Perikinetic and orthokinetic aggregation of small solid particles in the presence of strong repulsive forces

This paper deals with aggregation of small particles in a fully developed turbulent flow field for the wide range of the Péclet number including the perikinetic and orthokinetic regimes. Colloidal particles smaller than the Kolmogorov length microscale are considered. Convective movements of these particles are characterised by the relaxation time much shorter than the Kolmogorov time microscale. A basic aggregation kernel is determined by solving the convection-diffusion equation for the pair probability function of the solid particles present in the DLVO potential field for the sub-Kolmogorov scale flow structure. The simplified aggregation kernels are proposed as well to offer a computationally less expensive method. An aggregation kernel based on the modified Fuchs stability ratio approach including effect of competition between maximum particle velocities caused by the repulsion forces and fluid flow is derived using a concept of small scale turbulent diffusion that competes with particle velocity generated by repulsion forces. The aggregation rate constants obtained using this method are close to predictions of the full model. Proposed approach is extended to take into account hydrophobic effects and particle-bubble interactions.