Lubrication analysis and numerical simulation of the viscous micropump with slip

Abstract

A viscous micropump is a device such that a cylindrical rotor is eccentrically placed in a channel, and when the rotor is forced to rotate the viscous resistance between the small and large gaps between the cylinder and the channel walls generate a net flow along the channel. Assuming that the gaps between the cylinder and the channel walls are small compared to the radius of the rotor, the hydrodynamic theory of lubrication may be utilized to study the viscous pump. Here lubrication theory is used to obtain an analytical solution which relates the flowrate, rotation rate, pressure drop and applied torque as functions of the geometric parameters of the viscous pump. This analysis differs from a previous similar study of the effects of slip in two ways. Firstly, the applied pressure is implemented as a pressure load that the pump must overcome in its operation, and secondly different slip lengths are used on each of the channel walls and the rotor. Numerical simulations are performed to confirm the results of the lubrication analysis, utilizing a finite element analysis modified with a penalty method to implement the slip boundary conditions. Results indicate that slip just on the channel walls, with no-slip on the rotor, improves the performance of the pump with respect to the flux through the pump, but the pressure load that the pump may overcome is reduced. Slip just on the rotor and slip on the channel walls and the rotor reduces the performance of the pump. Comparison between the lubrication and numerical solution shows excellent quantitative agreement for small values of the channel spacing and good qualitative agreement for larger channel spacing for the cases of no slip or slip on the channel walls, which are the results of practical interest. With slip on the rotor, there is good agreement for small values of slip. For the case of slip everywhere, one of the assumptions used in obtaining the lubrication solution noticeably breaks down. © 2011.