Three-dimensional simulation of gaseous slip flow in different aspect ratio microducts

Abstract

Three-dimensional lattice Boltzmann method based simulations of a microduct have been undertaken in this paper. The objectives are to understand the different physical phenomena occurring at these small scales and to investigate when the flow can be treated as two dimensional. Toward this end, the Knudsen number and aspect ratio (depth to width ratio) are varied for a fixed pressure ratio. The pressure in the microduct is nonlinear with the nonlinearity in pressure reducing with an increase in the Knudsen number. The pressure behaves somewhat similar to two-dimensional microchannels, even when the aspect ratio is unity. The slip velocity at the impenetrable wall has two components: along and perpendicular to the primary flow direction. Our results show that the streamwise velocity near the centerline is relatively invariant along the depth for an aspect ratio of more than three, suggesting that the microduct can be modeled as a two-dimensional microchannel. On the other hand, the velocity component along the depth is never identically zero, implying that the flow is not truly two dimensional, although for practical purposes a two-dimensional treatment might suffice. A curious change in the vector direction in a plane normal to the flow direction is observed around an aspect ratio of four. These three-dimensional results are significant because they will help in theoretical development and flow modeling at microscales.