Brownian dynamics simulations of coagulation of dilute uniform and anisotropic particles under shear flow spanning low to high Peclet numbers. 
Brownian dynamics simulations are performed to study the binding kinetics in the dilute-sphere limit by considering interactions of two spheres under shear flow across the entire range of Peclet numbers, spanning both perikinetic (diffusion-controlled) and orthokinetic (flow-controlled) coagulation regimes.  The dilute regime is attained by carrying out two-sphere simulations in periodic boxes of different sizes and aspect ratios and extrapolating toward the infinite box limit.  Effects of particle type (Janus and isotropic particles), shear rate, hydrodynamic interactions, and inter-particle potential are explored.  We find that rectangular boxes with appropriate aspect ratios overcome a particle "shadow effect" that cannot be overcome with cubic boxes unless huge boxes are used.  With rectangular boxes, we obtain converged binding kinetics for the whole Peclet number range, while cubic boxes of increasing size allow converged results only in the absence of flow.  We consider the effect of binding both in a secondary minimum controlled by a combination of electrostatic repulsion and depletion attraction, as well as in a primary minimum governed by induced-dipole attraction.  Results are computed using both realistic interaction potentials and by replacing the potential with a simple cutoff gap distance at which binding is deemed to occur.  Results agree with several existing reports including Smoluchowski predictions in the zero- and infinite-shear-rate limits, and high-Pe perturbation results of Feke and Schowalter [J. Fluid Mech.  133, 17-35 (1983)] at Peclet numbers (Pe) above 100.  Finally, we compute binding times for anisotropic Janus particles which have both repulsive and attractive faces, for a wide range of Pe number.