An Inverse Problem Approach to Extract the Growth Kernel in Particulate Processes

Mathematical models of particulate processes usually include a population balance equation to describe the dynamics of the size distribution. The structure of the population balance equation is the same in all models of particulate processes and the specific physical and chemical interaction of the particles is described by individual kernels. Usually first principles modeling is used to develop the kernels, but in cases in which this is intractable, inverse problem techniques have been proposed in the literature to extract the kernels from experimental data. In this work we introduce an approach that can be used for extracting the growth kernel. This approach is applicable even when the assumption of separable growth rate that has been made in previous approaches does not hold and when coagulation with known dynamics and growth are taking place simultaneously.