Smoluchowski (1) developed collision frequencies for these two cases of coagulation. One case describes the collision of particles by Brownian motion (perikinetic coagulation) and the other neglects diffusion as particle collisions are induced by the surrounding fluid flow (orthokinetic coagulation). In both cases inter-particle forces are neglected. When both mechanisms are present, the combination affects the collision rate and the resulting particle size distribution.

Swift & Friedlander (2) concluded that the collision frequencies for Brownian motion and laminar shear are independent and additive for a wide range of conditions. Contradictory Van de Ven & Mason (3) showed by solving the convective diffusion equation for conditions with a low influence of shear (Pe << 1) that the two mechanisms are coupled and are not simply additive. Shear enhances the coagulation rate proportional to the square root of the Peclet number, which represents the ratio between the convective (inertial) and diffusive terms. Feke & Schowalter (4) studied the regime for high Peclet numbers (Pe >> 1) where the dominant mechanism is shear. Their analysis of binary collisions also revealed a dependency between the contribution of Brownian motion and shear. They concluded that the combination of both can either increase or decrease the collision frequency. All of these models treat collisions between two particles by calculating the flux of a particle to a reference sphere. The flux is typically computed from the pair probability function, which gives the probability to find two particles at a certain position.

Ernst and Pratsinis (5) showed by population balance simulations that shear-induced coagulation leads to pseudo self-preserving distributions that end to gelation. Heine and Pratsinis (6) simulated Brownian coagulation at high concentrations with Langevin dynamics (LD) and showed that classic Smoluchowski equation can not describe highly concentrated systems (particle volume fraction above 1%). They found out that for complete particle coalescence upon collision, the self-preserving size distribution is still obtained for high concentrations. In the limiting cases, where either peri- or orthokinetic aggregation dominates, the process of coagulation is understood well. The transition regime on the other hand is not well understood.

Here Brownian and shear-induced coagulation are investigated by LD simulations for a multi-particle system of coalescing spheres. Initially all particles are monodisperse. Simulations are done for monodisperse and polydisperse systems. In monodisperse simulations particles are redistributed after a collision. If particles collide in polydisperse simulations, full coalescence takes place. Collision frequencies and particle size distributions are obtained for a wide range of Pe, including the two limiting cases of pure shear-induced coagulation and pure Brownian coagulation.

1. Smoluchowski, M. V., (1917). Z. Phys. Chem., 92, 129-.

2. Swift, D. L., & Friedlander, S. K. (1964). J. Colloid Sci., 19, 621-647.

3. van de Ven, T. G. M. & Mason, S. G. (1977). J. Colloid Polymer Sci., 255, 794-804.

4. Feke, D. L., & Schowalter, W. R. (1985). J. Colloid Interface Sci., 36, 203-214.

5. Ernst, F. O., & Pratsinis, S. E. (2006). J. Aerosol Sci., 37, 123-142.

6. Heine, M. C., & Pratsinis, S. E. (2007). Langmuir, 19, 9882-9890.