food particle technology. part i: properties of particles

Journal of Food Engineering 6 (198’7) l-32

Food Particle Technology. Part I: Properties of Particles and Particulate Food Systems

H. Schubert

Institute for Food Engineering, Federal Research Centre for Nutrition, Engesserstr. 20. D-7500 Karlsruhe, Federal Republic of Germany

(Received 3 September 1985; revised version received 20 January 1986; accepted 25 February 1986)

ABSTRACT

In Part I the properties and the characterization of individual particles and particulate systems are reviewed, special emphasis being given to particle size and shape, particle size distribution, interparticle adhesion, porosiy, capillary action in porous media, ‘instant’ and flow properties of powders. The p~cu~~ar~ties of particulate foodstu~s, which become evident through the use of special techniques for measuring these fundamental characteristics, are considered in detail.

1. INTRODUCTION

In the past 20 years, particle technology has changed from a largely empirical to a structured discipline, involving scientific research in many parts of the world. Decisive contributions to this development were made by Rumpf (1975). Particle technology is that branch of process engineering concerned with the production, processing, analysis and use of particles.

The differences between integral and particulate matter occur mainly when the particles are small, i.e. of the order of micrometres to millimetres. This part of the field is known as fine particle technology or powder technology. This paper is concerned predominantly with fine solid particles, the largest sector of particle technology.

Advances in this field have so far received little attention in food technology, although foods are frequently in the form of fine particles during processing or when used by the consumer. The chemical, pharmaceutical and other process industries are now using the results of research into

Journal of Food Engineering 0260-8774/87/$03.50 - 0 Elsevier Applied Science Publishers Ltd, England, 1987. Printed in Great Britain

2 H. Schubert

particle behaviour extensively. The benefits to be obtained also deserve the attention of food technologists although, in view of the special characteristics of foods, additional research is necessary if the advances in particle technology are to be applied successfully to food products.

It is the purpose of this paper to describe some important aspects of particle technology and to illustrate them by examples from food technology.

2. PROPERTIES OF INDIVIDUAL PARTICLES AND OF PARTICULATE SYSTEMS

The properties of particulate systems differ from those of the integral form of the solids of which the particles are composed. Many such properties depend on the particle size. Figure 1 shows qualitatively some selected individual particle and particle system properties. The figures indicate only a general tendency as deviations from this general behaviour may sometimes be observed. Some properties of individual particles will be considered first (Fig. l(a)). The fracture resistance, a,, increases with decreasing particle size (as there are then fewer flaws in each particle and a greater proportion of the particle deformations are plastic): size reduction therefore requires increasingly more energy if fine particles are to be produced. This is also one reason for the existence of a grinding limit, i.e. the particle size below which grinders are not capable of producing smaller particles. With decreasing size the homogeneity of the particles also generally increases. This property is used, for instance, traditionally in cereal grain milling to separate the different components after comminution.

The terminal settling rate Us, illustrated here by a flour particle in air, first increases rapidly as a function of increasing particle size ( ug CC x2)

and then more slowly ( I+ a Jx). Small particles settle very slowly. Wheat flour particles of 1 pm size take more than 6 h to fall a distance of 1 m in still air. Of special importance is the ratio, S,, surface area per unit volume of particle, which is inversely proportional to particle size. Small particles accordingly have a large S, value. If a lump material of 1 cm3 in volume is subdivided into equal spheres of 1 ,um diameter, the surface area obtained is more than 3 m2. The surface per unit volume is particularly important in heat and mass transfer, the rates of which for small particles (x < lo-100 pm) are proportional to S,. Extremely small particles can dissolve very rapidly and may be dried within a fraction of a second, but also may cause violent dust explosions. Because of their large surface per unit volume, microorganisms are capable of exchanging metabolites and nutrients solely by diffusion at their external surface.

Food particle technology - Part 1

10-l 1 10 lo2 PARTICLE SIZE x

lo3 Pm loL

I 10-l 1 10 lo2

PARTICLE SIZE x IO3 pm loL

Fig. 1 Qualitative dependence of some individual particle and some system properties on particle size. D is particle deposition in fibrous filters, F is adhesion force, His homogeneity of a particle, S, is surface per unit volume, W is weight of a particle, vg is terminal

settling rate, a, is particle fracture resistance.

The properties of particles do not always increase or decrease regu- larly with increasing particle size. An example of this is particle deposition, D, in fibrous filters. Particles of x = 1 pm are the most difficult to collect. The deposition of small particles is promoted by diffusion, that of larger ones by inertial, gravitational and electrostatic forces (Loffler, 1983).

Most important in particle technology is interparticle adhesion. This usually increases in proportion to the particle size but the ratio of particle adhesion, F, to particle weight, W, is of primary importance: this ratio is inversely proportional to the square of the particle size. For particles of 1 ,um, for example, F/W is larger by a factor of lo6 than for particles of 1 mm diameter. This fact explains why small particles adhere much more strongly to each other and to surfaces than large particles do.

Adhesion forces are also largely responsible for the cohesive strength of powders which, at constant porosity, is approximately inversely pro-

4 H. Schubert

portional to the particle size: thus fine powders show a tendency towards agglomeration or to form lumps. Hence, the flowability of powders increases with increasing particle size. A similar behaviour is also observed in their wettability and dispersibility. These properties are of importance in ‘instant’ food powders.

The magnitude of interparticle adhesion forces, as compared to other competing forces such as gravity, accounts for the difference between cohesive and non-cohesive powders. In non-cohesive powders, interparticle forces are negligible but in cohesive powders they are significant. The majority of dry food powders are non-cohesive (and thus free- flowing) only when the particle size exceeds about 100 pm. In wet powders considerably stronger adhesion forces appear and the boundary between the cohesive and non-cohesive occurs at larger particle size. Since the adhesion forces may be varied over a wide range, many powder properties may be influenced as desired.

Interparticle adhesion also influences many bulk properties. Three examples are shown in Fig. l(b). The porosity (the void fraction of the total volume) increases with decreasing particle size because the interparticle adhesion allows a looser structure. Very fine particles such as flow conditioners (anticaking or free-flowing agents, dry lubricants) of a size below lym can attain porosities of more than 95%. If they are poured into a container of volume 20 litres, the mass of its contents may be less than 1 kg although the density of the solid is over 2 kg/litre.

