Numerical treatment of the population balance equation using a Spline-Galerkin method

Abstract This paper describes a numerical technique for solving the Lifshitz-Slyozov equation of continuity which applies to certain mass transfer proceses. The Lifshitz-Slyozov equation which describes a mechanism involving the transfer of atoms (or undissociated molecules) from smaller particles to larger particles dispersed in a supersaturated medium (Ostwald ripening) is also considered together with collision and subsequent coalescence of particles (ripening plus collection). Special attention is given to the case in which the net growth rate appearing in the Lifshitz-Slyozov equation is a nonsmooth function of the type I ( υ ) α υ β , where υ is the particle volume and O