Coagulation of microcrystalline cellulose dispersions

Coagulation of Microcrystalline Cellulose Dispersions ROBERT EVANS ! AND PHILIP LUNER Empire State Paper Research Institute, College of Environmental Science and Forestry, Syracuse, New York 13210 Received January 14, 1988; accepted May 13, 1988 The effect of particle shape on some aspects of the coagulation behavior of rod-like microcrystalline cellulose (MCC) dispersions is discussed. It is shown, by means of elementary DLVO theory and an ad hoc approximation for the angular dependence of the interaction between rod-shaped particles, that the torque between two MCC particles in a coagulating dispersion does not significantly affect their relative orientation during a Brownian collision. The effect of particle shape on the process of floc growth and syneresis in a turbulent field is qualitatively described. Experimental evidence indicates that prolonged conditioning in a turbulent field results in alignment of primary particles and the evolution o f strong, cuspidate MCC floes with a narrow size distribution. © 1989AcademicPress,Inc. INTRODUCTION

Microcrystalline cellulose (MCC) dispersions have been used as models for cellulosic waste water systems and fines (1) and for studying the general colloidal behavior of dispersions of rods (2). The most commonly used MCC is Avicel (FMC Corp.). The purpose of this study was to explain some of the observed coagulation behavior of MCC (e.g., Refs. (1, 3 )) using the theory of colloidal stability and taking into account the geometry of the partides. Most investigators (e.g., Refs. (1, 4, 5)) have calculated interaction potentials in cellulosic dispersions assuming plate-plate or spheresphere geometry, precluding explanations of effects due to the observed (3, 6) rod-like shape of the particles. Our mathematical treatment will be confined to the special case in which the interaction force and torque between cylindrical particles are greatest, i.e., collision perpendicular to their long axes and along their line of centers. This will allow a simple assessment of the maximum extent to which random diffusion can be perturbed by the inCurrent address: Commonwealth Scientific and Industrial Research Organisation, Division of Forestry and Forest Products, Melbourne, Victoria 3168, Australia.

terparticle forces during pairwise interaction. The analysis of the initial stages of MCC coagulation is applicable also in a turbulent field because turbulence can generally be neglected on a scale less than the order of a micrometer (7). EXPERIMENTAL

The MCC dispersion was prepared by shearing Avicel PH101 (20 g) in distilled water (180 ml) in a Waring blender for 10 min, diluting under agitation to 2 liters, and allowing the suspension to settle in a refrigerator at 10°C for 10 days. Part of the supernatant dispersion (500 ml) was decanted for use and the sediment discarded. The mean aspect ratio,/3, for the particles in this dispersion was estimated by electron microscopy to be ca. 20 and the mean radius, a, ca. 10 nm. Effective fioc volumes were determined with a Coulter Model TA II counter and 0.15 mole din-3 sodium chloride solution as the conductive medium. Floc conditioning in 0.15 mole din-3 sodium chloride solution was carried out in a l-liter jar fitted with four baffles; turbulence was generated with a fiat paddle stirrer driven by an Electrocraft E550-003 dc motor and E550-M controller.

464 0021-9797/89 $3.00 Copyright© 1989by AcademicPress,Inc. All rightsof reproductionin any formreserved.

JournalofColloidand InterfaceScience, Vol, 128,No. 2, March 15, 1989

465

COAGULATION OF CELLULOSE DISPERSIONS GEOMETRY

The pairwise interaction geometry to be considered is shown in Fig. 1. Interactions between cylindrical or prolate ellipsoidal particles have been studied by many authors (e.g., Refs. (8-18 )). Throughout the development of the theory of colloid stability, it has been found necessary to introduce various assumptions to simplify the derivation of the interaction equations; this work is no exception. There are no analytic solutions which accurately describe these interactions at both small and large interparticle separations, for both short-range and long-range forces and, in the case of anisotropic particles, at all mutual orientations. One problem we have addressed is the estimation of the maximum extent to which interparticle forces might be expected to align rod-like MCC particles during a Brownian collision. Such an estimate requires, among other things, knowledge of the mutu~il torque which is calculated from the angular dependence of the interaction potential. Brenner and Parsegian (9) have introduced a factor 1 /sin 0 into the electrostatic interaction equations

