Thermal diffusion and mixture separation in the acoustic boundary layer

Abstract

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.

Acoustic fields in binary gas mixtures: Mutual diffusion effects throughout and beyond the boundary layers

“…To emphasize the main properties of the phenomena (strong coupling between temperature and concentration variations inside the boundary layers) the appropriate form of the operator on the left hand side is a "product" of two spatial second order operators, 9 leading to (expression of the complex wavenumbers k hD and k Dh are given in Appendix A)…”

“…17,18 Finally, the diffusion coefficient D, which depends on the gas composition and the temperature and inversly proportional to the static pressure, is determined by interpolating experimental results. 2,19 The thermal diffusion ratio k T , as suggested in recent works, 9,12 is expressed by different functions of x for each gas mixture. For the gas mixtures considered (He-Ar and He-Xe), the component 1 is chosen to be helium.…”

“…9 The acoustic pressure p in a spherical cavity satisfies the propagation equation (16a), in which the dissipative effects in the bulk are expressed in the wavenumber k a [Eq. (16b)], associated to the following boundary condition (out of sound source):…”

Simulation of ultrasonic-driven gas separations

“…The latter has been investigated recently both experimentally and theoretically by Swift, Spoor, and Geller, [1][2][3] and been shown to be an effective means of separating even isotopes by coupling the diffusion due to thermal gradients created by acoustic waves at boundaries and transport by the acoustic waves. In contrast, barodiffusion, although in existence for several decades, has not been evaluated since the advent of more efficient and powerful transducers, such as those developed for machining, welding, surgery, and various other medical applications.…”

Numerical modeling of CO2 separation process

“…A scientific investigation of this phenomenon can be found in studies conducted in the 80s and 90s of the 20th century. In particular, they are the works of Rott from the 60s and 70s, and Weatley and Swift from the 80s and 90s, and others [1][2][3]6]. The simplest method to induce a thermoacoustic wave is the application of the Rijke tube [8,9].…”