In this paper aggregation of small solid particles in the perikinetic and orthokinetic regimes is considered. An aggregation kernel for colloidal particles is determined by solving the convection-diffusion equation for the pair probability function of the solid particles subject to simple shear and extensional flow patterns and DLVO potential field. Using the solution of the full model the applicability regions of simplified collision kernels from the literature are recognized and verified for a wide range of Péclet numbers. In the stable colloidal systems the assumption which considers only the flow pattern in a certain boundary layer around central particle results in a reasonable accuracy of the particle collision rate. However, when the influence of convective motion becomes more significant one should take into account the full flow field in a more rigorous manner and solve the convection-diffusion equation directly. Finally, the influence of flow pattern and process parameters on aggregation rate is discussed.

In many systems of engineering interest the moment transformation of population balance is applied. One of the methods to solve the transformed population balance equations is the quadrature method of moments. It is based on the approximation of the density function in the source term by the Gaussian quadrature so that it preserves the moments of the original distribution. In this work we propose another method to be applied to the multivariate population problem in chemical engineering, namely a Gaussian cubature (GC) technique that applies linear programming for the approximation of the multivariate distribution. Examples of the application of the Gaussian cubature (GC) are presented for four processes typical for chemical engineering applications. The first and second ones are devoted to crystallization modeling with direction-dependent two-dimensional and three-dimensional growth rates, the third one represents drop dispersion accompanied by mass transfer in liquid-liquid dispersions and finally the fourth case regards the aggregation and sintering of particle populations.