## Coalescence of agglomerates

In the literature it is generally agreed that successful coalescence of agglomerates occurs only when the agglomerates have excess surface liquid, making the surface plastically deformable. Surface plasticity is also required to round the resulting larger agglomerate. The excess surface liquid is supplied during the liquid addition phase of the process or, in the subsequent wet massing phase, by liquid forced onto the agglomerate surface by consolidation.

According to the analysis by Ouchiyama and Tanaka (1982) of the coalescence mechanism, the probability for a successful coalescence between two colliding agglomerates is size dependent. Because of the mass and, hence, the kinetic energy of the colliding agglomerates, there must be an upper size limit beyond which coalescence is impossible. Ouchiyama and Tanaka derived the limiting agglomerate size 6:

where A and a are constants, ac is the compressive strength and A" is a parameter expressing the deformability of the agglomerate. Coalescence of particles larger than 5 will not occur because the separating forces due to the kinetic energy exceed the binding forces. This corresponds to the situation described by Ennis etal. (1991) where the Stokes' number StD in equation 9 exceeds the critical number because of increasing particle mass. Kristensen etal. (1985b) suggested that a high value of 5 is associated with a high probability of achieving coalescence at random collision and, hence, a high growth rate.

The parameter K of equation 10 is related to compression force P acting between the two agglomerates and the area of contact As; K = As/P. For a small deformation of length A/ of a sphere, the area of contact is approximately As = icDAl/2, where D is the diameter of the spherical agglomerate. Hence, K can be expressed as:

The compressive strength of the agglomerate equals the crushing force divided by the projected area of the agglomerate, i.e. oc = 4P/ (irD2), c.f. equation 6. Inserting this equation and equation 11 into equation 10 and rearranging gives (Kristensen etal., 1985b):

Oc where A{ and a are constants and Al/D is the normalized strain of the agglomerate caused by the compression force P.

Equation 12 expresses the effect of agglomerate deformability upon the rate of growth by coalescence and presents the physical prerequisites for granule growth. The numerator expresses the strain produced by impact. As discussed earlier in the section on strain behaviour, the strain depends primarily on the packing density of the particles and the liquid saturation. Significant strain arises when the liquid saturation is increased to the limit where the cohesive strength of the agglomerate is governed by the strength of mobile liquid bondings as expressed by equation 5. The denominator of equation 12 can, therefore, be substituted by the tensile strength a, (equation 5).

Equation 12 predicts that a reduction of the particle size reduces the rate of growth by coalescence because of the effect of particle size on ac and a,. It can be compensated for by increasing the liquid saturation so that the strain behaviour is improved. The effect of improved strain will, according to equation 12, overrule the counteracting effect of the tensile strength because the normalized strain Al/D in the equation is raised to its third power. This can be achieved by increasing the amount of granulating liquid and/or increasing the consolidation of the agglomerates. This agrees well with the general experience that the finer the particles of the starting materials, the greater the amount of binder liquid required for efficient granulation.

The main implication of equation 12 for agglomeration processes is that the rate of growth by the coalescence mechanism is controlled primarily by the liquid saturation S given by the expression:

where H is the moisture content (humidity on dry basis) and p is the density of the solid. The equation assumes that the particles are insoluble in the liquid, and that the liquid has unit density.

Equation 13 shows that the liquid saturation is controlled by the amount of liquid phase present in the moistened powder and the porosity of the agglomerates. Because of the effect of the liquid saturation on agglomerate growth, consolidation of agglomerates during the process must have a pro-

f 600

2 300

25 30 35

% v/v Binder solution

Fig. 11 Effect of binder solution upon granule growth in the liquid addition phase of granulation of calcium hydrogen phosphate in a Fielder PMAT 25 high shear mixer. Aqueous binder solutions: Kollidon 90, 3% (■); Kollidon VA64, 10% (O); Kollidon 25, 3% (□); Methocel E5, 3% (A); Methocel E15, 2% (A). Reproduced with permission from Ritala et al. (1988), Drug Dev. Ind. Pharm. 14, 1041-1060, Marcel Dekker Inc. USA.

### 25 30 35

Fig. 11 Effect of binder solution upon granule growth in the liquid addition phase of granulation of calcium hydrogen phosphate in a Fielder PMAT 25 high shear mixer. Aqueous binder solutions: Kollidon 90, 3% (■); Kollidon VA64, 10% (O); Kollidon 25, 3% (□); Methocel E5, 3% (A); Methocel E15, 2% (A). Reproduced with permission from Ritala et al. (1988), Drug Dev. Ind. Pharm. 14, 1041-1060, Marcel Dekker Inc. USA.

nounced effect upon the growth rate. This is important, especially for wet granulation in high shear mixers where the intensive agitation may give rise to a pronounced densification of the agglomerates. Jaegerskou etal. (1984) found that the intragranular porosity of calcium hydrogen phosphate (dgw = 14 (¿m) was reduced steadily in the wet massing phase reaching a final value of about 20%. In contrast, granulation of the less cohesive lactose (dgw = 52 fim) showed that the final granule porosity was achieved early in the wet massing phase.