Many other properties such as mixability, colour, water-vapour sorption, flavour, etc, depend upon particle properties. Nowadays many of these properties can be described quantitatively. Considerable advances have also been made in the description of fluidized solid flow (Molerus, 1982) in particle transport equipment and in fluidized beds.

3. CHARACTERIZATION OF PARTICULATE SYSTEMS

3.1 Characterization of individual particles

3.1.1 Particle size analysis Particle size is the most important physical particle characteristic. In the case of simple shapes such as the sphere or cylinder, the size is explicitly determined by one or several dimensions. In the majority of cases, however, particles are of irregular shape so that a large number of dimensions would be required to describe the size and shape. Since this is not practicable, essential characteristics must be defined which, depending on the circumstances, provide adequate description. Because of the measuring problems involved, particularly in the case of very fine

Food particle technology - Part I 5

particles, the choice of suitable characteristics defining the particle size is sometimes tied to particular measuring methods.

To determine the particle size, in principle, any measurable physical property which correlates with characteristic geometric dimensions or ‘equivalent’ dimensions can be used. Equivalent dimensions are dimensions of an imaginary regular particle with the same physical property as that of the irregularly-shaped particle being measured. The equivalent settling rate diameter, for instance, is frequently used; it is the diameter of a sphere of the same density as the irregularly-shaped particle which in the same fluid has the same settling rate. In the viscous flow regime, i.e. for Reynolds number ReSO-25, this equivalent settling rate diameter is obtained from

x;= 18qv,

g(p, - P”)

where Re = (,q, v,x,)/q, r] is coefficient of dynamic viscosity of the fluid, V~ is terminal settling rate of the particle, g is acceleration due to gravity, pP, ,on are density of the particles and of the fluid, respectively. Equation (1) applies, for instance, to cereal flour particles in the ranges of X, < 50 pm for sedimentation in air and x, < 100 pm for sedimentation in ethanol.

The attributes usually used to characterize particle size may be classified as follows:

(1)

i:; (4)

geometrical characteristics (such as linear dimensions, areas, volumes); mass; settling rate in a fluid; field interferences such as electrical field interferences, light scattering or diffraction.

Today many devices are available commercially employing one or other of these attributes from which the particle size or the equivalent diameter can be determined. However, not all particles of a powder are of the same size. It .is therefore necessary to measure a great many particles and produce a particle size distribution. An example is shown in Fig. 2. The cumulative distribution QAx) as well as the frequency distribution q,(x) may be measured. Either can be converted into the other, since q,(x) is the first derivative of Q,(X); x represents the particle size, frequently an equivalent diameter. Subscript r indicates whether the distribution is according to number (r= 0), length (r= l), area (r = 2) OI volume (Y= 3) (see, for example, Leschonski et al., 1974). The cumulative distribution function Q,(X) indicates, for instance, the volume proportion of particles between x,,,~” and x (see Fig. 2).

H. Schubert

0.5

Xmin X50 X max

Particle size x -

Fig. 2 Cumulative and frequency distribution of particle size.

This mode of description is advantageous mainly because it allows several characteristic distribution values to be calculated and converted. Of special importance in this respect are the various mean values, such as the weighted mean particle size of the area frequency distribution

%(X)

%lla”

x1,2 =

- I -w(x 1 dx (2)

%I,”

which is inversely proportional to the surface per unit volume of all particles of the distribution. A very simple and frequently used mean particle size is the median value xsO which is obtained from the cumulative distribution at Q, = 0.5 or 50% (see Fig. 2).

Before measuring a particle size distribution, a representative sample must be withdrawn from the powder. To minimize sampling errors a special sampling technique (Sommer, 1979) is necessary, which includes sample splitting to provide the necessary quantity for each particle-size- distribution measurement.

The characterization of individual particles in a collection is possible only if the particles are separable from each other. Because of the strong adhesion forces in relation to particle weight, fine particles in particular require careful dispersion, otherwise agglomerates are measured.


Depending on the particle measuring method used, the particles are dispersed in gases (Zahradnicek, 1976) or in liquids (Koglin, 1974). Disper- sion in gases is satisfactory for particles larger than 2-5 pm; finer particles have to be dispersed in liquids by means of dispersing agents to overcome the adhesion forces by repulsion forces. The choice of dispersing liquid is especially important for food powders since the particles must not swell or otherwise dissolve in or react with the fluid. After extensive experiment at the author’s institute, Hoffmann has established a list of suitable dispersing liquids for all the common food powders, in which it is still necessary to differentiate between the different particle-size measuring methods. A selection of dispersion liquids is shown in Table 1.

TABLE 1 Dispersing Liquids Suitable for Use in Particle Size Analysis of Food Powders”

Wet sieving Sedimentation Electrical refraction or impedance scattering of of particles

light ( Coulter counter)

Wheat flours Defatted flour soya Milk powder Pea-protein concentrate Protein concentrate from brewers’ spent grain Microcrystalline cellulose

1,273 1,1+4,3,5 6+7,8+9 3,8, 10 3,8,11 8+9,10 12,13 2,13 8+9,10,14 2,3, 10, 11 2,3, 10, 12 8+9

12 2, 12 10 12,15 12,15 lo,16

0 Dispersant: 1, ethanol, 2, isobutanol; 3, benzene; 4, diethyl phthalate; 5, cyclohexane; 6, methanol; 7, 5% aqueous lithium chloride; 8, isopropanol; 9, 5% aqueous ammonium thiocyanate; 10, Isotone (Coulter Electronics); 11, butanol; 12, distilled water + Triton X lOO@ (Coulter Electronics); 13, octanol; 14, 2% aqueous sodium hydroxide; 15, acetone; 16, 1% aqueous sodium chloride.

The numerous measuring methods and devices for particle size analysis will not be discussed here in detail. In recent years, rapid methods have been developed which usually require expensive equipment. A survey of on-line measurement of particle size distribution in gases and liquids was published by Leschonski (1978). It should be noted, however, that not all methods are suitable for foods, even if they are well proven for other substances such as minerals. For instance, the densities of foods are in general not very different from those of liquids.

