Lattice boltzmann method for crystallization processes

Abstract

Crystallization is a key unit operation used in several industries such as pharmaceutical, chemical and semiconductor industries. Like other particulate processes, the dynamics of crystallization processes can be described using population balance equations (PBEs). PBEs are integro-partial differential equations which take into account various ways (nucleation, growth, aggregation and breakage) in which particles of specific state can either form or deplete from a system. For most practical problems, PBEs do not have an analytical solution and thus need to be solved numerically.

In this work, a lattice Boltzmann method (LBM) is introduced for efficient simulation of multi-dimensional crystallization processes. In LBM, kinetic equations of some fictitious particles resembling groups of molecules are considered. Unlike molecules, which have random motion, these particles are allowed to move only in certain directions based on symmetry and isotropy requirements. Interactions of these particles recover the original governing equations at the macroscopic level.

In this thesis, LBM is first discussed for the advection equation and then applied to solve PBEs for crystallization processes with growth and nucleation by identifying the analogy between these equations. A coordinate transformation scheme is proposed in order to improve the performance of the LBM for crystallization processes with size dependent growth rate. This transformation is based on the functional form that is used to describe the size dependent part of the growth rate and can be applied to other discretized methods used for solving PBEs as well. The performance of the proposed scheme is verified by comparing the results with those obtained using well established high resolution (HR) finite volume (FV) method. These comparisons show that LBM provides same level of accuracy while requiring lower computation time than HR method.