Mechanical Techniques - Particle Size Separation

Figure 1 Main factors affecting particle behaviour in a medium.

Sullivan JJ and Wekell MM (1987) In: Kramer DE andListon J (eds) Seafood Quality Determination, p. 357.New York: Elsevier, North Holland.

Thibault P, Pleasance S and Laycock MV (1991) Analysisof paralytic shellRsh poisons by capillary electro-phoresis. Journal of Chromatography A 542:483}501.

Wright JLC, Boyd RK, De Freitas ASW et al. (1989) Identi-Rcation of domoic acid, a neuroexcitatory amino acid, intoxic mussels from eastern Prince Edward Island. Cana-dian Journal of Chemistry 67: 481}490.

Zhao JY, Thibault P and Quilliam MA (1997) Analysis ofdomoic acid and isomers in seafood by capillary elec-trophoresis. Electrophoresis 18: 268}276.

MECHANICAL TECHNIQUES: PARTICLESIZE SEPARATION

A. I. A. Salama, Natural Resources Canada,Devon, Alberta, Canada

Copyright^ 1999 Minister of Natural Resources,Canada

Introduction

Particles of many kinds and various sizes have playedan important role in man’s interaction with his phys-ical environment. They abound in the soil and earthbelow; they are also present in water, air, chemicalproducts, and many other sources. If particles werespherical or cubical, it would be easy to characterizethem. Unfortunately, most of the particles present inour environment are of irregular size and shape.Therefore, it is desirable to try to develop methodolo-gies and techniques to characterize particles of irregu-lar size and shape, and this is the main objective ofparticle size analysis. Moreover, particle size analysisis important in studying particle behaviour in amedium as in many analytical sciences and industrialapplications.

Particle size analysis in physical, chemical, andbiological processes involves many concepts and tech-niques; however, this article focuses on the methods ofparticle size analysis utilizing mechanical techniques.

This article will Rrst introduce some basic principlesused in particle size analysis. This will be followed bya summary of the applicable particle size ranges for thedifferent methods and the size ranges of mostcommon particles found in industrial, chemical, envir-onmental, and clinical applications. The most com-mon mechanical techniques and methods used inparticle size analysis will be brieSy presented.

Particle Properties

Particle size analysis plays an important role in manyanalytical sciences and industrial applications. Toassist in developing useful methodologies and tech-

niques it is essential to identify the main factors thatcontrol the behaviour of particles in a medium. Suchfactors include particle density, shape, size, size distri-bution, concentration, and surface characteristics,and the carrier medium dynamics (Figure 1). Thisarticle focuses on particle size analysis using mechan-ical techniques in relation to clinical, industrial, andenvironmental applications: therefore, the particlesunder consideration could be solid or liquid and themedium could be liquid or gas. In aerosol systems themedium is gas (air).

Density

Particles originating from a solid will have the samedensity as that of the parent material. However, if thematerial undergoes hydration or surface oxidizationor if it agglomerates in clusters, its speciRc gravity willchange. The particle density plays an important rolein the separation of solids as in centrifugal and gravi-tational sedimentation, for example.

Particle Shape

Shape factors The method of formation inSuencesthe resultant particle shape. In comminution, attritionor disintegration, the generated particle resembles theparent material. On the other hand, if the method offormation is condensation from vapour, the smallestunitary particle may be spherical or cubical. In manycases condensation is followed immediately by solidi-

III / MECHANICAL TECHNIQUES: PARTICLE SIZE SEPARATION 3277

Rcation and formation of chain-like aggregate(e.g. iron oxide fumes, carbon black).

Based on experimental data it has been found thatfor a collection of groups of particles having an aver-age diameter Dpi for group i, the total surface area canbe expressed as:

Ap"��(�niD

2pi) [1]

where ��

is deRned as the surface shape factor. Thetotal volume can be expressed as:

Vp"�v(�niD3pi) [2]

where �v is deRned as the volume shape factor. Thesurface and volume shape factors may be related toa combined shape factor kp as:

kp"�s

�v

[3]

In the case of spherical or cubical particles it can beshown that the shape factor is 6. For irregularparticles, values vary from 6 to 10. Some other rela-tionships can be obtained by using eqns [1]}[3]:

Av"Ap

Vp

" kp

DHp[4]

DHp "�niD3pi

�niD2pi

[5]

Am" kp

�pDHp[6]

where Av"speciRc surface area (surface area per unitvolume): DHp "speciRc surface diameter: Am"sur-face area per unit mass: �p"density of the particlematerial. The surface and volume information areused in estimating the equivalent spherical particlediameter which is used in studying particle behaviourin a medium.

Fractal geometry Mandelbrot introduced the basicconcepts and theories of a new type of geometrycalled fractal geometry, in order to describe ruggedstructures. The main idea put forward by Mandelbrotis that the boundary of a rugged system can be de-scribed in its embedding space by a fractal dimensionwhich describes its space Rlling effect. In the caseof a fractal surface the estimate of surface area (A�)tends to increase without limit as the step size (resolu-tion) � of an elemental square decreases. This can beexpressed as:

A�"ka��(��2) [7]

where ka is a constant and the fractal dimension � isgreater than 2. Hence a plot of ln(A�) versus ln(�) willhave a slope of [!(�!2)], where ‘ln’ designatesa natural logarithm.