8 H. Schubert

In the majority of cases experience has shown the following measuring methods to be suitable for foods:

(a) analysis of photographic images including scanning electron micrographs;

(b) dry (x 2 40 pm) and wet (x 2 5 pm) sieving; (c) electrical impedance of particles; for example, Coulter Counter

TA II (0.6 pm I x I 800 pm), Elzone Counter (0.25 pm I x I 1020

pm); (d) evaluation of laser diffraction patterns; for example, Malvern

( 1 ,uml x I 1800 pm), Cilas ( 1 pm< x I 192 pm), Leeds and Northrup (0.1 ,umlxl20 pm or 2 ~m1x<lOOO pm).

Because of the time taken in sample preparation, method (a) is time- consuming despite automatic image evaluation. Method (b) is also time- consuming but indispensable for many purposes including quality control. Methods (c) and (d) are rapid methods using automatic measuring equipment suitable for on-line measurements. Whereas with method (c) the particles can be measured only in an electrically-conducting liquid, it is possible with method (d) to measure particle-size distribution in liquids and gases. Particularly because of their rapidity, diffraction counters working according to method (d), using the Fraunhofer diffraction pattern of particles, have been increasingly used in recent years (Polke and Bieger, 1979). Figure 3 shows a comparison of methods (c) and (d) for pea flour. The particle size x is the equivalent volume diameter (method (c)) or the equivalent diameter of a sphere showing the same characteristics of Fraunhofer diffraction (method (d)). The differences between the measurements on particles dispersed in air and in liquid demonstrate that the fines were not completely dispersed in air.

Particle size analysis has been developed to a comprehensive discipline requiring special knowledge and experience taught in special courses (Leschonski, 1982) which deal in detail with measurement of other properties such as surface per unit volume and particle shape. The measurement of particle shape (Scarlett, 1979), for which new methods have been developed (Weichert and Huller, 1979) has gained increasing importance for food particle technology (Davis and Hawkins, 1979).

3.1.2 Particle adhesion Particle adhesion in a gaseous environment is an important property in characterizing individual particles but, apart from a few exceptions, it has not been possible so far to calculate the adhesion forces between real particles with sufficient accuracy. Models were therefore developed to enable adhesion forces to be estimated: in the majority of cases, these models are based on the assumption of ideally smooth, rigid spheres.

Food particle technology - Part I

“2 5 10 20 50 100 200 Particle size x - IJm

Fig. 3 Cumulative particle size distributions of particle-size milled pea flour.

Even if surface roughness and deformation of the contact areas inevit- able in real particles are responsible for deviations between model calculations and measured values, the calculations still provide useful information as to how the different variables influence adhesion.

Adhesion mechanisms with and without material bridges can be distinguished. The most important adhesion forces between food particles are shown in Fig. 4. Solid bridges may be formed by sintering, by chemical bonds and/or by crystallization. The crystallization of amor-

with material bridges

9

chemical bondi-

5 slnter bldge

bonding by

crystolllsed soiute

liquid bridge

VISCOUS bondmg

,vithout matenal bndges

van der Waals

electrostatic

(conductor I

Fig. 4 Adhesion mechanisms between solid particles and a solid plate in a gaseous environment.

10 H. Schubert

phous constituents frequently causes an undesirable stickiness to occur in food powders. These processes have been studied in detail for sucrose and lactose (Niediek, 1982) and also measured as a function of tempera- ture and water content (Downton et al., 1982). Crystallization of solutes at contact points between particles during drying frequently leads to strong particle adhesion.

Liquid bridges represent the dominating adhesion mechanism in nearly all those cases where sufficient moisture is present, but liquid bridges may also arise from capillary condensation in moist atmospheres. Adhesion forces due to liquid bridges can be calculated. The results of such calculations are available for many particle geometries as diagrams using dimensionless numbers (Schubert, 1982). Figure 5 shows a simple example of adhesion forces between two equal spheres. The distance, ‘a’, between the surfaces of the spheres as shown in the figure arises in real particles from surface roughness, the significance of which for adhesion forces will be explained below.

Adhesion without material bridges is primarily due to van der Waals’ and electrostatic forces. Van der Waals’ forces (F&,, ) are always present; they may be calculated for two spheres of diameters X, and x2 separated from each other by distance a between the two surfaces from

3.0

2.5

F

= 2.0

1.5

1.0

0.5

0 r\ lcrl, \;?.1oyo-ypo-3 1

Y42 % _-I I \\, I\ -y

0 0.05 010

\ I I

0.15 Q 0.20

X

Fig. 5 Adhesion force F of a liquid bridge between two equal spheres - related to the surface tension y of the liquid and the sphere diameter x - as a function of the distance ratio a/x for complete wetting (contact angle 6 = 0). Parameter is the volume V, of the

liquid bridge related to the volume V, of the sphere.


F = E,x, % vdW 16;rt(x, +x2) a*

(3)

The vander Waals’interactionenergy E, is between 10-i” and 2 X lo- Ix J. Van der Waals’ force is a maximum for particles in contact with each other; the contact distance is assumed to be a= a,, = O-4 nm (Krupp, 1967). It should be noted that eqn (3) applies only to ideally smooth rigid spheres, and to a sphere at a plane surface (where x,/x2 -, 0).

Electrostatic adhesion forces occur in cases where particles have opposing charges. These charges may be already present as excess charges or arise only when the particles come into contact due to differences in the values of the electron work function (contact potential). Electrically non-conducting particles frequently have excess charge up to a maximum per surface of around s,,, = 100 e/pm* (elementary charge e = 1.6 x lo- I9 As). For ideal electrical insulators the adhesion forces F,,,i can be calculated from Coulomb’s law,

2 2

Fei,i= JG~l~2~1~2

E,E(xI+x2+2a) (4)

Equation (4) applies to spheres of diameters x1 and x2 where si, s2 are electric charge per unit surface area of the corresponding spheres, E*, t are relative and absolute dielectric constants of the surrounding medium. a is distance of separation between the spheres. Equation (4) also applies to the sphere-plate system when x,/x2 -+ 0.

