Semi-analytical investigations using the orientation-free discrete gas-kinetic theory are performed in order to link the non-equilibrium but stationary solitons found in the randomly and approximately boundary treatment for the interactions between gases and solid-surfaces with vorticity at the pseudo-flat walls. The stationary solitons thus obtained from the integrable system of partial differential equations are subjected to different but limited dissipations depending on the intrinsic parameter of rarefaction. We also address the linear stability of our results in brief.
We demonstrate the molecular sieving could be realized via a wavy-rough nanoannulus. By using the boundary perturbation method, we analytically obtain the flow rate (up to the second order) inside the wavy-rough nanoannuli. Our results show that for smaller forcing (along the nanoannulus-axis direction) there are significantly different flow rates for different amplitudes of wavy-roughness. This implies the fine-tuning of the solid-fluid interface of nanoannuli could be an efficient way for the molecular sieving.
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