Kaye applied fractal geometry in his studies of theproRles of carbon black agglomerates. In subsequentstudies he demonstrated the usefulness of fractal ge-ometry in studying boundary and mass fractal dimen-sions of aerosol systems, fractal structures of Rneparticle systems, fragmentation, description of por-ous bodies and gas adsorption.

Surface Characteristics and InterfacialPhenomena

The surface characteristics of small particles includesurface area, rate of evaporation and condensation,electrostatic charge, adsorption, adhesion and lightscatter. In certain circumstances, changes in the envi-ronment of a particle during sampling and particlesize analysis may change its size or state of aggrega-tion or its surface characteristics. Such changes mustbe considered in the selection of a suitable samplingdevice or method for particle size analysis.

Surface area One of the important characteristics ofsmall particles is the rapid increase in exposed surfacearea per unit mass as size decreases, which leads toincreased chemical reaction rate. Fine powders oforganic and inorganic oxidable materials (such ascoal, iron, Sour, sugar, and starch) burn vigorously orexplode violently when in the form of an aerosol.Moreover, an increase in surface area increases thetoxicity of some granular materials.

Evaporation and condensation Evaporation andcondensation are diffusion mass transfer pro-cesses which proceed at rates proportional to thesurface area exposed. The temperature and partialpressure in the vicinity of the surface control the timerequired for small particles (e.g. water) to evaporateinto still air. The evaporation time is given by:

�"RT8M

�pD2p

D�p

[8]

where �"evaporation time (s); �p"density ofparticle material (kg m�3); Dp"particle diameter(m); D"diffusion coefRcient of vapourfrom particle (m2 s�1); �p"difference betweenthe particle pressure at the particle surface and inthe surrounding Suid (N m�2); R"gas constant(8.3144 J mol�1 K�1); T"absolute temperature (K);M"molecular weight of evaporating particulatematerial. Finer particles can act as centres for

3278 III / MECHANICAL TECHNIQUES: PARTICLE SIZE SEPARATION

Figure 2 Mechanisms producing natural charge on particles.

Figure 3 Processes affecting particle motion in a medium.

condensation of moisture, leading to an increase intheir size.

Electrostatic charge Electrostatic charge representsan excess or deRciency of electrons on the particlesurface. This charge may be assumed to reside on theparticle surface in an absorbed gas or moisture Rlm.Mechanisms which produce natural charge on par-ticle surfaces are shown in Figure 2. The electrostaticcharge generated on a particle is proportional to theparticle surface area, which is the principle used in thedesign of electrostatic classiRers and precipitators.Furthermore, the presence of electrostatic charge onparticle surfaces controls the behaviour of particles inan electric Reld (see II/PARTICLE SIZE SEPAR-ATION/Electrostatic Precipitation).

Scattering properties Scattering of radiation arisesfrom inhomogeneities, such as dispersed dust orwater drops, in the Suid medium. Scattering is oftenaccompanied by absorption, and both scattering andabsorption remove energy from the incident beams.The quantitative response of the intensity of transmit-ted and/or scattered beams can be used to character-ize the size of a particle.

Kinetic Behaviour of Particles

The equivalent spherical particle diameter of an ag-gregate of irregularly-shaped particles can be deter-mined by studying the inertial motion of particles ina medium. Such inertial motion can be found in manyapplications such as pulmonary deposition, design ofindustrial ventilation, particle collectors, and electro-static precipitation. The various processes that affectparticle motion in a Reld are shown in Figure 3.

Medium Resistance

For a small spherical particle moving in a medium atlow velocities (i.e. laminar Sow), the drag (mediumresistance) force acting on the particle is given byStokes’ Law as:

FR"3��mDpVpm"CD

�mAV2pm

2[9]

where FR"medium resistance (N); Dp"particlediameter (m); �m"medium density (kg m�3); �m"medium viscosity (kg m�1 s�1); Vpm"relative velo-city between particle and medium (m s�1); A"pro-jected area of particle normal to its motion (m2).

It is useful to relate the magnitudes of the inertialand viscous forces in the form of a dimensionlessReynolds’ Number as:

Rep"�mDpVpm

�m

[10]

The relationship between the drag coefRcientCD and the Reynolds’ Number can be found in anySuid mechanics textbook. However, for spheres withRep(1,CD"24/Rep.

In Rnite containers a particle experiences an in-crease in the drag force due to two effects. Firstthe Suid streamlines around the particle impinge onthe container walls and are reSected back causingincreased drag on the particle. The second effectoccurs because the Suid is stationary at a Rnite dis-tance from the particle, and there is a distortion of theSow pattern which reacts back on the particle.Taking into consideration these two effects, thedrag force may be modiRed as:

FR"3��mDpVpm �1#kDp

L � [11]

where L represents the distance from centre of par-ticle to the container walls and k"0.563 for a singlewall or container bottom and k"2.104 for a cylin-drical container.

