Non-equilibrium characteristics of mass and heat transfers in the slip flow

Abstract

Slip flow is a common phenomenon in micro-/nano-electromechanical systems. It is well known that the mass and heat transfers in slip flow show many unique behaviors, such as the velocity slip and temperature jump near the wall. However, the kinetic understanding of slip flow is still an open problem. This paper first clarifies that the Thermodynamic Non-Equilibrium (TNE) flows can be roughly classified into two categories: near-wall TNE flows and TNE flows away from the wall. The origins of TNE in the two cases are significantly different. For the former, the TNE mainly results from the fluid–wall interaction; for the latter, the TNE is primarily due to the considerable (local) thermodynamic relaxation time. Therefore, the kinetic modeling methods for the two kinds of TNE flows are significantly different. Based on the Discrete Boltzmann Modeling (DBM) method, the non-equilibrium characteristics of mass and heat transfers in slip flow are demonstrated and investigated. The method is solidly verified by comparing with analytic solutions and experimental data. In pressure-driven flow, the DBM results are consistent with experimental data for the Knudsen number up to 0.5. It is verified that, in the slip flow regime, the linear constitutive relations with standard viscous or heat conduction coefficients are no longer applicable near the wall. For the Knudsen layer problem, it is interesting to find that a heat flux (viscous stress) component in the velocity (temperature) Knudsen layer approximates a hyperbolic sinusoidal distribution. The findings enrich the insights into the non-equilibrium characteristics of mass and heat transfers at micro-/nano-scales.