Saturation of the thermoacoustic separation of a binary gas mixture

Abstract

Spoor and Swift have previously shown [Phys. Rev. Lett. 85, 1645–1649 (2000)] that sound waves can produce the separation of a binary mixture of gases in a duct. This phenomenon is caused by the conspiracy of two effects at the thermoviscous boundary layer: (i) oscillating temperature gradients drive thermal diffusion perpendicular to the direction of sound propagation; and (ii) viscosity sets up a time-averaged counterflow process. In order to assess the relevance and potential uses of this mechanism, it is important to determine the concentration gradient at which the separation process saturates. Here, it is shown that the saturation is determined primarily by ordinary diffusion and by a remixing flux due to the oscillatory motion. Both of these remixing processes are proportional to the concentration gradient, but only the latter process depends on the acoustics, being proportional to the squared volume flow rate and inversely proportional to the frequency. For He–Ar mixtures, saturation concentration gradients near 10%/m have been achieved, in agreement with detailed calculations of these processes. Evidence to date supports the possibility of more challenging separations, e.g., of isotopes. [Work supported by the DOE Office of Basic Energy Sciences.]