Particle Motion

Particle motion in a gravitational/drag Veld The lin-ear motion of a particle in a direction X relative totime t and under the inSuence of the drag, gravi-tational, and buoyancy forces is governed by:

�6�pD

3p�

d2Xdt2 �"

�6(�p!�m)D3

pg!3��mDp

dXdt

[12]


where g denotes gravitational acceleration. If the par-ticle starts from zero velocity it will accelerate until itreaches a terminal velocity given by:

�dXdt �t��

"Vgt"�D2

p(�p!�m)18�m � ) g [13]

from which the particle diameter can be expressed as:

Dp"�18�m

(�p!�m)g) Vgt�

1/2

[14]

Note that eqns [12] to [14] are applicable for Rep(1.For a particle settling in air, it is usual to neglect the

buoyancy correction, since �p is of the order of unity,the air density is of the order of 10�3 g cm�3, andviscosity of ambient air is 1.8�10�5 kg m�1 s�1.Equation [13] reduces to:

Vgt"3.03�104 �pD2p [15]

where Vgt, �p, and Dp are expressed in m s�1, kg m�3,and m, respectively.

Particles with diameters less than or close to themean free path of the Suid molecules begin to slipbetween molecules and settle at a higher velocity thanthat predicted by eqn [13] for settling velocity. Cun-ningham considered this so-called slip effect andintroduced a correction term to the terminal settlingvelocity as:

Vgtc"CcVgt [16]

Cc"�1#2��Dp � [17]

where Cc denotes the Cunningham slip correctionfactor, � is the mean free path of medium molecules,and � is a constant of approximately one.

Particle motion in a rotational (centrifugal) Veld Ina centrifugal Reld the radial motion of a particle at adistance R from the centre of rotation is governed by:

�6�pD

3p�

d2Rdt2 �"�

6(�p!�m)D3

p2R!3��mDp

dRdt

[18]

where is the angular velocity of the particle. Assum-ing that the particle movement outward is resisted byviscous drag, Stokes’ law provides a reasonable ap-proximation for the drag. Therefore, the terminalradial velocity at equilibrium is given by:

�dRdt �t��

"Vrt"�D2

p(�p!�m)18�m � )2R [19]

which is equivalent to eqn [13].

To evaluate the performance of a centrifugal separ-ation process, a separation factor ‘SF’, deRned as theratio of centrifugal acceleration to gravitationalacceleration:

SF or g-force"2Rg

[20]

is used. For dust-collecting cyclones (particles'100 �m), SF"200, while conventional centri-fuges used in precipitation of submicron particles andlarge molecules in liquid suspension have SF"5000.See II/PARTICLE SIZE SEPARATION/Hydrocyc-lones for Particle Size Separation.

Particle motion in an electrostatic Veld When par-ticles larger than 1 �m are passed through a coronadischarge as the result of bombardment charging,they acquire charges from electrons and adsorbed gasions proportional to the surface area of the particle.The saturation charge acquired is given by:

Qpb"ne"�01�D2pE [21]

�" 32

2#21[22]

where Qpb"saturation bombardment charge ac-quired (C); n"number of electron charges acquired;e"electron charge (1.6022�10�19 C); 0"permit-tivity of vacuum (8.8542�10�12 F m�1); 1"rela-tive permittivity of medium (gas); 2"relativepermittivity of particle material; E"external electricReld strength (V m�1). For particles less than 0.2 �m,diffusion charging predominates and the chargesacquired at time t are given approximately by:

Qpb"ne"DpkT2e

ln �1#�DpViN0e2

2kTt� [23]

where Qpd"diffusion charge acquired (C);k"Boltzmann constant (1.3807�10�23 J K�1);T"absolute temperature (K); N0"ion density (ionsm�3); Vi"ion velocity (root mean square, m s�1).Based on the acquired charge on the particle andassuming that air resistance is approximated byStokes’ Law, the particle terminal velocity in an elec-tric Reld is given by:

Vet"Cc�EQp

3��mDp� [24]

where Cc"Cunningham slip correction factor;�m"medium (gas) viscosity; Qp"acquired (bom-bardment or diffusion) charge on the particle.


Figure 4 Common methods of particle size analysis. HAverage particle diameter but not size distribution. HHSize distribution may beobtained by special calibration.

Particle motion in a thermal gradient Veld It hasbeen observed that particles in suspension move fromhotter to colder regions. Later it has been shown thatin a thermal gradient Reld and at atmospheric pres-sure, the thermal force acting on a particle is given by:

Ft"(!9�)�Dp

2 � ��2

m

�mT� �2#�p

�m��1

�dTdx�

[25]

where �p"thermal conductivity of the particle ma-terial (J m�1 s�1 K�1); �m"thermal conductivity ofthe air (J m�1 s�1 K�1); T"absolute temperature(K); dT/dx"temperature gradient in the air (K m�1).The negative sign in the equation indicates that theforce is in the direction of negative thermal gradient.By setting the thermal force equal to the resistiveforce of the medium, the terminal velocity of a par-ticle is given as:

Vtt"(!1.5) �Cc�m

�mT� �2#�p

�m��1

�dTdx� [26]

The particle velocity and the Sow velocity and geo-metrical conRguration are used in the design of ther-mal precipitators.

Common Methods of Particle SizeAnalysis and Particle Size Ranges

To assist in covering the scope of the differenttechniques used in particle size analysis, an attemptwas made to survey the current literature on particle

size analysis techniques. The results of this investiga-tion are summarized in Figure 4. It should be empha-sized that this summary is not exhaustive. There areother sophisticated techniques which are outside thescope of this article. Of more importance is the identi-Rcation of the size ranges of most common particlesfound in industrial, environmental, chemical andclinical applications (Figure 5). From an industrialpoint of view, the different types of gas partic-ulate collecting equipment are summarized inFigure 6. Some basic deRnitions of particle size rangesof gas and atmospheric dispersoids and soil are in-cluded in Figure 7.

