Mass transfer between a flowing fluid and a solid wavy surface

Abstract

AbstractThis paper considers the transfer of mass or heat between a fluid and a small amplitude solid wavy surface. A periodic variation of the transfer rate can occur because of wave induced variations of the normal convective flow and of the properties of the turbulence. Solutions of the mass balance equations are presented for the laminar flow at a large Schmidt number or Prandtl number and for turbulent flow at large and small wave numbers. For turbulent flows at intermediate wave numbers, the prediction is limited by inadequacies of present theories that model the wave induced variation in the turbulent diffusion of heat or mass. In order to provide guidance for this modeling, new measurements on the variation of the mass transfer rate along a solid wavy surface are presented for a Schmidt number of 729. An analogy between momentum and mass transfer is explored as a means for evaluating the turbulent diffusion terms.The amplitude of the function describing the mass transfer variation is found to decrease with decreasing wave number and the phase to increase with decreasing wave number. The phase angle and the amplitude of the variation in the mass transfer rate relative to the average mass transfer rate are insensitive to changes in Schmidt number or Prandtl number. For turbulent flows, the phase change can be large enough that the maximum in the mass transfer rate can exist somewhere in the trough of the wave. This result is of considerable significance in interpreting wavelike dissolution patterns.