The detrimental effect of hydrodynamic interactions on the process of Brownian flocculation in shear flow

Abstract

AbstractThe problem of Brownian flocculation of spherical particles in strong shearing flow without hydrodynamic interactions is studied in detail using the singular perturbation method. All other types of interparticle interactions, such as van der Waals or Lennard-Jones forces, are also ignored. In the limit of strong external flow, the strength of which is measured by the Péclet number ($Pe\gg 1$), a complicated boundary layer structure for the pair probability density function ($P_{2}$) is identified and the complete stationary spatial distribution of $P_{2}(\boldsymbol {x})$ in the domain is found. The results, in particular the total mass flux in the accumulation process, are compared qualitatively and quantitatively with the case where the spheres interact hydrodynamically and it is demonstrated that the hydrodynamic interactions tend to decrease the rate of flocculation. An explicit simple formula for the flocculation rate for a general form of hydrodynamic interactions is provided. The limit of small Péclet number is also discussed to confirm the conclusion on the detrimental influence of hydrodynamic interactions on the rate of Brownian flocculation in shearing flow.