for crossed thin cylinders to allow for changes in the mutual angle 0 between infinitely long cylinders. Although inappropriate at very close approach and, for finite cylinders, as 0 approaches zero (8, 9), this factor at least reflects the anisotropic nature of the interaction. Expressions have also been published for the van der Waals interaction between inclined thin cylinders (12). None apply to finite cylinders for all separations and mutual angles. For the purposes of the present investigation a simple expression for the interaction energy, V, between cylinders which approximates the angular dependence over the full range of 0 (0 to ~'/2) is required. Continuous functions which exhibit the following properties are sought: (i) V-~ VJsin 0 as 0 --~ 7r/2, (ii) OV/O0 --~ 0 as 0 --~ 7r/2, (iii) V--~ Vp as 0 --~ 0, (iv) OV/O0 --~ 0 as 0 --~ 0, and (v) Vshould vary much more rapidly near 0 = 0 than near 0 = ~r/2. Two examples of many possible functions which satisfy all of these conditions are

I I

V = Votanh RO / sin 0

[ 1]

R = VplVc,

[21

where 2~

./

/

/ ,/

,/

/

//,/ / //"/'/

'~-÷ ~

and an incomplete elliptic integral of the first kind (19), Vc V = ~ - FZ(~b\a)

v~[fo~

= "-7 q5 I

FIG. 1. Interaction geometry for model cylindrical microcrystalline cellulose particles of diameter a and aspect ratio B. The reduced minimum surface separation (based on particle radius) is ~ and the angle between the long axes of the particle pair, projected along the line of centers, is 0. Collision is assumed to occur only at the particle midpoints.

dz

]~,

(1 - sin2asin2z)'/2J

[3]

where a = r / 2 - 0 and ~b is determined by the limiting value of F(4~\a) at 0 = 0 (19), F(~b\Tr/2) = In t a n ( r / 4 + ~ / 2 ) ;

[4]

therefore

4~ Journal of Colloid and Interface Science,

+

[51

Vol. 128,No. 2, March 15, 1989

466

EVANS AND LUNER

=

-~

In c o t ~ ,

[6]

Vrc = 41ratff2exp ( - ×a3) exp(-×ar)

where ~ = ~-/2 - ~b. When R >> 1 these equations can be simplified by series expansion and truncation to give ~ (or ~b) directly:

Vw = 4(Tr×a)l/2~ae~Z (1 + 3/2) 1/2 Rr =/3[~r( 1 ~a

],/2

+ 312)1

), = 2 exp

-

.

[7]

AS our conclusions were unaffected by the choice of either of the above ad hoc expressions for V, we shall confine the remaining discussion to the simpler Eq. [ 1] which will be used to estimate the force and torque between pairs of interacting MCC particles.

"

[81 [9]

[lO]

Equation [9] is a simplification of those given by Spaarnay (8) and by James and Williams (17). The van der Waals attraction equations chosen are the simplest possible examples derived by the Deryagin method, which overestimates the attraction at large separation: H 63

v.~ = -

--

V~p =

1263/2

[11]

INTERACTION t~H

It is apparent from the above equations that the ratio, R, of the interaction between parallel and crossed (perpendicular) cylinders is central to the analysis. Selection of appropriate expressions for the interaction energies Vac, Vav, Vrc, and V~o must be guided by the requirement that Ra and Rr be reasonable functions of interparticle separation. Ideally, both R~ and R~ should decrease monotonically with increasing separation and asymptotically approach unity. Many published interaction expressions do not give reasonable R functions owing to differing or restricted ranges of applicability. For some combinations of Vp and Vc, R increases with separation; for other combinations R is constant or approaches zero. Clearly, such behavior is artifactual. Rather than dwell on each of these cases we shall simply state the interaction expressions chosen for use in our analysis and emphasize that they satisfy the need for a reasonable form for Ra and Rr over the separation range of interest. This situation is far from satisfactory but will improve with the development of more tractable and consistent formulae for the interactions between anisotropic particles. The electrostatic repulsion expressions chosen for crossed and parallel cylinders (linear superposition approximation) are Journal of Colloid and lnteoCace Science, VoL 128, No. 2, March 15, 1989

Ra = 231/2 •

[12]

[13]