Mechanical Techniques for ParticleSize Analysis

Based on the information given in Figures 4}7, it canbe seen that the most common mechanical techniquesfor particle size analysis relevant to analyticalsciences and industrial applications are: sieving, sedi-mentation (gravitational or centrifugal), elutriation,electrostatic precipitation, thermal precipitation, hy-drodynamic chromatography and impaction. Eachtechnique will be brieSy presented; the details of eachtechnique can be found in the references listed in thebibliography.

Sieving

Sieving is an obvious and most widely used techniquefor particle size analysis. The particles are classiRedbased on their size, independent of any other particlecharacteristics such as density and surface properties.


Figure 5 Typical particles and gas dispersoids.

Figure 6 Different types of gas particulates collecting equipment (�, diameter).

Micromesh sieves are used to classify particles of sizerange 5}20 �m, while particles of size range20}125 �m are classiRed in the standard woven wiresieves. Coarse particles ('125 �m) are classiRed in

punched plate sieves. Punched plate sieves are com-monly used in industrial applications where the open-ings are circular or rectangular; the sieves can takedifferent conRgurations.


Figure 7 Some size range definitions.

Table 1 International sieve standards

Country Standard Sieve type

Great Britain BS 410 Woven wireUSA ASTM E11 Woven wire

ASTM E161-607 Micromesh(electroformed)

Germany DIN 4188 Woven wireDIN 4187 Perforated plate

France AFNOR NFX 11-501 Woven wireInternational ISO R565 1972(E) Woven wire

Perforated plate

Table 2 Sedimentation methods and techniques

Incremental methods Cumulative methods

Solids concentration variation Sedimentation rateLine start Line startHomogeneous suspension Homogeneous suspension

Suspension density variationList startHomogeneous suspension

The sieving test is conducted using up to 11 sievesstacked with progressively larger aperture openingstowards the top, and placing the powder on the topsieve. A closed pan (receiver) is placed at the bottom.There are several schemes for shaking the sieves bymechanical or ultrasonic means. The residues in eachsieve are recorded and expressed in percentage ascumulative values against the nominal sieve aperturevalues.

The common methods for Rne sieving are machine,wet, hand and air-jet sieving. Wet-sieving is recom-mended for material originally suspended in a liquidand is necessary for powders which form aggregateswhen dry-sieved. In such tests the stack of sieves isRlled with liquid and the sample is fed to the top sieve.Sieving is accomplished by rinsing, vibration, recip-rocating action, vacuum, ultrasonication or a combi-nation of these.

Table 1 presents the different internationalsieve standards and the corresponding sieve types.There are several sieve aperture progression ratioscommonly available depending on the differentinternational standards. In the USA, a progressionratio of 21/2 is used. This ratio corresponds to success-ive particle groups of 2 : 1 particle surface ratio. Theprogression rate of 21/3 (100.1) which has beenadopted by the French corresponds to successive par-ticle groups of 2 : 1 particle volume ratio. Theprogression ratios of 100.1 and 100.05 are recommen-ded for narrow size distributions.

The probability of a particle passing through sieveapertures depends on the particles size distribution,the number of particles on the sieve (sieve loading),the method of sieve shaking, the dimension and shapeof the particle, and the ratio of open area of sieve tototal area. In addition, the sieving operation can beaffected by the friability and cohesiveness of thepowder.

Sedimentation

Sedimentation of Rne powders in a suspension is animportant tool in the determination of particle sizedistribution. Table 2 presents a classiRcation of themethods and techniques used in sedimentation(gravitational or centrifugal). To conduct particle sizeanalysis using sedimentation, the suspension can beprepared using the line start (two-layer) or the homo-geneous suspension techniques. In the two-layertechnique, the powder is introduced at the top ofa column of clear liquid. In the homogeneous suspen-sion technique, the powder is uniformly dispersed inthe liquid. As the particles start to settle the change insolids concentration at a particular Rxed height withtime or the sedimentation time rate is measured. Thesolids concentration or density measurements is usedin the incremental methods, while the settling ratemeasurement is used in the cumulative methods. In-cremental methods may be divided as Rxed time andRxed depth methods, the latter being more popular,although a combination is sometimes used.

A powder is made up of three types of particles:primary particles, aggregates and agglomerates. The


Figure 8 Main gravitational sedimentation techniques.

primary particles are crystalline or organic structuresbound together by molecular bonding, while theaggregates are primary particles tightly bound to-gether at their point of contact by atomic or molecu-lar bonding. The force required to break these bondsis considerable. In case of agglomerates, the primaryparticles are loosely bound together with weak vander Waals forces. It is often necessary to disperse thepowder in a liquid prior to analysis. Dispersion isaffected by the use of wetting agents which breakdown the agglomerates to their constituent parts.This process is facilitated by mechanical or ultrasonicagitation.

Gravitational sedimentation In gravitational sedi-mentation there are four main techniques: volumesample, mass sample, manometry and sedimentationvessel-wall pressure sensing as shown schematicallyin Figure 8.

