Thermal diffusion and mixture separation in the acoustic boundary layer

Oscillating thermal diffusion in a sound wave in a mixture of two gases is remarkably effective for separating the components of the mixture. We consider this separation process in boundary-layer approximation, with zero temperature gradient and zero concentration gradient along the direction of sound propagation. In the boundary layer, the combination of thermal diffusion with the oscillating temperature gradient and oscillating velocity gradient leads to second-order time-averaged fluxes of the two components of the mixture in opposite directions, parallel to the wave-propagation direction. The oscillating thermal diffusion also adds to the dissipation of acoustic power in the boundary layer, modifying thermal-relaxation dissipation but leaving viscous dissipation unchanged.