H was calculated by the methods of Parsegian and Weiss (20) and of Hough and White (21). The refractive index of cellulose I crystals has been given as 1.584 by Hermans (22). A Cauchy plot (21 ) based on this refractive index together with the dielectric data published by Freeman and Preston (23) gave an effective UV resonant frequency of 19.7 × 10 ~5tad s -~, or 13.0 eV. The resonance bandwidth was arbitrarily chosen to be 2.0 eV. It has been demonstrated (24) that the effective dielectric constant of cellulose can be greatly increased by water. Although the extent to which this applies to MCC particles is unknown, the fact that they are not perfectly crystalline indicates that some swelling by water is possible. Consequently, the zero-frequency contribution to the electrodynamic interaction may be much smaller than that for dry cellulose across water (ca. 0.5 kT). Electrolyte would further reduce this contribution. We have therefore chosen not to include the zero-frequency term in the summation. Neglecting retardation and the possible ef-

C O A G U L A T I O N OF CELLULOSE DISPERSIONS

fect of water on particle refractive index, we found a value of H = 2.4 kT for cellulose I across water. The effect of the dielectric anisotropy (11) of the cellulose crystals was not significant; the value of H for perpendicular crystals is only ca. 7% less than that for parallel crystals. The distance dependences of Ra and R r a r e shown in Fig. 2, and V/Vc as a function of 0 for varying values of R is shown in Fig. 3. When R = ~ , the relationship reduces to V/ V~ = I / s i n 0 as required. Superposition of the attraction and repulsion terms and inclusion of the estimate of angular dependence described above gives the total interaction potential between particle pairs:

t

i

i

I

I

467 i

l

I

I

I

I

I

I

I

v_ 6 4

2

0

I

20

40

60

I

80

6/deg FiG. 3. Angular dependence of V/Vc for varying values of R (from Eq. [l]). The value of R for each solid line is equal to the intercept of that curve with the ordinate (0 = 0). The broken line is for R = ~ , at which Eq. [ I] reduces to V/Vc = 1/sin 0.

V = [V,~ × tanh R,O + V,c X tanh RrO]/sin O. [14] It has been found (1) that the critical coagulation concentration of sodium nitrate for MCC dispersions prepared in our laboratories is ca. 2.4 X 10 -4 mole dm -3. Figure 4 is the theoretical stability diagram for crossed and parallel MCC particles in water at the critical coagulation concentration. The curves are arbitrarily terminated at 6 = 0.1 (1-nm separation). Calculations for very small separations are not accurate for several reasons; e.g., (i) Surface roughness and hydration are neglected.

(ii) The use of the zeta potential as the stability-determining potential becomes suspect when the separation of the "planes of shear" no longer approximates the surface separation. (iii) The continuum theory of van der Waals forces breaks down when the surface separation is of the order of molecular dimensions (25). (iv) The dielectric properties close to the interface between the medium and the particles are different from those of the bulk substances and would increase in importance with decreasing particle separation.

I - -

I ~ l l l

I

I I I|1111

[

I'l

Illl

15

I I 1111

10 15

8-0

V kT 5

10 0

-5 0.1 I

0.1

I

L IIIIIl

l

1

I

I IIII

10

8 FiG. 2. Energy ratios Ra and Rr as functions of reduced surface separation & From Eqs. [ 10 ] and [13 ] with/3 = 20 and ~a = 0.5.

li" $

FIG. 4. Stability diagram for MCC particle pair at the critical coagulation concentration of sodium nitrate (2.4 X 10 -4 mole din-3). The two curves represent the extremes with respect to mutual angle, 0. ×a = 0.5; 4' = 14 mV; H = 2.4 kT;/3 = 20. Journal of Colloid and Interface Science, Vol. 128, No. 2, March 15, 1989

