(11a) A New Approach in Solving Population Balance Equations

A new approach to solve population balance equations (PBE) is presented. The solution of the PBE is sought in the finite domain of the internal variable, between the minimum and the maximum size values, while the size distribution function is represented by a series expansion over a complete system of orthonormal functions. The moments evolution equations are developed integrating the PBE over the finite size domain. Some properties of the approach followed are: an explicit expression for the size distribution function f is available; no problem specific assumption is made regarding the shape of f; the completeness of the set of trial functions in the size distribution function expansion provides properties of convergence and the convergence to the solution is reasonably fast for computational purposes. The rapidity of convergence is verified by specific applications to the particle growth (constant, linear, diffusion-controlled), with and without nucleation.