are analy-zed, it can be seen that wall slip pheno-menon might be the answer or closely related with melt instability of the mate-rial. In addition to illustrate the flow an-omaly clearly, the shear stress under the assumption of pseudoplastic behavior of the material (under no-slip boundary condition) is also shown in comparison to the experimental data. The curve of the pseudoplastic behavior was determi-ned based on the power law model, whereby the coefficients K and n were determined from the flow curves of the

4 Fig. 4: Pressure over time diagram of all pressure transducers, at 25°C

5

Fig. 5: Different behavior of melt instability with increasing shear rate at 25°C

Fig. 6a: Wall slip identification by varying shear rate at 25°CFig. 6b: Wall slip identification by varying shear rate at 45°C

6(a)

(b)



HCR. The consistency factor K has been verified by parallel plate rheometer tests. The determined values for K are in the same order of magnitude for both measuring methods.

In Figure 6, the effect of temperature on the critical point can also be noticed. It is shown that with increasing tempe-rature, the value of critical wall shear stress will also shifted to lower values. On the other hand, at the point of shear rate where critical shear stress appears, the shear rate will be shifted to higher value. Therefore, the range of wall-sti-cking area will be broader, as can be seen from Figure 6b. With rising temperature, there will be a reduction in viscosity be-cause the molecules of the material are easier to move because of an increase in thermal energy. The findings from this study suggest that the critical shear stress for this silicone rubber compound with hardness of 60 shore A is around 0.13 MPa at room temperature. In addi-tion, as has been mentioned before, ext-rudate distortion is one of the substanti-al indications of the flow transformation from wall adhesion to wall slippage be-havior, as can be seen from figure 5. This result also reveals that with rising value of shear rate, the flow instability is beco-ming more serious. Wall slip is believed as the participant of the melt fracture phenomenon, since it appears at the corresponding value or lower critical shear stress as does the shark-skin melt fracture appear [25]. Determination of slip velocity and slip ratio of wall-slipping areaAs has been mentioned before, the iden-tification of wall slip is closely related to the identification of wall slip velocity. The higher the value of this velocity means the stronger the wall slippage is. Respectively, if the value of wall slip ve-locity is zero means wall slip does not exist [12]. The determination of wall slip velocity in silicone rubber compounds should be made. Since the experiment performed in this study reveals that the material experiences wall slippage after critical shear stress. With the help help of modified Mooney correction for wall slip-page [11, 12, 14, 19], the calculation of the velocity of wall slip will able to be performed. The determination of wall slip velocity can only be performed after the determination of wall sticking and wall slipping area. The calculation of wall slip velocity is starting from the formula of the total volume flow rate, as shown

below:

�̇�𝑉𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑙𝑙 = �̇�𝑉𝑠𝑠𝑙𝑙𝑠𝑠𝑎𝑎 + �̇�𝑉𝑠𝑠ℎ𝑡𝑡𝑎𝑎𝑡𝑡 . (6)

The wall slip velocity is derived from the slip volume flow rate, as below:

�̇�𝑉𝑠𝑠𝑙𝑙𝑠𝑠𝑎𝑎 = 𝐵𝐵 ∙ 𝐻𝐻 ∙ 𝑣𝑣𝑠𝑠𝑙𝑙𝑠𝑠𝑎𝑎 (7)

and the shear volume flow rate is calcu-lated from [23,25]:

�̇�𝑉𝑠𝑠ℎ𝑡𝑡𝑎𝑎𝑡𝑡 = 𝑛𝑛 ∙ 𝐵𝐵 ∙ 𝐻𝐻2

2 ∙ (1 + 2𝑛𝑛)∙ (𝜏𝜏𝐾𝐾

)1𝑛𝑛 (8)

From all of the equations above, the slip velocity that is experienced by the mate-rial can be determined from:

𝑣𝑣𝑠𝑠𝑙𝑙𝑠𝑠𝑎𝑎 = �̇�𝑉

𝐵𝐵 ∙ 𝐻𝐻−

𝑛𝑛 ∙ 𝐻𝐻2 ∙ (1 + 2 ∙ 𝑛𝑛) ∙ (

𝜏𝜏𝐾𝐾

)1𝑛𝑛 (9)

It is reported that equation 9 is the value of the minimum slip velocity undergoes by the material, not the absolute wall slip velocity [26]. In Figure 7, the effect of applied shear rate to the wall slip veloci-ty can be pointed out. After the wall slip velocity is established, slip length can al-

so be calculated. Slip length is the amount of the fluid that is slipped and can be calculated with equation 10 [27]. In Figure 8, it is shown that the slip length of the material is ranging around, which is considered as a huge slip [27]. From Figure 7, it can be seen that with increasing shear rate, the slip velocity of the material will also be higher. Conse-quently, the value of slip length will also be higher. This phenomenon shows that with higher shear rate, the material will experience lower drag flow, when it is compared to the bulk material [28].

𝑏𝑏 = 𝑣𝑣 ∙ 𝜂𝜂𝜏𝜏𝑤𝑤

(10)

ConclusionsIn this study, the rheological behavior of silicone rubber compound as non-New-tonian fluids under wall slippage has been analyzed by means of high-pres-sure capillary rheometer. The critical shear stress, which is observed for the material is found to be around 0.13 MPa at room temperature, determined by the

Fig. 7: Wall slip velocity as a function of shear rate at 25 °C and 45 °C

7

Fig. 8: Slip length as a function of shear rate at 25°C and 45°C

8



sudden onset of pressure drop after this value, which indicates the change in boundary condition from wall-sticking to wall-slipping. With this value the region of wall-sticking and wall-slipping can be classified, where wall-sticking region is below the critical shear stress and wall-slipping region is above this value. Wall slip velocity and slip length has also been estimated, which value are increasing with higher shear rate that is applied to the material. From the value of slip length, it can be concluded that the sili-cone rubber compound under investiga-tion is experiencing huge slip with the value of slip length ranging from 78-102 µm.

AcknowledgementThe research project ZF4018906EB6 of the Institute of Plastics Processing and TSM GmbH is sponsored as part of the “Zentrales Innovationsprogramm Mittel-stand ZIM” by the “Deutsches Bun-desministerium für Wirtschaft und Ener-gie (BMWi)” due to an enactment of the “Deutscher Bundestag”. We would also like to thank the following companies for their support in the course of the project and the provision of materials and pilot plants:

BIW Isolierstoffe GmbH, Ennepetal, Brabender GmbH & Co, KG, Duisburg, Harburg-Freudenberger Maschinenbau GmbH, Freudenberg, Momentive Perfor-mance Material, Leverkusen, Wacker Chemie AG, München. We would like to extend our thanks to all organizations mentioned.

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