468

EVANS AND LUNER

For this model no significant secondary minimum (3) exists even when the particles are parallel and overlap their full length. Again we point out that the simple van der Waals attraction expressions chosen for the analysis significantly overestimate the attraction in the region of a secondary minimum, owing to the use of the Deryagin approximation and the neglect of electrodynamic retardation and other factors. Explanations of the high sensitivity of MCC toward electrolyte (1, 3 ) on the basis of the secondary minimum aggregation are therefore not supported by these results. Ease of redispersion is more likely to be due to coagulation into shallow primary minima such as that evident in Fig. 4 (curve 2). However, for reasons enumerated above, the depth of primary minima cannot yet be predicted accurately. Depending on the angle between the particles, the potential barrier to approach lies between about 2.5 kT and about 14 kT; particles which approach with their axes close to parallel will not be able to coagulate. Although the potential barrier may prevent coagulation in the parallel configuration (curve 1, Fig. 4), rotational Brownian motion allows the particles eventually to approach in the crossed configuration for which the barrier is much smaller (curve 2). The stability-determining dimension is therefore the minimum dimension (i.e., the rod diameter), and the length of the particles, in this context, is of relatively minor significance. Indeed, the particles will tend to rotate toward the perpendicular configuration. A particle pair following curve 2 will reach the point where curves 1 and 2 intersect. The minimum energy path then becomes curve 1 and there will be a tendency for the pair to rotate toward the parallel configuration. Rotational relaxation of the panicles, if unhindered, would eventually cause the panicles to become parallel. However, for reasons discussed in the next section, total alignment after coagulation may not be possible. Slow coagulation cannot easily occur in the parallel orientation and the ease of repeptization (by agitation) of MCC (1, 3) can be Journal of Colloid and Interface Science, Vol. 128, No. 2, March 15, 1989

cited as evidence against the particles' rotating to the parallel orientation after coagulation. MCC can be coagulated with dilute acid and then redispersed by washing with distilled water. According to our model, redispersion is possible only if most of the particle pairs do not become parallel. The coagulation geometry of the real MCC dispersion is more complex than that of our model system. Most collisions would be off center and the energy difference between the parallel and crossed configurations would be less than that indicated above. In addition, the rate of approach of two rod surfaces would include a component due to rotational motion. ROTATIONAL RELAXATION DURING RAPID COAGULATION The purpose of the remaining sections is to outline some of the consequences of particle shape with regard to the rapid coagulation behavior of MCC. At first, it may seem that the MCC particles should coagulate entirely parallel to each other since this is by far the most energetically favorable configuration (Fig. 4 ). However, during a Brownian encounter, the rotational relaxation rate of the particles may be too slow to allow alignment before collisions with other particles produce a relatively rigid floc structure. Four factors which need to be considered during the encounter of two nonspherical particles are (i) translational diffusion, (ii) rotational diffusion, (iii) interparticle torque, and (iv) interparticle force. As the particles approach, interaction forces perturb translational and rotational Brownian motion. In the absence of interparticle forces, the mean-square reduced distance and angle through which each particle moves in time t are given by (26)

469

C O A G U L A T I O N OF CELLULOSE DISPERSIONS

2 kTt a 6 2 = 2---~T a

[151

2kTt A02 = ~

f.

[16]

d6 a~ =

2 OV afT 06

dO dt

20V fR O0 '

[17]

[181

[20]

[23]

as

V=

H 66 sin 0

[24]

(given by [11] to [14] with Vr = 0 and/3 = oo ), then

dO d--~ = Q6 cot 0

[25]

which, after integration, gives Q 2f - 62)]. cos 0 i - cos 0f = exp[~-(6

2.28

[21]

The approximation is good in the range 10 -,-
[26]

When the final angle 0r and final separation 8f are chosen as zero (i.e., maximizing the effect of torque on the angular perturbation), we find [271

COS 0 i = e x p / T ) .

After series expansion and truncation (0i ~ lr/ 2, Q6.2,/2 ~, 1),

Oi ~ Qt/26i,

These coefficients will be required only in the dimensionless ratio:

2/3¥0.5

ov / ov

In general this must be solved numerically; but for a very simple interaction potential such

[19]

8~rna3/3 fR = 3(ln 2fl -- 0.5)

3 [ln2/3-0.5]

dO

[-Qr?\

8~rna/3 In 2/3 + 0.5

[22]

Thus the rms angular diffusion rate for particles of aspect ratio 20 is ca. 4.3 ° for an rms translational diffusion distance of one particle radius. Considering interparticle force and torque in the absence of diffusion, [ 17 ] and [ 18 ] give d---~= Q 00 / 06 "

where the interaction potential Visa function of both ~ and 0 (Eq. [ 1] ), Although the particles are much more likely to collide asymmetrically, interparticle force and torque are greatest for the case in which the rods collide at their midpoints. Restriction of the analysis to this special case allows an estimation of the maximum perturbing influence of interparticle torque on collision angle. An incidental computational benefit is that the contribution of rotation to the rate of approach of the rod surfaces can be neglected. ThereforefT becomes the translational friction coefficient for motion perpendicular to the direction of the long axis of a particle, and the appropriate friction coefficients for our model system are (26, 27)

a2fT

AO = Q1/2 A6 ~ ~-~ &brad.