With electrically conducting particles, electrostatic adhesion arises only after the particles have made contact and is due to the contact potential which is frequently between U= 0.1 and 0.7 V. The adhesion force due to a contact potential between two spheres or between sphere and plate (x1 /x2 -, 0) can be stated by:

Fe,,, = m,&tiX1X2 2(x1 + ~2) a

(5)

A comparison between the adhesion forces represented by eqns (3)-(5) is shown in Fig. 6. As mentioned before, however, for particle adhesion the ratio F/W between adhesion force and particle weight is more important than the absolute value of the adhesion force. In Fig. 6, therefore, the ratio F/W for two equal spheres is plotted against sphere diameter. The distance between the two surfaces in contact is assumed to be a, = O-4 nm, the particle solid density pS = 1.5 g cme3. As Table 2 shows, this is a reasonable mean density value for many food particles, but since F/W= ps ‘, a conversion of the values shown in Fig. 6 for other solid densities is very simple.

12 H. Schubert

F= theor. ddhesion f&ce’~~~, , ,

W=weight of one sphere _ <X \

(9 = 1.5 g/cm31 ‘\\,

I 1 10 lo2 Pm lo3

Sphere diameter x

Fig. 6 Calculated adhesion force F between two equal spheres (as a fraction of the weight W of one sphere) for various interparticle adhesion mechanisms vs. sphere

diameter.

TABLE 2 Densities and Bulk Densities of Some Food Powders

Food Solid derlsityp, Bulk density p,, g cm --; g cm --.<

Wheat flour 1.45-1.40 0.55-0.65 (0.4-0.75) Rye flour I.45 0.45-0.7 Corn flour I.54 0.5-0.7 Corn starch 1.62 0.55 Potato starch 1.65 0.65 Rice, polished 1.37- 1.39 0.7-0.8 Cocoa powder (10% or 22% fat content) 1.45 or 1.42 0.35-0.4 or 0.4-0.55 Sucrose 1.60 0+x5- 1.05 Instant dried whole milk 1.3(-1.45) 0.45-0.55 Instant dried skimmed milk 1.2(-1.4) 0.25-0.55

Figure 6 shows on a log scale that all adhesion forces related to the particle weight are inversely proportional to the square of the particle diameter (F/WCC X-*), except for the electrostatic adhesion of insulators

lFel,il WCC x-1 ). Particle adhesion decreases in the order: liquid bridge


forces: van der Waals’ forces: electrostatic forces. The strong adhesion between small particles is remarkable. The interparticle force between spheres of 10 pm diameter, for instance, is in the case of a liquid bridge 2.6 x lo5 greater than the particle weight.

The dependence of adhesion. forces upon the distance between particles is important. Large volume liquid bridges - as Fig. 5 shows - are little influenced by the distance between particles, whereas small volume bridges formed by capillary condensation, for instance, are strongly affected. As eqns (3)-( 5) show, van der Waals’ forces decrease rapidly with separation distance ( FvdW~ a-‘), whereas the decrease in electrostatic forces with separation distance is less in the case of electrical conductors (F,,i 0~ a - * ) and negligible (sphere/sphere) or even zero (sphere/plate) in the case of electrical insulators. Attraction from greater distances is consequently due only to the electrostatic forces between charged particles. If the particles are already in contact, the adhesion is primarily due to solid bridges, liquid bridges and van der Waals’ forces.

The effect of distance on adhesion forces is of great significance in the case of real particles in which surface roughness, which is usually present, increases the separation distance. In the case of van der Waals’ forces and very small liquid bridges, adhesion is determined almost entirely by the size and shape of the roughness peaks. In such cases adhesion forces between real particles are frequently smaller by more than an order of magnitude than the values calculated for perfectly smooth model solids.

This effect can be illustrated by using the model of a very small sphere which has been placed between two equally large spheres, as shown in Fig. 7. Such finely divided solids are added to food powders, for instance, as flow conditioners to reduce interparticle adhesion and hence improve ‘flowability’ (Hollenbach and Peleg, 1983). However, the interstitial sphere may also be regarded as a model for a roughness peak. Figure 7 shows the ratio of adhesion force F between two spheres of diameter x2 = 10 ,um and the weight W of one of these spheres (p, = l-5 g cm-“) vs. the diameter x, of the interstitial sphere. According to eqn (3), the van der Waals’ force between the two spheres of diameter xx is

Here a, is the distance between the interstitial sphere and the large sphere in contact, again assumed to be 0.4 nm. For a given x2, the adhesion force FvdW passes a minimum at

x: = $x,a$ - 2U” (7)

14

3 lo5 3 1o-2 3

0.1 pm 1 Diameter x1 of the interstitiat sphere

Fig. 7 Calculated adhesion force F between two equal spheres (as a fraction of the weight W of one sphere) VS. diameter x, of an interstitiai sphere.

For the sphere diameter xz = 10 pm as selected in Fig. 7 the minimum adhesion force appears at X: = O-01 1 pm. A compa~son with Fig. 6 reveals that this van der Waals’ force is smaller by a factor of cu. 300 than the adhesion force between a pair of perfectly smooth spheres. In case of electrostatic attraction between electrical conductors (not shown in Fig. 7), the adhesion force takes a similar course to that of the van der Waals’ force.

The adhesion of the electrical insulator, on the other hand, is inde- pendent of x1 and thus also of roughness. Large liquid bridges are also little influenced by roughness. This is illustrated in Fig. 7, for example, where the course of the related liquid bridge force is shown for a ratio of liquid bridge volume Vi, to sphere volume I’S, of I’,,/ r/, = 0.0 1; this corresponds to a bridge angle of /!I = 20-27”, depending on the size of xl_ Very small liquid bridges resulting from capillary condensation from the moist atmosphere behave quite differently. Figure 7 shows two examples for relative air hu~dities of 50 and 80%, which correspond to water activi-


ties a, = 0.5 and 0.8. The related adhesion force decreases rapidly with increasing diameter x1 of the interstitial sphere until finally the liquid bridge becomes unstable (Schubert, 1982) and breaks (dotted line in Fig. 7). Thereafter the related adhesion force increases with increasing diameter x1 proportionally to x1 and practically independently of a,; in this case liquid bridges have formed between the sphere of diameter x2 = 10 ,um and the small sphere (x1).

