Yang Fluidization, Solids Handling, and Processing

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uniformity and morphology are important when, for example, the coating is applied for a sustained release application.

Coating Mass Uniformity and Distribution. Basically, there have been two approaches to model the accumulation of mass (coating material) on the surface of bed particles; (i) the use of population balances and (ii) the probabilistic modelling of the spray-particle interaction. We will look at each of these approaches and see how it may be possible to combine these methods to give a fuller picture of coating performance.

Population Balance Approach to Modeling Coating. The population balance approach to modelling is ideally suited to processes in which the product and starting material have a distinct distribution of particle sizes, e.g., coating a wide size distribution of solids in a fluidized bed. The presentation of the equations describing the population balance for the coating process are taken from Randolf and Larson (1988) and Liu and Litster (1993a) and are given below

Equation (5) above relates the change of number of particles of a given mass (size) with the net growth rate G, the feeds and product streams into and out of the process ( Qk) and the net birth ( B) and death rates ( D) of the particles. A more complete formulation of Eq. (5) is given on a volume basis in Eq. (40) in Sec. 3.6, and will be used to describe granulation processes. For coating operations, we consider the situation of a batch process for illustration purposes. The development is more complicated for continuous operations, and the reader is referred to the above references for further information. For the case of batch coating processes, we have that Qk = 0, since there are no feed or product streams. Furthermore, we shall assume that the birth rate (B) and the death rate (D) due to coalescence, nucleation and breakage are both negligible. With these assumptions, Eq. (5) reduces to:

In order to use Eq. (6), it is necessary to know what is the initial mass (the measure of size used in Eqs. (5) and (6)) distribution of particles and the growth rate function, G.

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Liu and Litster (1993a) solved the set of equations given above and compared the number mass distribution predicted by the model with that observed experimentally. The comparison was reasonably good as shown in Fig. (4). It is worth mentioning at this point that the raw data of Liu and Litster (1993a) and Robinson and Waldie (1979) display a considerable amount of scatter, Fig. 5. The data in Fig. 5 shows that, for a particle of given mass, the amount of coating received varies considerably. For example, from Fig. 5(a) we can see that particles of original mass 4 g have an amount of coating added in the range of 0.7 g to 1.4 g. This variation in the coating amount for particles of the same initial mass cannot be predicted by the population balance approach as used by Liu and Litster (1993a), since their model is deterministic. Clearly, there appears to be a significant scatter in the data about the average value and in order to estimate the magnitude of this scatter, a stochastic or probabilistic model must be used. The level of scatter demonstrated in the experiments shown in Fig. 5 and other work can cause significant variation in the thickness of the applied coat, leading to significant variation in the functional behavior of the coat.

Probabilistic Approach to Modeling Coating. The concept that the amount of material coated onto identical particles, during a batch or continuous process, may vary significantly was first considered by Mann and Coworkers (1972, 1974, 1981 and 1983). For a batch process, Mann (1983) considered the movement of particles in a fluidized bed coater to be a renewal process. As each particle passes through the spray zone (see Fig. 3), it receives a small mass of coating, x. The total amount of coating received is the sum of all the discrete additions received over the course of the process. Thus, the total mass of coating that a single particle receives is given by:

If we consider different particles, we can see from Eq. (11) that the variation in the total amount of material deposited on each particle is a function of the number of times the particle passes through the spray zone, N, and the amount of material that it receives in each pass, x. Since both x and

N vary, we expect that Xtotal will vary between particles in the same batch. Mann (1974) has shown that for a batch coating process in which the

operating time is greater than about 20 times the average circulation time,

Figure 4. Number mass distribution of particles. (From Liu and Litster, Powder Technol., 74:259–270, 1993, with kind permission from Elsevier Science S.A., P.O. Box 564, 1001 Lausanne, Switzerland.)

from Elsevier Science of coating mass.

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then the characteristics (mean and variance) of the distribution of the number of particle passes can be determined from the distribution of cycle times, i.e., the times between successive passes. This is very useful, since the cycle time distribution can be measured experimentally while the distribution of the number of particle passes cannot be measured easily. Furthermore, Mann

(1983) showed that the coefficient of variation for Xtotal, for a batch coating process in which N and x are independent, random variables, could be

expressed as:

where ttot is the total coating time for the batch operation. Equation (12) shows that the variation in the amount of coating received per particle is the sum of two effects. The first effect concerns the variation in the number of passes a particle makes through the spray zone during the process and is given by the first term on the right hand side of Eq. (12). The second effect concerns the variation in the amount of material that a particle receives each time it passes through the spray and the average number of passes through the spray. This second effect is given by the second term on the right hand side of the equation.

Cycle Time Distribution. The variation in the number of times a particle circulates in a fluidized bed has been determined by measuring the cycle time distribution of a tagged magnetic particle in spouted beds with and without draft tubes (Mann, 1972; Cheng, 1993; and Waldie and Wilkinson, 1986). The results of Cheng (1993) showed that for beds with draft tubes, the circulation times for tagged particles of different sizes and dimensions were basically the same for the same operating conditions. Cheng (1993) and Mann (1972) also measured the variance and mean cycle times, and the results of Cheng (1993) are shown in Fig. 6. It is clear that as the mean cycle time increases, so does the variance. Typical mean circulation times varied between 2 to 10 seconds (for a 150-mm diameter bed with a 75-mm diameter draft tube). Since typical coating operations have a duration of at least one hour, it can be seen from Eq. (12) that the first term on the right hand side often contributes very little to the overall variation in coating mass uniformity. However, this may not be the case when the bed contains dead zones which lead to a very wide distribution of circulation times.

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At present, there is little information or work been performed to address the problems of coating mass uniformity. Either of the two approaches above may be useful in modeling the spread or variation in coating uniformity. However, effective diffusion coefficients, DG, and coefficients of variation for particle coating, [Var(x)/{E(x)}2]1/2, must first be established from experiment. Therefore, without additional extensive work in this area, it will be impossible, in general, to predict a priori, the uniformity of coating mass for a batch of particles in a given piece of equipment at given operating conditions.

Models for Continuous Coating. From the results of coating experiments given in the section above, it is clear that considerable variation in the amount of coating per particle can occur during batch coating operations. The variation in mass uniformity between particles in a continuous coating process with feed and product withdrawal can be expected to be considerably greater due to the well mixed nature of a spouted bed. For this reason, most coating in the agricultural and pharmaceutical industries is still done in batch processes. Population balance equations and probabilistic models have been presented by Liu and Litster (1993a), Choi and Meisen (1995) and Mann (1981) for continuous systems.

Coat Morphology. It has been observed that, even for solids with a narrow distribution of coating mass, there may still be wide variations in the performance of the coated product. This is especially important when the coating provides a functional use. For example, if the product is to possess a sustained release property, then it is very important that each particle’s coat provides the desired retarding action on the release of the active ingredient. If the product is intended for use in the agricultural chemicals market, a nonuniform coat might lead to premature release of an insecticide into the soil thus affecting the yield of a crop. On the other hand, if the product is for use in the pharmaceutical market, then the consequence of a nonuniform coat could be the premature release of a large quantity of drug (dose-dumping) into the patient’s body rather than its gradual release over a six to twenty four hour period. The seriousness of dose-dumping leads us to a consideration of the structure or morphology of the particle coat.