Title:Analytical Modeling of Slip Flow in Parallel-plate Microchannels
VOLUME: 5 ISSUE: 4
Author(s):Navid Kashaninejad, Weng Kong Chan and Nam-Trung Nguyen
Affiliation:School of Mechanical and Aerospace Engineering, Nanyang Technological, University, Singapore, 638075, Singapore.
Keywords:Air gap thickness, analytical flow rate, general velocity profile, parallel-plate microchannels, slip flow.
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 given 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 μm, 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 μm, and
larger than 7.5 μm, 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 μm, Navier-Stokes equation cannot be used to model the air flow, and instead molecularbased
approaches should be implemented. 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.
