An efficient numerical technique for solving multi-dimensional batch crystallization models with size independent growth rates

Abstract

This article introduces an efficient numerical technique for solving multi-dimensional batch models. The method requires initial crystal size distribution (CSD) and initial solute mass. The initial CSD is used to calculate the initial moments as an initial data for the reduced moments system. The solution of the moments system coupled with an algebraic equation for the mass gives moments and mass at the discrete points of the computational time domain. These values are then used to get the discrete values of growth and nucleation rates. The discrete values of growth and nucleation rates along with the initial CSD are sufficient to get the final CSD. In the derivation of current technique the Laplace transformation of the population balance equation (PBE) plays an important role. The method is efficient, accurate and easy to implement. For validation, the results of the proposed scheme are compared with those from the high resolution finite volume scheme.