Steady streaming and mass transfer due to capillary waves in a two-layer system

The work deals with stationary (dc) streaming flows resulting from standing capillary waves at the interface between two immiscible liquid layers, and with their effect on the mass transfer rate of a passive scalar (for example, a protein). Planar layers in a narrow channel are considered. Secondary streaming flows in the Stokes layers near the interfaces are calculated, as well as the corresponding vortical flows arising in the bulk. It is shown that the vortices can significantly enhance the mass transfer rate of a passive scalar which is to be extracted by one liquid from the other. The corresponding Sherwood number is of order [\u*(int)\lambda/D-1](1/2), in where \u(int)*\ is the magnitude of the interfacial streaming velocity, lambda is the wavelength, and D-1 is the diffusion coefficient in liquid 1. This means that the effective diffusion coefficient is of order D-1[u(int)*\lambda/D-1](1/2), which can be more than an order of magnitude higher than D-1. The results obtained are discussed in the context of potential novel bioseparator devices for protein extraction. (C) 2002 Published by The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.