Asymptotic Solutions of the Boundary Value Problem of Convective Diffusion Around Drops with Volumetric Nonlinear Chemical Reaction

We consider a stationary problem of convective diffusion around a droplet, which is streamlined by a liquid flow at low Reynolds numbers, taking into account a nonlinear volumetric chemical reaction. The characteristic feature of the problem is the presence of two dimensionless parameters: a constant of rate of the volumetric chemical reaction kv, and Peclet number Pe which determine the concentration distribution in the flow. The quantity constant of rate of the volumetric chemical reaction kv and Peclet number Pe assumed to have a constant value. It is a boundary value problem for a quasilinear partial elliptical equation with a small parameter multiplying in higher derivatives. Small parameter corresponds to large Peclet numbers. The limiting equation, when the small parameter is equal to zero, has singular points of the saddle type. Several boundary layers appear outside the drop. The matching conditions for solutions are formulated at the boundaries between neighboring areas. The principal terms of the asymptotics of the solution are constructed around the drop. MSC 76M45.