Analytical Modeling of Slip Flow in Parallel-plate Microchannels

Abstract

This paper presents analytical modeling of slip liquid flow in parallel-plate microchannels, and can be divided in two parts. In the first part, classical relationships describing velocity, flow rate, pressure gradient, and shear stress are extended to the more general cases where there exist two different values of the yet-unknown slip lengths at the top and bottom walls of the channel. These formulations can be used to experimentally determine the values of slip length on the channels fabricated from two different hydrophobic walls. In the second part, the emphasis is on the quantification of the slip length analytically. Generating mechanism of slip is attributed to the existence of a low-viscosity region between the liquid and the solid surface. By extending the previous works, the analytical values of slip length are determined using exact, rather than empirical, values of air gap thickness at different ranges of air flow Knudsen number. In addition to the exact expressions of air gap thickness, the corresponding ranges of the channel height where slip flow can be induced are also found analytically. It is found that when the channel height is larger than 700 孬 air flow is in continuum regime and no-slip boundary condition can be used. For the case where the channels height is smaller than 700 孠and larger than 7.5 孬 slip boundary condition should be used to model the air flow in the channel. Finally, for the channel with the height smaller than 7.5 孬 the Navier-Stokes equation cannot be used to model the air flow, and instead molecular-based approaches should be used. The results of this paper can be used as a guideline for both experimentalists and theoreticians to study the slip flow in parallel-plate microchannels.