'

where fT and fR are the translational and rotational hydrodynamic friction coefficients. According to Stokes' law, the mutual translational and rotational velocities due to interparticle force and torque are (26)

fT =

The relative effect of rotational and translational diffusion is found by eliminating t from [15] and [16],

[28]

which has the same form as the result based on diffusion alone. Returning to the general expression [ 23 ], we require the partial differentials of [ I ] with respect to 6 and 0:

ov

(

aR

06 = V 2 0 - ~ c s c h 2 R 0 + ~

l OVc

06 ]

[29]

Journal of Colloid and Interface Science, Vol. 128,No. 2, March 15, 1989

470

EVANS

OV - - = V ( 2 R csch 2RO - cot 0). O0

AND

[30]

F r o m [ 21, dR R{ 10Vp d7 = 08

[31]

vc 6 6 1 '

therefore dO d6

1

2 R csch 2RO - cot 0 Q

+

=a

[

2O(~-~-/-d-~-cs-~--~O-----

'l

[32]

(i/v~)(avdaa)j

G/O - cot 0

(GlV~)(av~/aa) + [(l - G)IVd(avda6)

[33]

G = 2RO csch 2RO.

[34]

where

Specific derivatives o f interest, based on Eqs. [8] to [131, are i av~o Vrp O~

1 2(2 + tS)

[35]

1 OV~0 Yrc 6q¢~

dR~ = d6

[36]

# 4

[~(1 -~/2)3J ×a ],/2

LUNER

W h e n / 3 --* 0, P --~ 0 and dO~d6 -+ Q6 cot 0 as required (see Eq. [ 25 ] ). Equation [41] was solved using a fourthorder R u n g e - K u t t a technique by starting from a range o f 8 and 6 near zero and allowing the particles to retrace their trajectories as if the sign o f the interaction potential had been reversed; the simulation was terminated when the interparticle energy fell to - 1 kT. The greatest angular change occurred when the initial value for 8 was ca. 6 ° (Fig. 5 ); i.e., two particles starting f r o m a separation of ai = 2.5 will, under the influence o f van der Waals attraction alone, rotate relative to each other a m a x i m u m o f about 2.7 ° ( f r o m 6 ° to 3.3 °) before colliding. This is only about one-quarter o f the rms angular change to be expected from Brownian diffusion alone. Use o f m o r e accurate expressions for the v a n der Waals attraction and introduction o f electrodynamic retardation lead to even smaller effects (i.e., m a x i m u m perturbation o f less than 1 o). T h e principal conclusion to be drawn is that pair-

-A~eg 3\

~

~

.

[37] i

1 av.p = _ 3 Vao 06 26

1 OVal= Vac 08

[381

1

[391

6

dR a=_ #__#_ d6

i

483/2 "

U n d e r the conditions of rapid coagulation, the repulsion is virtually zero so that we m a y equate the interaction with the van der Waals attraction. F r o m [33], [38], and [39], dO 2 Q 6 [ O c o t O - P ] d-'a = 0 2-~P

'

[41]

where

#o

I

[40]

#o

P = ~-777 csch aw z .

[42]

Journal of Colloid and Interface Science, Vol. 128, No. 2, March 15, 1989

0

1

2

12

3 o~

FIG. 5. Perturbation of the angle, 0, between two MCC particles due to the action of interparticle torque during a collision under the influence of van der Waals attraction and hydrodynamic friction (Eq. [41] with/3 = 20). Rapid coagulation conditions apply: electrostatic repulsion energy is zero• The initial angles, 0~, and initial separations, 8i, are determined by the particle pair configurations for which the interaction energy is equal to - 1 kT. At lower energies it is assumed that thermal diffusion dominates.

