2D Navier–Stokes Simulations of Microscale Viscous Pump With Slip Flow

Abstract

In this paper we provide numerical solution of the Navier–Stokes equations coupled with energy equation for gaseous slip flow in two-dimensional microscale viscous pumps. A first-order slip boundary condition was applied to all internal solid walls. The objectives are to study the performance of the pumps and to study the effect of velocity slip on its performance. Mass flow rate and pump efficiency were calculated for various pump operation conditions when an external pressure load is applied at the pump exit plane. Geometric parameters were held fixed in this work. Microviscous pump performance was studied in detail for several values of the Reynolds number, pressure load, eccentricity, and slip factors. Our numerical results for no-slip were compared with previously published experimental and numerical data and were found to be in very good agreement. Slip values and eccentricity were found to be major parameters that affect the performance of pump. Pump head decreases with increasing slip factors. Maximum pump efficiency increases with increasing slip factor up to Kn approaching 0.1. However, the maximum value of pump efficiency is found to experience a steep degradation for Kn approaching 0.1. The values of moment coefficient always decrease as both slip factor and distance of the rotor from the lower wall increase. Also, as slip factors and distance of the rotor from the lower wall increase, less net flow rate is predicted. For a given fixed driving force at the rotor surface, there is an optimum value for the behavior of pump efficiency with distance of the rotor from the lower wall. Future research should be conducted to modify the current design to make this concept work for higher Knudsen numbers.