The liquid bridge forces caused by capillary condensation hence may decrease by a factor of more than 1000 (cf. Fig. 7) as compared to perfectly smooth particles without the interstitial sphere. This illustrates the effect of flow conditioners on powders which are stored in moist atmospheres (see also Schlitz and Schubert, 1980).

Since the size and shape of actual roughnesses, in contrast to the model considerations in Fig. 7, are largely unknown, it is necessary to measure the adhesion forces between real particles if quantitative information is required. Such measurements generally yield adhesion force distributions over a wide range even with equal-size particles. This is due to roughnesses of different size which are irregularly spread over the surfaces. Hence, depending on the random contact, the geometry of the contact area changes in the micro-range. Adhesion force distributions often range over more than one order of magnitude even for monosize particles (Schlitz, 1979).

In addition to the above influences there are many other factors to be taken into account such as adhesion force enhancement due to inelastic deformation of the contact areas of the adherents. Interactions of particles in liquids where repulsive and attractive forces frequently com- pete with each other also belong to the field of interparticle adhesion. Review papers provide a survey of the entire field (Schubert, 198 1 a, c). A research project at present attracting much attention is the adhesion of microorganisms to solid surfaces (Ellwood, 1979; Notermans and Kampelmacher, 1983). Much of classical particle adhesion knowledge may be used in this field. The same applies to particle adhesion involved in surface fouling in food processing (Hallstrom et al., 1981).

3.2 Characterization of powders

3.2.1 Porosity bulk density Porosity E has been defined as the ratio of void volume V, to total volume I’, of the powder:

16 H. Schubert

In eqn (S), V’> is the solid volume. If the particles themselves are porous (particle porosity EJ then

F’l -(I -Ep)(l -&J (9)

where the bulk porosity E,, is the ratio of void volume between particles to the total volume. The bulk density of a powder is also frequently used:

Ph=(I-&p)(l-&b)Pu=(l-&)P, (IO)

where p, is the solid density. Table 2 lists the bulk densities of some food powders. In the case of bulk material made up of closely sized, non- porous particles, if adhesion forces may be neglected, i.e. if the particles are sufficiently large, the porosity is about E = 0.4. If interparticle adhesion is significant, porosity increases. Especially in wet powders, or upon exceeding the relative humidity (RH) at which capillary condensation may take place (frequently at RH > 0.6-0.7) porosity increases, or the bulk density decreases as compared to the dry condition. Scoville and Peleg (1981) and Moreyra and Peleg (198 1) studied and quantified these effects in model substances and various food powders.

Bulk density is of importance because consumers expect that the mass indicated on the package corresponds to a volume filling the package almost completely. This frequently presents difficulties in food processing. In many cases producers wish to offer powders combining a large volume with a small mass. As may be recognized from eqn (lo), this can be accomplished by producing porous particles. In practice, porous particles may be produced as hollow spheres or by ‘instantizing’ fine particles to larger agglomerates of the desired porosity sp. The following example demonstrates the wide range of variability in bulk density. A beverage powder (sugar-cocoa mix) which is sold direct to consumers is usually expected to show a bulk density of p,=O.30-0.35 g cmm3. A powder of the same composition intended for use in vending machines, however, is required to have a bulk density of pb = 0.5-0.6 g cmm3 (Kniel, 1980).

3.2.2 Capillar?, action in powders, pore size distribution Many food powders are obtained from the wet phase and have to be dried, frequently after mechanical dewatering. Prior to consumption, or in the course of further processing, most of the powders have to be rewetted. Both dewatering and reconstitution - mostly with water - are governed by capillary behaviour. It is therefore necessary to characterize powders with regard to their capillary properties. For this reason capillary pressure curves (Schubert, 1982) have been established which indicate the capillary pressure p, in a porous medium as a function of the liquid saturation S; S is the ratio of liquid volume to void volume of the

porous solid system. The capillary pressure curve indicates a distribution comparable to the particle size distribution. The measuring methods are explained in detail elsewhere (Schubert, 1982).

Figure 8 shows a typical capillary pressure curve. Starting from the porous system filled with liquid (S= 1) the capillary drainage curve D, applies until finally at S= S, only isolated liquid remains. If liquid is admitted to the pores in the state S = S,, the capillary imbibition curve I applies until finally at S = 0.8 1 the capillary pressure p, = 0 prevails. Sub- sequent dewatering leads to curve D. The capillary pressure curve accordingly shows a hysteresis which may be explained by the existence of narrow pore necks followed by larger cavities, and by the contact angle hysteresis (receding contact angle (r, < advancing contact angle 6,, see drawing in Fig. 8). A frequently used characteristic capillary pressure is the entry suction p, which is obtained approximately, for complete wetting (6, = 0), from

w - 4 Y PC=: -

&X1,2 (11)

-0 i, 0.2 Ok 0.6 0.8 1 Liquid saturation S

Fig. 8 Capillary pressure of a bulk material (glass spheres, weighted mean diameter .*11.2 = 79 ym, porosity E = 0.38) vs. degree of liquid saturation (p,(S) = capillary pressure

curve).

18 H. Schubert

(y = surface tension of the liquid; X ,,z see eqn (2)). The constant was found to be b = 6-8 (Schubert, 1972). According to eqn (1 l), the capillary pressure increases with decreasing particle size.

Although the capillary pressure curve holds a key position for the understanding of the capillary action in porous systems, and is necessary also for the quantitative description of wetting and dewatering processes, it is not sufficient to describe capillary processes completely. In wetting of powders, a dynamic capillary pressure may play an important role in addition (Schubert, 1978~). This wetting behaviour is of importance for instant powders: it is discussed below in section 3.2.3.

