On the Maxwell gas-wall interaction model for micro/nano gas flows

Abstract

A systematic study on the goodness of Maxwell model in the modeling of micro/nano gas flows in the entire Knudsen range is presented. We evaluate the model by examining key macroscopic properties such as temperature, density and pressure, in a couple classical benchmark problems namely thermal Couette and thermal transpiration problems. Our reference solutions are obtained from a hybrid DSMC/MD algorithm developed in house. We have found that while the extended Maxwell model, that is, the Maxwell model with three accommodation coefficients, is in general more accurate than the classical Maxwell model, the differences in the magnitudes of the predicted macroscopic quantities are quite small except the pressure profile of the thermal Couette problem, in which case the classical Maxwell model predicts a pressure trend that is opposite to that predicted by both the extended Maxwell model and the hybrid MD/DSMC simulations. This fact is also demonstrated in our study of the thermal transpiration coefficient, γ. The value predicted by the extended Maxwell model depends highly on the tangential accommodation coefficient which is consistent with the experimental findings, while the classical Maxwell model, as is well known, predicts a coefficient that is independent of the accommodation coefficient. We have also found that there is a correlation between the reflected velocity components. Neither the extended Maxwell model nor the CL model is able to capture this correlation.