On the solution of population balance equations by discretization - III. Nucleation, growth and aggregation of particles

A new discretization method for solving population balance equations for simultaneous nucleation, growth and aggregation of particles is proposed. The method combines the best features of our discretization technique (Kumar and Ramkrishna, 1996, Chem. Engng. Sci. 51, 1311-1337), i.e., designing discrete equations to obtain desired properties of a size distribution directly, applicability to an arbitrary grid to control resolution and computational efficiency, with the method of characteristics to offer a technique which is very general, powerful and overcomes the crucial problems of numerical diffusion and stability that beset the previous techniques in this area. The proposed technique has been tested for pure growth, simultaneous growth and aggregation, and simultaneous nucleation and growth for a large number of combinations obtained by changing functions for nucleation rate, growth rate, aggregation kernel and initial condition. In all cases, the size distributions obtained from the proposed technique and those obtained analytically are in excellent agreement. The presence of moving discontinuities, which is unavoidable due to the hyperbolic nature of the governing equation, is addressed with no additional difficulty in all of the test problems. (C) 1997 Elsevier Science Ltd.