The capillary pressure so far has been assumed to be a suction pressure, i.e. liquid is sucked into the pores by capillary action. This is indeed always correct for sufficiently small contact angles, i.e. powders having good wettability. Mercury, however, which forms a contact angle of 6 = 140” with most solids, behaves differently. In this case mercury must be pressed into the pores to overcome the capillary pressure. This effect is used in the so-called mercury porosimetry to determine the pore size distribution. Since, because of the lower capillary pressure, large pores are filled first, followed by finer pores which are subsequently filled under increasing applied pressure, it is possible to deduce from the capillary pressure curve the pore size distribution. To evaluate the measured results, pore models are required: usually, a cylindrical model is preferred. The excess pressure which is identical with the capillary pressure p,, and the pore diameter dare correlated by the equation

4Y p<. = / cos b (12)

where y is surface tension of mercury, and b is contact angle. Pore size analyses to characterize porous systems are gaining in importance. In addition to mercury porosimetry (measuring range: 5 nm < d < 200 pm), and adsorption methods (0.2 nm < d < 2 nm), sorption isotherms in the range of capillary condensation (3 nm < cl < 0.5 pm) and micrographs (d > 0.1 pm) may also be used to determine pore size distribution. The pertinent literature is discussed in a review paper by Orr ( 1980).

3.2.3 ‘Irutunt ‘properties of powders Fine powders are difficult to wet with water or aqueous liquids (for instance, milk) and tend to form lumps which hinder dispersion. By agglomeration of fine powders of about 100 pm into particles of up to several millimetres in size, wetting is improved and lump formation avoided. The causes of this behaviour have been elucidated (Schubert,


1978b, 1982). Materials with poor wetting properties such as fatty particles, for example, which form a large contact angle with the liquid, may also be changed in respect of their surface properties by reducing the contact angle and thus improving wettability; this is often done by spraying with lecithin. The commercial treatment of powders to improve their wetting, dispersing and, in the case of soluble particles, their dis- solving characteristics is called ‘instantizing’. The different instantizing processes are described in a great many publications but the main principles of these processes have been compiled by the present author in a previous paper (Schubert, 1980).

If a powder is spread on the surface of a liquid, the following processes take place:

(a) penetration of liquid into the porous sysem due to capillary action (the ability of the powder to be penetrated by the liquid is called ‘wettability’);

(b) (c)

sinking of the particles below the liquid surface (‘sinkability’); dispersion of the powder with little stirring (‘dispersibility’);

(d) solution of the particles in the liquid, provided the particles are soluble (‘solubility’).

The properties wettabihty, sinkability, dispersibility and solubility are all subsumed under the term ‘instant properties’. In the case of particulate solids having good instant properties, the processes (a)-(d) are expected to be completed satisfactorily in a few seconds if the layer thickness of the powder spread on the surface of the liquid is about 10 mm.

Many objective measuring methods to determine instant properties are available; they are discussed in a review paper (Schubert, 198 16). In many cases, the disadvantages and shortcomings of these methods are so great that they have not achieved practical importance, and subjective evaluation methods have therefore been preferred. In view of the known disadvantages of subjective evaluations, however, satisfactory objective measuring procedures have been developed for the most important properties, ‘wettability’ and ‘dispersibility’ (Schubert, 1980, 198 1 b). The wetting test has also proved useful for non-food products; the dispersion test used previously, however, is, because of the technical expense involved, suitable only for research purposes. Dispersibility is most reliably determined from the change with time in the particle-size distribution during dispersion; this is possible by using modern on-line particle-size analysers, but is too expensive for works practice. A rela- tively simple method for the determination of dispersibility has been developed for non-food powders (Polke et al., 1979) and has worked

20 H. Schubert

well. However, the method is not suitable for the majority of food powders. This underlines the fact that it is not always possible to apply methods of general particle technology directly to foods.

As far as food powders are concerned it is essential that, following a short dispersing phase, soluble particles be dissolved as completely as possible and the remaining particles be suspended in the liquid for a sufficiently long time, i.e. neither deposit on the bottom of the receptacle nor accumulate at the surface*. In accordance with a measuring method (Mel, 1978) standardized by the International Dairy Federation (IDF) to characterize the instant properties of dried milk, the following dispersibility value (which also includes the wetting properties) may be defined:

pc;“d c mt

(13)

where c,,,~ is mass concentration of the dispersed proportion and c,[ is total mass concentration of the mass of the sample in the total liquid mass. All dissolved and suspended particles are regarded as dispersed; the remaining particles, i.e. those deposited and those floating at the surface, mostly non-wetted, accordingly are not dispersed. They form the residual material, mass concentration c,,.

A dispersibility value may also be defined as:

Q=h (14) I.

If the dispersed total sample is divided according to the IDF test into residual mass and dispersed mass, the following correlation between D, and D, is obtained:

D

I

= 125QU +a 99D,+ 151

(15)

The constants 125,99 and 15 1 are obtained from the standardized divi- sion ratio according to IDE

In the IDF method the concentrations c,,,~ and c,,,~ are determined gravimetrically or from the sample weight. The time required for the determination of dispersibility is thus 4-5 h. A rapid photometric method has now been developed in which the concentration is related to the loss in light transmission T according to the Lambert-Beer law: In TK c,. This law is valid only at sufficiently low concentrations and

*This requirement is not sufficient for the dispersion of certain other particles such as colour pigments. The dispersion test described here is hence not suitable for all instant powders, only for food powders.


only when the particle-size distributions of the residual and dispersed material are the same. Either condition can be fulfilled by adequate pre- treatment. From eqn (14), for the photometric dispersion measure

In Td Dfr=-

In T, orfromeqn(15)

D

F = 125% 1 + D,r)

99D,,+ 151

(16)

(17)

D, and D, are the same within the limits of measuring accuracy. The equipment shown in Fig. 9 is used to measure photometrically the

dispersibility. In a modified IDF method, the powder is dispersed, divided into residual and dispersed fractions which are then separately homogenized and filled into the corresponding loading funnel (Fig. 9). Each fraction is pumped in turn continuously through a cuvette where the light transmission T, and Td are measured. The apparatus works automatically. The data are evaluated by a mini-computer. Dispersibility, which may fluctuate between 0 and lOO%, is indicated digitally. Measurements, including sample preparation, take only a few minutes.

transmission

Fig. 9 Instrument for measuring the dispersibility transmission.

of instant food powders by light

The instrument has been tested on nearly all instantized food powders and has been found useful. Figure 10 shows the results for various commercial instant dried skimmed and whole milk products. Four samples of each product were measured and the standard deviations determined (indicated by bar-lines in the figure). The photometrically-determined

22 H. Schubert

(II” ’ 2 .- T= o instant dried 33 iii skimmed milk

gO.8- l instant dried whole milk

-0

z

,/

+ C .-

E ; 0.6.

