Onsager's cross coupling effects in gas flows confined to micro-channels

Abstract

In rarefied gases, mass and heat transport processes interfere with each other, leading to the mechano-caloric effect and thermo-osmotic effect, which are of interest to both theoretical study and practical applications. We employ the unified gas-kinetic scheme to investigate these cross coupling effects in gas flows in micro-channels. Our numerical simulations cover channels of planar surfaces and also channels of ratchet surfaces, with Onsager's reciprocal relation verified for both cases. For channels of planar surfaces, simulations are performed in a wide range of Knudsen number and our numerical results show good agreement with the literature results. For channels of ratchet surfaces, simulations are performed for both the slip and transition regimes and our numerical results not only confirm the theoretical prediction [Phys. Rev. Lett. 107, 164502 (2011)] for Knudsen number in the slip regime but also show that the off-diagonal kinetic coefficients for cross coupling effects are maximized at a Knudsen number in the transition regime. Finally, a preliminary optimization study is carried out for the geometry of Knudsen pump based on channels of ratchet surfaces.

Knudsen pump inspired by Crookes radiometer with a specular wall

“…In the present case, an analogous scaling should be expected due to the similarity of the temperature field. Note that a similar scaling was employed by Wang et al [19] in the context of thermally induced channel flow at the tips of ratchet teeth protruding into a channel.…”

“…The better performance of this configuration most likely stems from the larger temperature gradients at the tips of the vanes due to directly prescribing the temperatures instead of indirectly generating a temperature profile via a specular boundary. Wang et al [19] considered a channel with one flat, diffusely reflecting wall and an opposing surface structured as a ratchet with parts of each ratchet tooth reflecting diffusely and parts fully specularly, similarly to the vanes considered here. The temperature profile in the channel is generated by prescribing different temperatures at the opposing walls.…”

“…Here, one of the surfaces is considered to be structured in a ratchet pattern, with the inclined face of the ratchet reflecting gas molecules specularly, while the rest of the boundary reflects diffusely. A similar implementation relying on a purely diffusely reflecting ratchet geometry was proposed by Würger [16] and analyzed further in [17][18][19].…”

Discrete unified gas kinetic scheme for flows of binary gas mixture based on the McCormack model

“…11, the molar concentration C of the Ne-Ar and He-Xe mixtures, which is defined as the deviated concentration of the light species from its equilibrium value, are shown and compared with the results from the DVM 27,64 . Due to the thermodiffusion, the light species mainly concentrate on the hot plate, whereas the heavy species concentrate on the cold plate 65 . Again the results predicted by the present DUGKS are in close agreement with those of the DVM.…”

Thermally induced gas flows in ratchet channels with diffuse and specular boundaries

“…In a recent study, Wang et al . 42 investigated thermally and pressure driven gas flows using the unified gas-kinetic scheme 43 in a ratchet channel with a different patterning of the specular and diffusively reflecting patches on the ratchet surface. In a variant of this arrangement, Chen et al .…”