COAGULATION

OF CELLULOSE

wise collisions, under the infuence of van der Waals forces alone, do not result in significant alignment of MCC particles in our model system, particularly as the analysis pertains to the case in which the effect of interparticle torque is greatest. Although H cancels out in [ 41 ], its magnitude determines the integration range. A larger value for H would allow angular perturbation to commence earlier in an encounter. What happens after collision depends more strongly upon H because relative translation has ceased. Interparticle friction, thermal energy, and particle concentration also influence the fate of the doublet; for example, ifinterparticle friction and particle concentration are both sufficiently high then collision of the doublet with other primary or multiple particles would prevent further rotational relaxation, giving a very open floc structure. Only the rapid coagulation behavior of MCC has been evaluated here. Slow coagulation was not considered as it is evident from Fig. 4 that a potential barrier favors collisions between inclined particles over those between parallel particles. After the barrier has been surmounted, the interparticle torque has a very short distance within which to align the particles; consequently, for slow coagulation, alignment during a Brownian collision should be even less than that for rapid coagulation. The effect of the weak interparticle repulsion is to selectively allow more collisions in the crossed configuration than in the parallel configuration. Van der Waals attraction alone has no significant effect on the collision geometry. COAGULATION

IN A TURBULENT

FIELD

Figure 6 is a phase-contrast photomicrograph (polarized light) of a cluster offlocs from a coagulated MCC dispersion which was conditioned by stirring in 0.15 mole dm-3 sodium chloride in a balled vessel for 48 h at an rms shear rate of 600 s -z. Individual flocs are shown in Figs. 7 and 8. Freshly formed MCC flocs (not shown) appeared to be unstructured and very irregular in size and shape. Examination of these conditioned flocs with a Coulter counter showed that prolonged tur-

DISPERSIONS

471

bulence greatly increased floc strength and narrowed the floc size distribution. Floc size was not significantly affected by subjecting the conditioned system to a shear rate of 1000 s -1 for 2 min. Normalized, smoothed distributions before and after treatment are compared in Fig. 9. The volume polydispersity (i.e., ratio of volume-average to number-average floc volume) was found to have decreased from 2.2 to 1.4. The polydispersity figure for fresh Avicel foes is greatly underestimated because the Coulter counter breaks down large weak floes during the measurement process and individual floc volumes below the resolution limit are either undetected or, if simultaneously present in the detection volume, recorded as the sum of their effective volumes. Microscopic examination indicated a very wide size distribution for unconditioned flocs. The shear conditioned flocs, however, were not disrupted during measurement and probably gave a realistic size distribution. Note that the Coulter counter detects only the nonconducting floe volume (cellulose); we estimate that cellulose occupies only about 3% of the apparent volume of the flocs shown in the photomicrographs. Narrowing of the size distribution may be explained by floc growth to the lower size limit of turbulent eddies (7), together with disruption of large floes. Floe strengthening is explained by alignment (rotational relaxation) of MCC particles and by an increase in the number of interparticle contacts, under the influence of external forces. The formation of cusps is taken to be evidence of particle alignment although the extremely low floc density referred to above may explain why the conditioned flocs, and the cusps in particular, did not exhibit significant optical birefringence. Dried from water, however, the floes collapsed to branched birefringent filaments. One of these dried flocs can be seen at the bottom of Fig. 6. Freshly coagulated Avicel exhibited no visible birefringence when dried from water. It was noted that cusps also formed to a small extent in coagulated MCC left undisJournal of Colloid and Interface Science, Vol. 128, No. 2, March 15, 1989

472

EVANS AND LUNER

F16.6. Phase contrast, polarized light photomicrograph of a cluster of MCC flocs conditioned in 0.15 mole dm-3 sodium chloride at 600 s -~ for 48 h. At the bottom of the figure is a dried floc exhibiting strong birefringenceand a branched structure.

turbed in 0.15 mole d m -3 s o d i u m chloride solution for several weeks, i n d i c a t i n g that hindered rotational relaxation occurs slowly u n der the influence of B r o w n i a n m o t i o n . Journal of Colloid and Interface Science, Vot. 128, No. 2, March 15, 1989

I n view of the above analysis a n d the Coulter c o u n t e r a n d light microscope observations, we can speculate o n the course o f events w h e n a n M C C dispersion rapidly coagulates i n a