Incremental methods Based on the results of motionof a particle in a gravitational/drag Reld, it can beshown that the solids concentration of settling sus-pension at depth h can be related to the cumulativeundersize mass distribution as:

C(h, t)C(h, 0)

"�DtDmin f(D) dD

�DmaxDmin f(D) dD

"� [27]

Dt"�18�m

(�p!�m)g)ht�

1/2

[28]

where dm(D)"f(D)dD represents the mass fractionhaving particle size between D and D#dD. In eqns[27] and [28], it is assumed that the volume of par-ticles (powder) in suspension is very small comparedwith the total volume of suspension. By plotting100� against the free-falling particle diameter Dt theresulting curve shows the cumulative undersize per-centage curve by mass.

Similarly, it can be shown that:

C(h, t)C(h, 0)

"�(h, t)!�m

�(h, 0)!�m

"� [29]

where �(h, 0) and �(h, t) are the suspension densityat a height h at t"0 and t"t, respectively. Byplotting 100� against Dt, the resulting curve showsthe cumulative undersize percentage size curve.

The pipette method In this method, the changes inconcentration occurring within a settling suspensionare determined by drawing off deRnite volumesat a set of discrete intervals of time by means of apipette. The solids concentration in the suspension isrequired to be between 0.2 and 1.0 vol%. If the con-centration exceeds 1% the hindered settling adverselyaffects the results of the analysis. Initially thepowder is made into a paste; this is followed by slowaddition of the dispersing liquid, using a spatula plusmixing, to form a slurry. Further dispersion may becarried out in an ultrasonic bath. The suspension iswashed into a sedimentation vessel. The analysisstarts with violent agitation of the vessel avoiding theuse of a stirrer. It is recommended that the containerbe continually inverted by hand for 1 min. Since ini-tially the particles are not at rest, it is advisable towait 1 min before withdrawing samples. The use ofa time scale progression of 2 : 1 which producesa 21/2 particle size progression is recommended. Thecollected samples are prepared to determine the solidsconcentration for particle size cumulative massdetermination.

Hydrometers and divers The variation in density ofsettling suspension may be monitored with hydro-meters, a method used widely in the cement industry.The method starts with a fully dispersed suspension andthe densities at known depths are recorded as the solidphase settles out. The hydrometer technique is useful forquality control but not as an absolute method.

Divers are an extension of the hydrometer tech-nique. They act as miniature hydrometers where eachdiver is calibrated to a particular density. Severaldivers of different densities are added to the fullydispersed suspension and each will settle at a heightwhere its density is equal to the suspension around it.


Sealed in each diver is a copper ring which enables anexternal search coil to monitor and determine thelocation of the diver using high-frequency alternatingcurrent.

The speciTc gravity balance The speciRc gravity bal-ance may be used to monitor the change within a sett-ling suspension. Such a balance comprises two bobs,one in clear Suid and the other in the suspensionbeing studied. The bobs are connected to the twoarms of a beam balance. The depth of immersion ofthe bobs is adjustable. The change in buoyancy iscounterbalanced by means of solenoids which areconnected to a pen recorder. From the trace of thepen recorder, the particle size distribution can becalculated.

Cumulative methods Cumulative methods have anadvantage over incremental methods in that theamount of sample required is small (about 0.5 g),which reduces the interaction between particles. Thisis a useful feature when only a small quantity ofpowder is available or when dealing with toxicmaterials.

Line start method In this case the size distributionmay be directly determined by plotting the fractionalweight settled against the free-falling diameter of par-ticles. Special care needs to be exercised to eliminatethe streaming problem, especially when the suspen-sion at the top has higher density than the liquid.

Homogeneous suspension method Let us considera powder with a mass distribution such that dM"f(D)dD, where dM represents the fractional mass ofparticles having a diameter between D and D#dD.Let us assume that the powder is completely dispersedin a liquid, and consider a suspension chamber ofheight h. It can be reasoned that mass per cent P whichhas settled out at time t is made up of two parts:

(1) all the particles with a free-falling speed greaterthan that of Dt as given by Stokes’ Law or somerelated law, where Dt is the size of particle whichhas a velocity of fall h/t:

(2) particles smaller than Dt which started off atsome intermediate position in the chamber. Thefalling velocity of one of these smaller particles is , the fraction of particles of this size that havefallen out at time t is ( t/h).

This mechanism can be represented mathematically as:

P"�Dmax

Dt

f(D) dD#�Dt

Dmin

th

f(D) dD [30]

which after some manipulation can be rewritten as:

P"M#tdPdt

[31]

eqn [31] may be written in a different form as:

M"P! dPd ln(t)

[32]

Both eqns [31] and [32] can be used to determine M.The most obvious way is to tabulate t and P, andhence derive dP, dt, and Rnally M (cumulative per-centage oversize) versus Dt. Equation [32] isrecommended in cases of wide size distribution.

Centrifugal sedimentation Gravitational sedi-mentation for particle size analysis has limited Sexi-bility. Firstly, the only means of varying the particlevelocity is by selecting a medium with differentdensity or viscosity. Secondly, gravitational sedimenta-tion cannot handle particles smaller than 5 �m. Thirdly,most sedimentation devices suffer from the ef-fects of convection, diffusion and Brownianmotion. These difRculties can be reduced byspeeding up the settling process by centrifuging thesuspension. Furthermore, by the use of a centrifugalReld, a substantially lower size limit and reducedanalysis time can be achieved. As with gravitationalmethods the data may be cumulative or incrementaland the sample may be homogeneous or two-layer.

