Low-pass filtering effects of viscous sublayer on high Schmidt number mass transfer close to a solid wall

Numerical simulation of high Schmidt number turbulent mass transfer at a solid wall is carried out. Particular attention is paid to the response of the concentration field to the wall-normal velocity fluctuation inside the viscous sublayer. Spatio-temporal correlation shows that the high Schmidt number concentration field becomes insensitive to the wall-normal velocity fluctuation. In addition, there exists a significant time lag in the response of the concentration field to the wall-normal velocity fluctuation. As a result, the instantaneous distribution of the local mass transfer rate is drastically changed. These facts explain why the analogy between the momentum and mass transfer does not hold close to the wall. Based on a one-dimensional advection–diffusion equation, we derive a transfer function connecting the wall-normal velocity and the concentration fluctuations. It is shown that the present model can reproduce the fundamental dynamical features of high Schmidt number concentration field.