Transient Flows of Newtonian Fluid through a Rectangular Microchannel with Slip Boundary

Abstract

We study the transient flow of a Newtonian fluid in rectangular microchannels taking into account boundary slip. An exact solution is derived by using the separation of variables in space and Fourier series expansion in time. It is found that, for different forms of driving pressure field, the effect of boundary slip on the flow behavior is qualitatively different. If the pressure gradient is constant, the flow rate is almost linearly proportional to the slip parameter $\mathcal{l}$ when $\mathcal{l}$ is large; if the pressure gradient is in a waveform, as the slip parameter $\mathcal{l}$ increases, the amplitude of the flow rate increases until approaching a constant value when $\mathcal{l}$ becomes sufficiently large.