Calculations of size distribution from centrifugaldata are more difRcult than calculations fromgravitational data, since particle velocities increase asthey move away from the axis of rotation (i.e. theparticle velocity depends on its radial position). Oneway to overcome this difRculty is to use a rela-tively small settling radial zone at a far distance fromthe centre of rotation (i.e. the centrifugal force actingon all particles is approximately the same). Anothersolution is to use the line start technique. The mostcommon techniques used in centrifugal sedimenta-tion are schematically presented in Figure 9 whereS and D designate source and detector, respectively.

Line start method Rewriting eqn [19] as:

Vrt"dRdt

"�D2

t (�p!�m)18�m � ) 2R [33]

together with separation of variables and integrationof eqn [33], yields:

Dt"�18�m

(�p!�m)2t) ln�

RS��

1/2

[34]


Figure 9 Main centrifugal sedimentation techniques.

where t is the time for a particle of size Dt tosettle from the surface of the Rll (at distance Sfrom the centre of rotation) to a radial distance R.Hence, at time t, all particles at R will be of size Dt.Monitoring the per cent solids or density of the sus-pension at speciRed intervals of time will producethe particle size distribution which can be repre-sented using cumulative values at different valuesof Dt.

Homogeneous suspension method Equation [34]still applies: however, at time t, all particles ofsize greater than Dt will have settled out radiallyto a distance R. Conversion of the sedimentationcurve into a cumulative curve is not as simple in thiscase as for that of gravitational sedimentation. Dif-Rculties involved in evaluating the sedimentationcurve may be overcome in the case of a centrifugalReld by assuming a constant centrifugal Reld, i.e. for(R!S) interval is small enough to allow theapproximation:

ln �RS�+(R!S)

R[35]

when the value (R!S) is one twentieth of R, thecumulative curve can be obtained directly by thepipette technique with an error of 1%.

Elutriation

In Suid classiRcation, the effects of differentforces on the movement of suspended particles con-trol the separation of dispersed particles. As discussedin the kinetic behaviour of particles, the Reld forcesare gravitation, as with elutriators, or centrifugal orCoriolis force in classiRers. The medium is usuallywater or air. In general all Suid classiRers can bedivided into two classes, counterSow equilibrium(elutriation) and inverse Sow separation. The elutri-ation is presented brieSy below.

In the elutriation technique, the Reld and the dragforces act in opposite directions and particles leavethe separation zone in one of two directions, depend-ing on their size. Particles of a certain size stay inequilibrium in the separation zone. The grading iscarried out in a series of vessels (cylindro-conicalform) of successively increasing diameter. Hence, theSuid velocity decreases in each stage, the coarse par-ticles being retained in the smallest vessel and therelatively Rner particles in the following vessels. Forair elutriation, the analysis is considered complete ifthe rate of change of weight in residues is less than0.2% of the initial weight in half an hour, and forwater elutriation the analysis ends when there is nosign of further classiRcation.

Using Stokes’ Law, the particle size retained in anintermediate vessel can be predicted approximately as

Dp"�18�m

(�p!�m)g) Vmax�

1/2

[36]

Vmax"2V"2QA

[37]

where Q"volumetric Sow rate, A"vessel cross-sectional area at the equilibrium zone. In eqn [37] it isassumed that the Sow proRle in the vessel is para-bolic. It is clear that elutriation is only suitable forrough dispersions. With small particles, sedimenta-tion may be speeded up by using a centrifuge. Thistechnique is utilized when classifying aerosols usinga stream of air which Sows in the direction oppositeto the centrifugal force.

Electrostatic Precipitation

The electrostatic precipitator consists of an ionizingcathode at high potential surrounded by a collectinganode; typically, these anodes consist of concentriccylinders, the inner one often being a single wire. Thegas suspension passes between the cylinders, picks upthe charge, and travels to the anode where the chargeis deposited. The transfer of electrons from one anodeto the other constitutes an electric current. The mag-


Figure 10 Thermal precipitation.

Figure 11 Cascade impactor.

nitude of this current is proportional to the number ofparticles deposited. Particle sizes can be determinedby varying the Sow rate or applied potential.

ClassiRcation in an electrostatic Reld by differ-ences in charge is related explicitly to particle size.This type of instrument has been used for collectingaerosol bacteria. The instrument consists of a glasscylinder with a central electrode. The inner surfaceof the cylindrical glass is coated with a suitable mater-ial to act as the other electrode and to collectsamples. The principal advantages of this type ofinstrument are high collection efRciency overa wide size range, low resistance and high Sow-ratecapacity.

Thermal Precipitation

Particles in a thermal gradient medium move in thedirection of negative gradient, i.e. from hotter tocolder regions. Based on this principle, the instrumenttypically consists of two parallel round microscopicplates and a heated wire in between as shown inFigure 10. The sample is drawn between the platesand the particles deposit on the glass plates and arecollected for further analysis.

