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Figure 19. The Washburn Test for measuring wetting dynamics.

The effect of fluid penetration rate and the extent of penetration on granule size distribution from drum granulation experiments is illustrated in Fig. 20 (since no example for fluidized bed granulation is available). From Fig. 20, it is clear that for fluids with a similar extent of penetration, increasing the penetration rate increases the average granule size for various levels of liquid loading.

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Table 4. Summary of the Effects of Operating Parameters on Wetting in the Granulation Process

In general, adhesion tension should be maximized from the point of view of increasing the rate and extent of both binder spreading and binder penetration. Maximizing adhesion tension is achieved by minimizing contact angle and maximizing surface tension of the binder solution. These two aspects work against each other, as surfactant is added to a binding fluid, and in general there is an optimum surfactant concentration which must be determined for each formulation. In addition, surfactant type influences adsorption and desorption kinetics at the three-phase contact line. In general, the major variable to control adhesion tension is surfactant concentration.

Decreases in binder viscosity enhance the rate of both binder spreading and binder penetration. The prime control over the viscosity of the binding solution is through binder concentration. Therefore, liquid loading and drying conditions strongly influence binder viscosity. In general, however, the dominantly observed effect is that lowering the temperature lowers the binder viscosity and enhances wetting. It is possible that the opposite takes place, since binder viscosity should decrease with increasing temperature. However, this effect is generally not observed due to the overriding effects of drying.

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Changes in particle size distribution affect the pore distribution of the powder. Large pores between particles enhance the rate of binder penetration whereas they decrease the final extent. In addition, particle size distribution affects the ability of the particles to pack within the drop as well as the final degree of saturation (Waldie, 1991). In general, pore distribution will not strongly affect surface spreading outside of the competing effect of penetration. (Fine particle size may, however, impede the rate of spreading through surface roughness considerations).

As a last point, the drop distribution and spray rate have a major influence on wetting. Generally speaking, finer drops will enhance wetting as well as the distribution of binding fluid. The more important question, however, is how large may the drops be or how high a spray rate is possible. The answer depends on the wetting propensity of the feed. If the liquid loading for a given spray rate exceeds the ability of the fluid to penetrate and spread on the powder, maldistributions of binding fluid will develop in the bed. This maldistribution increases with increasing spray rate, increasing drop size, and decreasing spray area (e.g., due to bringing the nozzle closer to the bed or switching to fewer nozzles). The maldistribution will lead to large granules on the one hand and fine ungranulated powder on the other. In general, the width of the size distribution of the product will increase and the average size will generally decrease.

3.3Granule Growth Kinetics

It will be assumed for the present considerations that sufficient binder is present in the granulator as determined by the binder/powder ratio and that the binder is appropriately spread on enough granular surfaces so as to ensure that most random collisions between particles will occur on binder-covered areas. It will also be assumed that the particles are more or less spherical having a characteristic dimension, a. The simplified system of two colliding particles is schematically shown in Fig. 21. The thickness of the liquid layer is taken to be h, while the liquid is characterized by its surface tension γ and its viscosity μ. The relative velocity U0 is taken to be only the normal component between particles while the tangential component is neglected.

As the two particles approach each other, the first contact will be made by the outer binder layers; the liquid will subsequently be squeezed out from the space between the particles to the point where the two solid surfaces will touch. A solid rebound will occur based on the elasticity of the surface

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Strength of a Pendular Bridge. The system of two particles connected by a liquid bridge is presented in Fig. 22; this is essentially the picture of the two particles in Fig. 21 after the liquid bridge is formed and liquid is being squeezed out from the intergranular space. The distance between particles is taken to be exactly 2h, while the volume of the bridge is uniquely determined by a filling angle, φ, as shown. It was demonstrated by many researchers (a summary of pertinent work in this area is given in Ennis et.al., 1990) that under fairly general conditions the total force, F, induced by the bridge can be calculated from the summation of two effects: a surface tension contribution proportional to the bridge volume or the filling angle and a viscous contribution dominated by the relative velocity. The superposition of solutions gives fairly accurate results and this can be expressed analytically by

where Ca = μU0 /γ, is the so called capillary number, ε = 2h/a is a dimensionless distance, and C0 is the Laplace-Young pressure deficiency due to the curvature of the free surface of the liquid. The first term on the right hand side is the viscous contribution which, in dimensional form, becomes

while the second term is the so called capillary force

It is important to note that the viscous force is singular in the separation distance h and hence will predict infinite large forces at contact. Since this is physically impossible, a certain surface “roughness” has to be assigned to the granular surface as is shown in Fig. 21 where this parameter is assigned the value ha; this prevents particles from “touching.”

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Figure 22. Pendular liquid bridge between two spherical particles. (From Ennis, et al., Powder Technol., 65:257–272, 1991, with kind permission from Elsevier Science S.A., P.O. Box 564, 1001 Lausanne, Switzerland.)

Conditions of Coalescence. The outcome of the collision of two binder-covered particles is determined by the ratio of the initial kinetic energy of the system and the energy dissipated in the liquid bridge and in the particles. This can be expressed analytically by the definition of a so called Stokes number, St

St = (initial kinetic energy)/(dissipated energy)

where ρp is the particle density and m is the mass of the particle. Particle trajectory calculations show (Ennis et al., 1991) that if the Stokes number defined above is smaller than a critical value, St < St*, collisions are effective and coalescence occurs while if St > St* particles rebound. One has to note that μ in the above equation, can be taken to be the binder viscosity or an equivalent viscosity of the granular surface as explained in the previous