Discrete velocity method for rarefied gas flow within a microchannel

Abstract

This study focuses on a classic fluid dynamics problem of gas Couette flow between two parallel plates in relative motion. The main objective of this research is to analyze the rarefaction degree impact on the transport characteristics of a rarefied gas flow, both in planar and oscillatory configurations, using the Discrete Velocity Method (DVM). Depending on its rarefaction, the flow can belong to different regimes: continuum, slip, transition, and free molecular. The study highlights the challenges of solving the Boltzmann equation, particularly in the transition regime. The DVM is used to solve the Boltzmann equation in the rarefaction regime, determining the velocity and shear stress profiles for the planar Couette flow and the amplitudes and phases in the oscillatory Couette flow. The obtained results are validated with other numerical methods, such as Direct Simulation Monte Carlo (DSMC) and the linearized Boltzmann equation solution (BE). The results show a significant sensitivity of flow characteristics with the rarefaction intensity given by the Knudsen number (Kn). This shows the DVM’s accuracy as an effective and accurate alternative, particularly in slip and transition regimes. The study also extends to the analysis of oscillatory Couette flow, where the plates oscillate at a given frequency. This flow is analyzed using complex variables to capture the amplitudes and phases of the movement. This study demonstrates the applicability of DVM in practical situations, particularly in microfluidic and vacuum devices, where the understanding of flow characteristics is crucial.