5 WJ

CL 0.2V’ I I I 0.2 0.L 0.6 0.8 1 Gravimetrically determined dispersibility D,

Fig. 10 Comparison between the photometrically and gravimetrically determined dispersibility of instant dried skimmed and whole milk.

dispersibility, D,, is the same, within the measuring accuracy limits, as the gravimetrically-measured IDF value D,. None of the commercial instant dried whole milk products tested had satisfactory instant properties. According to IDF, D, should be L 85% for instant dried whole milk and h 90% for instant dried skimmed milk. The rapid method which, because of its ease in handling, is also suitable for routine measurements, enables instant properties to be determined with sufficient accuracy; the measurements may also be used for product and process control (Schubert, 1985).

3.2.3 Flow properties ofpowders To ensure that powders are easily discharged or metered from con- tainers, or fluidized and transported by pneumatic conveyors in the course of a process without difficulties, they must be sufficiently ‘flow- able’ and even ‘tricklable’. Numerous empirical studies have been made on the flowability of powders. However, none of these enables the flowability characteristics to be described independently of the particular application. This is because of the complicated flow behaviour of particulate solids which differs basically from the flow behaviour of liquids and fluidized solids. The pressure in a powder stored in a bin, for


example, does not increase linearly with height, but tends towards a maximum value. Only fluidized beds show some similarity to liquids.

Jenike ( 1970) established the fundamentals of powder mechanics, allowing the flowability of particulate solids to be characterized and bins and hoppers to be designed reliably. Only a brief explanation will be given here; for details see the original work by Jenike (1970), the survey papers by Schwedes (1970) and, with regard to food powders, by Peleg (1977). To obtain the first reliable data as a basis for statements of general applicability, Jenike developed a shear cell which is shown diagrammatically in Fig. 1 l(a). After consolidation to a certain porosity E, or bulk density ,ob, the powder is subjected to different normal loads N and caused to shear by the force S in the horizontal direction. If N is plotted vs. S, or the normal stress o = N/A, vs. the shear stress r = S/A, an experimental yield locus as shown in Fig. 12 is obtained indicating the yield point of the powder at a particular porosity E. If the yield point of the same powder is required at a lower porosity, the experiment is repeated at a higher consolidation degree. In this case the experimental yield locus would be above that shown in Fig. 12. There is an individual termination E to every yield locus; at this point steady-state flow is reached, i.e. no changes in stress or volume take place.

a) Jetike shear cell

cover

ring

powder

base

M b1 Annular shear cell

-loading

powder

shear tr

ring

*ough

I- C-R, -j

Ra

& W

Fig. 11 Devices for measuring the shear resistance of powders. (a) Jenike shear cell. (b) Annular shear cell.

24 H. Schubert

tension ’ compression Normal stress u ---

Fig. 12 Experimental yield curve and effective yield locus of a cohesive powder.

The stress condition of each point on the yield locus may be decribed by Mohr stress circles, Two Mohr stress semi-circles which are characterized by special properties are shown in Fig. 12. The larger semi-circle characterizes the stress conditions during steady-state flow since it is passing through point E. This stress circle intersects the axis at the two principal stresses o1 and 02, O, being the major, or the consolidation stress, and ~7~ the minor principal stress. The smaller semi-circle shown in Fig. 12 is characterized by the fact that the minor principal stress becomes zero; the major principal stress, f,, is called the unconfined yield strength by Jenike. Since the minor principal stress is zero, fc represents the compressive strength of the powder at the particular porosity. Jenike showed that a powder flows more easily out of a bin the greater the consolidation stress, o,, relative to the unconfined yield strength f,. The ratio flC = a,/fc is called the flow function ff,; it characterizes the flowability of powders, an important property in designing bins and hoppers. According to Jenike, powders may be classified according to their flowability, as shown in Table 3.

It should be noted that whilst the flow function 8: is a useful guide to the flowability of powders, it does not completely describe the flowing behaviour of particulate solids. A complete description is possible only by means of the yield loci measured at various porosities.

By using the Jenike shear cell, however, only a certain region of the yield locus curve can be determined experimentally. This region is indicated in Fig. 12 by a bold line, the remaining curve by a dashed line. The


TABLE 3 Flowability of Powders, Classified According to the Jenike

Flow Function #c = a,/fc

fs,<2 Very cohesive, non-flowing Cohesive 2<ff,<4 Cohesive powders

4<fs,<lO Easy-flowing Non-cohesive

10 <ffc Free-flowing powders

point of intersection with the vertical axis corresponds to the cohesion C. For non-cohesive powders C= 0. Since C depends not only on the powder properties, but also very much on the consolidation conditions, C is less suitable as an index of flowability than the flow function &, Another property used to describe powders is the tensile strength 0, which lies in the yield locus at the point of intersection with the horizontal axis. a, can be measured by using special equipment (Schubert, 1975). Since it is sometimes difficult to measure the yield locus in the region in which the Mohr circle is plotted to determine f,, a, may be used to interpolate the yield locus and hence to improve the measuring accuracy of f, (Eckhoff et al., 1978). This is of particular importance when slightly cohesive powders are to be investigated, such as instant food powders for vending machines.

Figure 12 also shows the tangent to the major stress circle from the origin. This straight line, as experiments have shown, touches (approximately) the major Mohr circles of all other yield loci of a given particulate solid under different consolidation conditions, i.e. at different porosities. This straight line which is called the effectve yield locus characterizes all steady-state flows of a material. The ratio of the two principal stresses 0, and B, and the effective angle of friction tir are correlated by the equation

o1 1 + sin &

a,=l-sin~r (18)

which is interpreted by Jenike as a general law describing the steady- state flow of powders.

