Stationary d.c. streaming due to shape oscillations of a droplet and its effect on mass transfer in liquid–liquid systems

Abstract

The work is devoted to stationary streaming flows resulting from standing capillary waves at interfaces between two immiscible liquids and their effect on the mass transfer rate of a passive scalar. In particular, oscillating liquid droplets immersed in another immiscible liquid are considered. Secondary streaming flows in the Stokes layers near the interface are calculated, as well as the corresponding vortical flows arising in the bulk. It is shown that the vortices can drastically 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 the order of [[mid ]uint[mid ]a/[Dscr ]1]1/2, where [mid ]uint[mid ] is the magnitude of the interfacial streaming velocity, a is the droplet radius, and [Dscr ]1 is the diffusion coefficient in liquid 1 (inside the droplet). This means that the effective diffusion coefficient is of the order of [Dscr ]1[[mid ]uint[mid ]a/ [Dscr ]1]1/2, which is two orders of magnitude higher than [Dscr ]1. The results obtained show that such flows can be of potential interest for novel bioseparator devices.