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Abstract:
This work focuses on the application of high resolution finite volume schemes for the solution of multidimensional population balance models in crystallization processes. The population balance equation is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born, die, grow or leave a given control volume. In the population balance models the one independent variable represents the time, the others(s) are "property coordinate(s)", e. g., the particle size in the present case. They typically describe the temporal evolution of the number density functions and have been used to model various processes. These include crystallization, polymerization, emulsion and cell dynamics. The high resolution schemes were originally developed for compressible fluid dynamics. The schemes resolve sharp peaks and shock discontinuities on coarse girds, as well as avoid numerical diffusion and dispersion. The schemes are derived for general purposes and can be applied to any general system in divergence form.
The accuracy of these schemes can be further improved by using adaptive mesh refinment techniques.Here a moving mesh techniques of H. Tang and T. Tang [37] is used which they have developed for hyperbolic conservation laws in conjuction with finite volume schemes. In this technique, an iterative procedure is used to redistribute the mesh by moving the spatial grid points. The corresponding numerical solution at the new grid points is obtained by solving a linear advection equation.
In this work, several models for batch and preferential crystallization are considered. In case of preferential crystallization, the model is further investigated with and without fines dissolution. The numerical results show the clear advantages of the finite volume schemes and are improved further when combined with a moving mesh technique.