Normally a sample Sow of 1}2 cm3 s�1 is recom-mended and the collection efRciency is high forparticles smaller than 5 �m. The collecting devicemay be modiRed so that the sample is collected dir-ectly on an electron microscope grid. ModiRcationsof the basic design include means of centering thewire in position, substitution of the wire by a ribbonto give more uniform deposits, and using inlet elut-riators to exclude coarse particles. The practical ap-plication of thermal precipitation in gas cleaningplants has only rarely been attempted.

Impaction

Impactor Inertial impaction devices cause an airsample to be drawn into a round or rectangularnozzle where the gas velocity is substantiallyincreased. The jet from the nozzle is dischargedagainst an adjacent Sat surface, causing the air todiverge sharply. Particles in the air have more inertiathan the air, and tend to continue forward as the airpasses off to the sides, causing some of the par-ticles to impact onto the surface. To prevent theparticles from re-entrainment, a viscous material suchas silicone Suid (or substrate) is used to coat the plate.The efRciency of impaction may be deRned interms of the dimensionless impaction factor as:

I"�Cc�pD

2paVj

18�mDj �1/2

[38]

where Dpa"particle aerodynamic diameter: Dj"jetdiameter or width: Vj"average air velocity at the jetoutlet.

ClassiRcation of a particle cloud into discretesizes using cascade impaction may be interpretedas measuring aerodynamic (equivalent sphericalparticle) diameter. Several impaction stages(cascade impactor) are used in the classiRcationof a polydisperse cloud (see Figure 11). The stagesare arranged to permit jet velocity to increase witheach succeeding stage (by successive reduction injet diameter or width), and to therefore cause par-ticles of progressively smaller sizes to be impacted. Ineffect, the cascade impactor classiRes particlesaccording to their aerodynamic size. The aerodynam-ic diameter can be expressed in terms of Stokes’


diameter as:

Dpa"DStokes�1/2p [39]

where DStokes is the measured diameter. The aerody-namic size is important because it controls the motionof a particle in an air stream. Therefore, it is signiR-cant for studies concerning lung inhalation, sprayeffectiveness, and gaseous cleaning devices. Aspecial duty impactor (Rve-stage cascade impactor)has been developed for sampling and grading acidmists in the size range 0.3}3 �m.

Impinger Another sampling instrument, referred toas an impinger, also utilizes inertial impaction: how-ever, deposition occurs at the bottom of a liquid-containing vessel. The downward-directed air-jet dis-places the liquid and uncovers the bottom of thevessel. The particles that impinge against the wetsurface are subsequently washed off by theliquid. The undeposited particles may be caught as airbubbles rise through the liquid. The particles areusually examined in the liquid suspension. Water isthe most commonly used liquid.

Hydrodynamic Chromatography

Size information about colloidally suspended par-ticles (0.01}1 �m) can be obtained by employing hy-drodynamic chromatography (HDC). A medium (anaqueous solution) is pumped through a columnpacked with impermeable spheres. A pulse of collo-idal suspension (0.2 cm3) containing about 0.01 wt%polymer is injected into the Sowing stream of thecolumn entrance. The mobile phase from the columnefSuent is passed through a suitable detectionsystem, such as a Sow through spectrophotometer ofthe type used in liquid chromatography, and the de-tector response of the colloid is determined as a func-tion of elution time. An extra step is needed to deter-mine the concentration of solids in the eluted solution.

It has been observed that the larger particles elutefaster than the small ones. It has also been found thatthe smaller the packing diameter the better the separ-ation. Other factors which affect the rate oftransportation through the bed are the size of bedparticles, the ionic strength, and Sow velocities, aswell as the particle size of eluting particles.

In general, HDC has been successfully applied tothe size characterization of a number of polymerlattices. The method is applicable to the size separ-ation of particles between 0.02 and 1 �m, if they arerigid. Moreover, it is expected that HDC has wideapplicability to sub-�m particles such as in lattices,carbon black, colloidal silica, paint, and photo-

graphic pigments, dyes, food colours, natural andartiRcial blood, and metallic fumes.

Another extension of HDC is to replace the packedbed with a long capillary. Capillary particle chro-matography (CPC) requires 30 kPa pressure and hasa separating range of 0.2}200 �m. In such techniquesthe particle transit time is a logarithmic function ofparticle size.

Liquid Particle Size Measurement Techniques

In the areas of combustion and chemical processesand in the pharmaceutical and agriculture industries,measurement of droplet size and velocity distribu-tions is important. In one respect the measurementof droplets is easier than that of solid particlesbecause droplets are usually spherical and smooth.In another respect the measurement of droplets ismore difRcult because they are not easy to collectand stabilize, and they may be volatile. Thus, an insitu measurement is usually preferable. The applica-tions commonly used can be grouped as spray diag-nostics (using ensemble scattering techniques and op-tical single-particle analysis) and spray measurement.

Acknowledgement

This work was supported in part by the Federal Panelon Energy Research and Development (PERD).

See also: II / Chromatography: Hydrodynamic Chroma-tography. Flotation: Cyclones for Oil/Water Separations;Historical Development; Oil and Water Separation. Par-ticle Size Separation: Electrostatic Precipitation; FieldFlow Fractionation: Thermal; Hydrocyclones for ParticleSize Separations; Sieving/Screening.

Further Reading

Allen T (1997) Particle Size Measurement, 5th edn.New York: Chapman and Hall.

