Species separation of a binary mixture under acoustic streaming

Abstract.

An analytical and numerical study of the action of ultrasonic waves on species separation within a rectangular cavity filled with a binary fluid (water-ethanol mixture) is presented. An ultrasonic wave was emitted on a portion of one of its vertical walls, while the opposite wall was perfectly absorbent. The two horizontal walls were differentially heated. A progressive acoustic wave was used to generate, at a large scale, a stationary flow of the viscous binary fluid (Eckart Streaming) within the cavity. The authors analytically determined the temperature T, mass fraction C and velocity fields under the parallel flow hypothesis used for cells with high aspect ratio $B\gg1$, in the presence of the gravitational field. From the analysis of the velocity fields the authors concluded that the associated flow is either unicellular or consists of three counter-rotating cells superimposed in the horizontal direction of the cavity. They also found the variation domains of the physical parameters leading to one or the other of these two types of flows. The algebraic equation allowing the calculation of the mass fraction gradient and hence the species separation between the vertical walls of the cavity was determined. The variation of the dimensional mass fraction gradient, for the water-ethanol mixture, as a function of the two control parameters of the problem, namely the acoustic parameter A and the temperature difference $\Delta T$ imposed on the two horizontal walls was studied.

Graphical abstract