Adsorption-Mediated Mass Streaming in a Standing Acoustic Wave

Oscillating flows can generate nonzero, time-averaged fluxes despite the velocity averaging zero over an oscillation cycle. Here, we report such a flux, a nonlinear resultant of the interaction between oscillating velocity and concentration fields. Specifically, we study a gas mixture sustaining a standing acoustic wave, where an adsorbent coats the solid boundary in contact with the gas mixture. It is found that the sound wave produces a significant, time-averaged preferential flux of a “reactive” component that undergoes a reversible sorption process. This effect is measured experimentally for an air-water vapor mixture. An approximate model is shown to be in good agreement with the experimental observations, and further reveals the interplay between the sound-wave characteristics and the properties of the gas-solid sorbate-sorbent pair. The preferential flux generated by this mechanism may have potential in separation processes.

Figure 1

(a) The experimental setup: a quarter-wavelength resonator in which a loudspeaker drives a standing wave at the resonant frequency and a controlled amplitude. The “stack” is coated with zeolite 13X adsorbent. Temperature is kept constant by heating and cooling at the stack edges, as indicated, measured by thermocouples. Humidity sensors at the stack edges measure the mass fraction of the water vapor. (b) The partial pressure of a representative gas “parcel” as it undergoes motion and compression; mass is exchanged in a direction dependent on the difference between the parcel’s partial pressure and the local sorbent equilibrium. (c) Conceptual mass transfer mechanism combining motion, sorption, and diffusion. Gas expansion drives desorption, followed by motion towards the higher pressure, where compression drives sorption. The resulting time-averaged mass transfer creates accumulation close to the pressure antinode (high pressure) and depletion near the pressure node (low pressure).

Figure 2

The scaled concentration difference generated across the stack, $\widehat{△C}\approx △C/C_m$, as a function of the pressure amplitude, scaled against the mean pressure. The solid lines are model calculations, while dots represent experimental data. Results are shown for two stack positions, scaled against a quarter wavelength: 0.068 (red round markers) and 0.18 (blue square markers). Experimental measurements in the absence of the stack are presented as black crosses. Experimental conditions correspond with ${\tau }_{\nu }\approx 2.34$, $K\approx 20$.

Figure 3

The scaled concentration difference generated across the stack, $\widehat{△C}\approx △C/C_m$ as a function of (a) ${\tau }_{\nu }\equiv h\sqrt{\omega /2\nu }$ (here, $K=20$) and (b) the partition coefficient, $K\equiv k_a/k_d$. In all calculations, $P=p_A/p_m=0.06$.