Barth HG (ed.) (1984) Modern methods of particle sizeanalysis. In: Chemical Analysis (A Series of Monographson Analytical Chemistry and its Application) pp. 1}75,vol. 73. New York: John Wiley.

Barth HG and Sun ST (1985) Particle size analysis. Analyti-cal Chemistry 57, 151R}175R.

Barth HG, Sun ST and Nikol RM (1987) Particle sizeanalysis. Analytical Chemistry 59: 142R}162R.

BoK hm J (1982) Electrostatic Precipitators. New York:Elsevier.

Hirleman DE, Bachalo WD and Felton FG (eds) (1990)Liquid Particle Size Measurement Techniques, vol. 2.American Society for Testing and Materials, STP; 1083.

Kaye BH (1981) Direct Characterization of Particles.New York: John Wiley.

Kaye BH (1989) A Random Walk Through Fractal Dimen-sions. Weinheim, Germany: VCH Publishers.


Mandelbrot BB (1983) The Fractal Geometry of Nature.San Francisco: W. Freeman Publishers.

Miller BV and Lines R (1988) Recent advances in particlesize measurement: a critical review. Critical Reviews inAnalytical Chemistry 20(2): 75}116.

Oglesby S Jr and Nichols GB (1978) Electrostatic Precipita-tion. New York: Marcel Dekker Inc.

Provder T (ed.) (1998) Particle Size Distribution III, Assess-ment and Characterization. ACS Symposium Series 693,ACS.

Salama AIA and Mikula RJ (1996) Particle and suspensioncharacterization. In Suspensions: Fundamentals and Ap-plications in the Petroleum Industry. Advances in Chem-istry Series 251, ACS.

Silverman L, Bellings CE and First MW (1971) Particle SizeAnalysis in Industrial Hygiene. New York: AcademicPress.

Syvitski James PM (1991) Principles, Methods and Applica-tions of Particle Size Analysis. Cambridge: CambridgeUniversity Press.

MEDICINAL HERB COMPOUNDS:HIGH-SPEED COUNTERCURRENTCHROMATOGRAPHYT. Zhang, Beijing Institute of New TechnologyApplication, Beijing, China

Copyright^ 2000 Academic Press

Introduction

Medicinal herbs are an important source of naturalproducts for medicine. They include various chemicalcomponents ranging from fat-soluble to water-soluble compounds. The isolation of the biologicallyactive components is the starting point of furtherresearch in chemistry and pharmacology as well as inthe utilization of these compounds.

Traditional Chinese medicine is an extremely richsource of the experience acquired over a long periodof time. In order to make greater use of traditionalChinese medicine, modern scientiRc methods are usedto Rnd the bioactive compounds in the traditionaldrugs and to use them as leading compounds for newdrug design. New drugs developed in this way includeanisodamine and the antimalarial agent Qinghaosu(artemisine).

For separating and purifying bioactive compoundsfrom medicinal herbs, modern chromatographic tech-niques, such as gas chromatography, high perfor-mance liquid chromatography, thin-layer chromatog-raphy and electrophoresis have signiRcantly raisedthe technical level and have shortened the time re-quired for research projects.

High speed countercurrent chromatography(HSCCC) has been recognized as an effectivemeans for separation and puriRcation of a wide varietyof bioactive components. It is a liquid}liquid partitionchromatography system based on a coil planet centri-fuge system without the use of any solid support. Thistechnique has developed rapidly during the past dec-

ade. It has been demonstrated to have preparativecapabilities and unique properties for fractionatinga variety of natural products and medicinal herbs.

Here some applications of the separation of bio-active compounds, such as alkaloids and Savonoids,in medicinal herbs by HSCCC are described.

Separations of AlkaloidsSeparations of Alkaloids Extracted fromStephania tetrandra S. Moore

Dried roots of Stephania tetrandra S. Moor (Menis-permaceas) or Fenfangji in Chinese is a traditionalChinese drug used for rheumatism and arthritis. Thetotal active alkaloid content in the natural products is2.3%. Three major alkaloids have been identiRed astetrandrine (I, 1%), fangchinoline (II, 0.5%) and cyc-lanoline (III, 0.2%). I and II are inseparable by con-ventional methods, while III is well separated fromthe other two. As illustrated in Figure 1, I and II areboth bisbenzylisoquinoline alkaloids, whereas IIIis a water-soluble quaternary protoberberine-typealkaloid.

A sample solution was prepared as a mixture ofI and II with puriRed III to obtain a 10 : 5 : 2 weightratio to simulate their composition in the naturaldrug. 3 mg of this sample was dissolved in 0.5 mL ofthe upper stationary phase of the selected solventsystem. The solvent system was composed ofn-hexane/ethyl acetate/methanol/water at two dif-ferent volume ratios of 3 : 7 : 5 : 5 in the Rrst experi-ment and 1 : 1 : 1 : 1 in the second. In both cases thelower phase was used as the mobile phase at a Sowrate of 60 mL h�1 in the normal elution mode. Theapparatus used in these experiments was a Pharma-Tech Model CCC-2000 analytical countercurrent

III /MEDICINAL HERB COMPOUNDS: HIGH-SPEED COUNTERCURRENTCHROMATOGRAPHY 3289

Mechanical Techniques - Particle Size Separation

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