Diffusion and Deposition of Brownian Particles in the Boundary Layer in Flow of a Dispersed Mixture Past a Permeable Surface

Abstract

The effect of mass transfer (owing to fluid injection or suction) with a surface in disperse flow on the processes of diffusion and deposition of Brownian particles in the boundary layer is studied. The equations of motion and diffusion of a dispersed mixture are presented in the boundary layer approximation with regard for the dependence of the effective viscosity of the suspension on the volume particle content. The boundary value problem is formulated in self-similar variables with regard for the fluid suction (injection) rate on the permeable surface. An analysis of the diffusion equation is carried out at small and large Schmidt numbers and in these limiting cases approximations of its solutions are found. In particular, it is shown that in the boundary layer, in the limit as the Schmidt number increases indefinitely, the derivative of the particle concentration with respect to the independent self-similar variable tends to the Dirac delta function. The results of numerical solution of the formulated boundary value problem obtained at various values of the constitutive parameters are discussed with reference to the plate boundary layer. It is found that in the presence of injection there exists a characteristic Schmidt number (depending on the injection intensity) such that a region without particles appears in the boundary layer at the higher Schmidt numbers. The effect of the injection intensity on the dimensions of this region is studied. The dependences of the diffusion particle flow toward the plate surface on the Schmidt number are analyzed in the case of the presence or absence of injection (suction).