Aggregation during Precipitation from Solution: A Method for Extracting Rates from Experimental Data

Abstract

This paper considers aggregation during precipitation from solution in a batch system. Unlike the aggregation of colloidal particles in ionic solutions which has been extensively studied, aggregation during precipitation from supersaturated solutions in which other size enlargement mechanisms occur is less well understood. Of particular interest is the development of a method to determine the rates of two active size enlargement mechanisms, namely growth and aggregation, from experimental data. We describe a novel technique which is capable of performing two main tasks: extracting the rates of growth and aggregation from experimental data and simulating changes in a particle size distribution during an experiment. A differential technique is developed which uses a discretized population balance to determine the rates from experimental data. The same discretized population balance is used to simulate changes in a particle size distribution for given growth and aggregation rates. Both these operations, unlike other more complicated techniques, can be performed on a personal computer and give results in a few minutes. The use of this method is illustrated by a study of the batch precipitation of calcium oxalate monohydrate. It is shown that growth rates can be determined without specific knowledge of the aggregation kernel and that aggregation rate constants can be determined for different aggregation kernels. Comparison of simulated and experimental particle size distributions and their moments show it is possible to distinguish between the kernels and determine which is appropriate for modeling the aggregation of calcium oxalate monohydrate; it is found that a size-independent kernel is most appropriate.