Solution of population balance equation of breakage model via shifted Legendre functions

Abstract

The stretched functional ordinary differential equations of population balance which can be used to describe the crystallization process of breakage models are solved by shifted Legendre functions. The key method is that the population density function is expressed by a series of shifted Legendre functions. The solution of the population balance equation is obtained by first transforming the ordinary differential equation into a series of algebraic equations of expansion coefficients which can be solved easily. The calculation procedure is simple and straightforward owing to the development of the recursive algorithm for the integration of the triple product of the shifted Legendre functions. Very satisfactory results of population density functions are obtained when they are compared with the numerical values obtained by MWR and the block pulse function.