COAGULATION OF CELLULOSE DISPERSIONS

473

FIG. 7. Same as for Fig. 6, single floc. turbulent field. The rapidity and poor reversibility of coagulation result in the formation offlocs which are not in the m i n i m u m energy state. For example, an unstable system of monodisperse rods would be in a m i n i m u m energy configuration when parallel and packed

in a hexagonal array. In a real system, we visualize the following sequence of events: (i) Pairs of rods collide at angles which are only slightly biased toward zero. (ii) Before rotational relaxation has a sigJournal of Colloid and Interface Science, Vol. 128, No. 2, March 15, 1989

474

EVANS AND LUNER

FIG. 8. Same as for Fig. 6, single floc.

nificant effect, further coagulation forms open structures of three or more particles. (iii) These structures coagulate with each other to form three-dimensional networks of rods. Friction prevents rapid alignment of the rods. (iv) In a turbulent field the networks collide and grow to a limiting size which is determined by the scale of turbulence and the interpartiele forces.

(vii) Multiple making and breaking of interfloc contacts in addition to interaction with small eddies provide the energy needed to overcome internal friction and allow rotational relaxation. Such internal rearrangement eventually results in strong flocs which are no longer disrupted by the turbulent field, or even by a field much more intense than that used for conditioning.

(v) Further collisions result in flocs too large to be stable under the action of the turbulent field; therefore they are pulled apart soon after they adhere.

(viii) Protrusions formed by rupturing floc doublets become the most likely parts to make contact in subsequent collisions, resulting in the eventual formation of highly cuspidate flocs.

(vi) Flocs slightly larger than the minimum stable size appear to be more likely to break into two roughly equal parts than into very different sized parts, thereby decreasing polydispersity.

Syneresis has been discussed by Yusa (28) in terms of random fluctuations in hydrostatic pressure at the floc surface. Although a similar mechanism may be active in the ease described above, it appears that the evolution of these

Journal of Colloid and Interface Science, Vol. 128, No. 2, March 15, 1989

COAGULATION OF CELLULOSE DISPERSIONS I

l

I

I

475

allel) configurations, producing the observed cusps and the large increase in floc strength.

I

APPENDIX: NOMENCLATURE

//

/

l/Ill 2

5

I0

20

50

100

EFFECTIVE DIAMETER/tim

FIG. 9. Smoothed, normalized floc volume distributions

before (broken curve) and after (solid curve)conditioning in a turbulent shearfield.Theseare apparent distributions obtained with a Coulter counter (see text).

paucidisperse, cuspidate flocs is also a result of strong interactions between flocs. A study of the rate of floc evolution as a function of concentration would determine the relative importance of collisions and hydrostatic fluctuations. SUMMARY AND CONCLUSIONS The behavior of unstable MCC dispersions can be qualitatively explained when the rodlike shape of the particles is taken into account. It is shown that even in the most favorable case interparticle torque has little infuence on relative orientation during pairwise collisions in the first stage of coagulation. At sufficiently high particle concentrations, pseudo-random collisions may therefore result in the formation of networks of three or more rods in which potential energy is high but internal rearrangement is severely restricted by friction. After floc growth, turbulence supplies most of the energy required to overcome internal resistance by generating small eddies which interact with the floc surface and by repeatedly making and breaking interfloc contacts. Anisotropic mechanical syneresis probably occurs mainly in the regions of floc-floc contact where the MCC particles are drawn into energetically more favorable (approaching par-

a e f F G H k P Q R t T V z a

8 ,/ 0 X 4~

cylinder radius electronic charge hydrodynamic friction factor incomplete elliptic integral of first kind auxiliary parameter Hamaker function Boltzmann's constant auxiliary parameter dimensionless friction factor ratio ratio of parallel/perpendicular interaction energies time absolute temperature total interaction energy d u m m y variable modular angle of incomplete elliptic integral aspect ratio reduced surface separation dielectric permittivity of medium static viscosity of medium angle between major axes of particle pair inverse Debye length auxiliary parameter amplitude of incomplete elliptic integral stability determining potential

Subscripts a c R i r p T f

attraction crossed (perpendicular) rotational initial state repulsion parallel translational final state ACKNOWLEDGMENTS

The authorsthank the EmpireStateResearchAssociates for financial support. Journalof Colloidand InterfaceScience,VoL 128, No. 2, March

15, 1989

476

EVANS AND LUNER REFERENCES

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