Asymptotic solutions for turbulent mass transfer augmented by a first order chemical reaction

We present asymptotic solutions for turbulent mass transfer in a smooth conduit at high Schmidt number in the presence of a first-order chemical reaction in the fluid. Far-field solutions are derived for a case dominated by (1) mass transfer at the wall and (2) the first-order chemical reaction. An approximate solution is derived for the regime where both are important. The solutions are in good agreement with numerical solutions and with the literature. At high Damköhler numbers the system is governed by a reaction–diffusion equation and the observed increase in mass transfer coefficient is caused by thinning of the mass transfer boundary layer due to the fast chemical reaction in the fluid. We present closed-form far-field solutions for Dirichlet, Neumann and Robin boundary conditions and comment on grid resolution requirements to accurately resolve the mass transfer boundary layer. The solution strategy presented can be straightforwardly extended to non-linear wall- and bulk-reactions.