Asymptotic behavior of the solution to a convection-diffusion problem with bulk chemical reaction in the wake of a particle

The problem of steady convective mass transfer between a particle and a continuum with a nonlinear bulk chemical reaction is considered for the case when the Peclet number $\operatorname{Pe}$ and the rate constant $k_\nu$ of the reaction tend to infinity. An asymptotic solution with respect to a small parameter $\varepsilon= \operatorname{Pe}^{-1/3}$ is obtained in the wake of the particle.