Effects of interfacial velocity boundary condition on turbulent mass transfer at high Schmidt numbers

Numerical simulation of high Schmidt number turbulent mass transfer across free and solid surfaces is carried out. Near a free surface, the concentration field quickly responses to the normal velocity fluctuation and the eddy diffusivity is almost unchanged even at high Schmidt numbers. In contrast, near a solid wall, the concentration field becomes less sensitive to the normal velocity fluctuation and the eddy diffusivity is drastically decreased with increasing the Schmidt number. This fundamental difference between the concentration fields close to free and solid surfaces can be attributed to the difference in the asymptotic behavior of velocity fluctuations toward the interfaces. Namely, the normal velocity varies quadratically with the distance from a solid surface, while linearly near a free surface. Strong damping of high-frequency concentration fluctuations near a solid surface agrees well with the theoretical analysis by Shaw and Hanratty [AIChE J. 23 (1977a) 160–169]. As a result, lower-frequency velocity fluctuations dominate the mass transfer at higher Schmidt numbers. These results imply that the analogy between momentum and mass transfer, which has been widely used in engineering applications, may not hold.