Asymptotic solutions for turbulent mass transfer at high Schmidt number

Abstract

We present closed-form solutions for high Schmidt number mass transfer in a hydrodynamically fully developed turbulent flow. Governing equations for the near- and far-field are developed for a large class of boundary conditions (BCs) for which the mass flux is a function of the concentration at the wall. We show that for this class of BCs, which includes nonlinear wall reactions, the mass transfer coefficient is independent of the BC and the Sherwood correlation is therefore universal. For Dirichlet, Neumann and Robin BCs, the far-field solutions are in good correspondence with the method of separating variables and near-field solutions are in good agreement with numerical simulations. However, in contrast with the far-field solutions, the Sherwood correlation in the near-field depends on the specific BC. As an example of nonlinear BCs, solutions for a second-order wall reaction are derived which are compared with numerical simulations and found to be in excellent agreement.