Influence of acoustic streaming on thermo-diffusion in a binary mixture under microgravity

An analytical and numerical study of the influence of acoustic streaming on species separation of a binary mixture under microgravity is presented. A rectangular cell filled with binary fluid is submitted to an ultrasonic propagating wave along a portion of one of its small walls while the opposite wall is perfectly absorbing. A temperature gradient is applied between the two other walls. The unicellular flow induced by the Eckart streaming may lead to significant species separation. In a first part, the hypothesis of parallel flow is used to determine the analytical solution which describes the unicellular flow and the separation is calculated analytically based on the acoustic streaming parameter, A, the acoustic beam width, ɛ, and the Schmidt number, Sc. Theses analytical results are corroborated by direct numerical simulations. In a second part, a linear stability analysis of the unicellular flow is performed. The eigenvalue problem resulting from the temporal stability analysis is solved by the Galerkin method, a spectral Tau–Chebychev method and by a finite element method. The thresholds for the stationary and oscillatory instability depend on the normalized acoustic beam width.