Many food powders tend to consolidate with time under the action of static pressure. Interparticle adhesion increases with time, and flowability decreases correspondingly. This effect is of importance for the discharge of material from bins after intervals of time during which the material may consolidate. The increase in adhesion force with time is

26 H. Schubert

primarily due to inelastic deformations at the contact points between the particles and to the formation of solid bridges caused by crystallization processes, for example. The influence of consolidation with time on the flow behaviour of powders can be measured by using the Jenike shear cell, provided that the particulate material is exposed to a normal load for different periods of time before shearing. Yield loci are obtained which are shifted towards higher shear stresses than without time- dependent consolidation. The flow function fs,, and hence also the flowability, decrease correspondingly. It is necessary, in all studies of the influence of time on the flow behaviour of particulate material, that the external conditions during exposure to normal load are kept constant. This applies particularly to the relative humidity, RH. Many food powders tend to consolidate with time only at RH > 0.5-0.6. The tem- perature during the compression may also be of importance, particularly in cases where interparticle adhesion is promoted by sintering or crystallization processes.

Jenike’s theory and the corresponding measurements are applied primarily to the design of bins and hoppers (ter Borg, 198 1). Mass flow bins in which the entire bulk material is in motion during the discharge process (compare Fig. 13(a)) are to be preferred. In plug flow bins, the base angles of which are less steep and smooth, the powder flows through an outlet with some powder remaining stationary at the sides (Fig. 13(b)). F or oo f d s of limited shelf life plug flow bins should be avoided since the ‘dead’ regions retain material for an indeterminate length of time. By using the Jenike procedure, the critical cone angle BC, which is a function of the effective friction angle 4, and the friction angle &, between bulk material and wall, may be taken from diagrams giving

ldk al MASS FLOW bl PLUG FLOW

Fig. 13 Mass flow and plug flow from bins.


When the cone angle 8 5 8,, mass flow occurs. For the particulate solid flow out of the bin, the outlet must have a minimum diameter d, otherwise the material forms a stable arch. According to Jenike’s stability criterion, a stable arch is possible only for 0; <f,; a; is the major principal stress acting at the abutment of an arch and which may be calculated from the equation (see Jenike, 1970)

(20)

The flow factor fl, as a function of 8, 9, and #w, may be taken from the diagrams of Jenike ( 1970). The condition ai =f, supplies the critical stress a’,, which acts at the abutment of an arch (see Fig. 14) from which, by means of equation

(21)

the critical minimum diameter d, of the outlet can be determined. In eqn (2 1 ), pb is bulk density, g is acceleration due to gravity; H( 0) is a function of the geometry of the hopper given by published diagrams (Jenike, 1970). If d > d,, the formation of a stable arch which would prevent the material from being discharged is avoided. Details of Jenike’s theory are beyond the scope of this paper; the reader is referred to Jenike’s original publication (1970) or to an excellent review paper presented by Arnold et al. (1979).

In practice it is often difficult to determine the f, curve experimentally in the presence of low stresses. To determine the point of intersection with the straight line ai = a,/fl, an extrapolation of the f, curve is neces-

1

Fig. 14 Graphical construction to determine the critical diameter of a bin outlet (for explanation see text).

28 H. Schubert

sary. Molerus (1982) suggested a method of avoiding these difficulties. Starting from interparticle adhesion he established a relation for the group of yield loci which in the relevant range may be represented as straight lines. Peleg (1971) has demonstrated in experiments that the yield loci of the majority of food powders may be approximated as straight lines. The linearized yield loci allow the conclusion that the function SC =f( a,) can also be represented as straight line. Molerus formu- lated the equation for such straight lines as a function of the bulk properties, which can be experimentally determined in shear tests (Molerus, 1982). The practical importance of this method will be discussed in ‘Part II’.

The accuracy of results obtained in this way would be increased further if, for the determination of a’,,, reliable shear force measurements could be made at very low normal stress; the Jenike shear cell is not suitable for such experiments, however (Eckhoff et al., 1978). Shear force measurements at very low normal stresses are, however, possible by using an annular shear cell as shown diagrammatically in Fig. 1 l(b). The powder is contained in a shear trough which rotates at angular speed w. The torsional moment h4 is measured at the non-rotating loading ring which transmits the normal load N. From M, shear force and hence shear stress can be derived by means of the equation

3M

‘=2n(R;- R;) (22)

which has been confirmed theoretically and experimentally (Gebhard, 198 1). The radii R, and Ri are explained in Fig. 11 (b). To transfer the shear stress to the powder, the loading ring is roughened at its surface in contact with the powder. One advantage of the annular shear cell over the Jenike device is the shorter time required for a complete measurement, but the greatest is the continuous shear displacement possible with constant sheared area. In the case of the Jenike device, despite an initial offset (see Fig. 1 l(a)), the practical shear displacement is so small that some cohesive food powders such as dried onion with more than 6% moisture, some soup mixes and citric acid cannot be measured (Peleg, 1977), since neither shear failure nor steady-state flow are reached. The annular shear cell (Walker, 19671, as further developed by Miinz ( 1976) and modified by Ehlermann of the author’s institute to meet the require- ments of foods, is therefore preferred. For this purpose the measuring accuracy particularly in the range of extremely low normal stresses has been improved. This device is connected to a computer and thus suitable for automatic operation.


However, the annular shear cell is a complicated and expensive device. For preliminary studies and comparative measurements, simpler methods and equipment may be preferable which were proposed especially by Peleg et al. for studies of the influence of moisture (Scoville and Peleg, 198 1; Moreyra and Peleg, 1981) and of flow conditioners (Hollenbach et al., 1982; Hollenbach and Peleg, 1983) on the flowability of different food powders. The compression behaviour of powders in the low pressure range, for instance, may be used to evaluate cohesion. For food powders, the equation (see also Peleg, 1977)

at, = ~,,o + b 1% ~1~0 (23)

is well proven, where pb and pbo are the bulk density at pressure p, and the reference pressure p,, (p, = ambient pressure), respectively; b is a constant called ‘compressibility’. There is a clear correlation between b and the cohesiveness. Powders showing a high compressibility have poor flowing properties. The change in loose bulk density may also serve as a measure of the effectiveness of anticaking agents, for example (Hollen- bath et al., 1982). This is explainable physically from the influence of interparticle adhesion on porosity or bulk density as mentioned above. If quantitative information regarding flowability is required, however, shear tests are necessary.

ACKNOWLEDGEMENT

Many of the results reported in this paper were obtained within framework of research projects which were kindly supported by Deutsche Forschungsgemeinschaft, Bonn.

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the the

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food particle technology. part i: properties of particles

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