Steady and oscillatory flow in the entrance region of microchannels

Abstract

The entrance region of a fluid channel is where the velocity distribution changes substantially from its initial condition at the entrance to that of fully developed flow. This region is particularly influential in microchannels as it may be a substantial portion of the total channel length, meaning that pressure drop and heat transfer are significantly different than for fully developed flow. Despite the fact that much work has been done on the development of steady flow, no reliable correlations exist for low Reynolds (Re) number flows in rectangular channels, and there is even less data available for oscillatory flows. It follows that a greater understanding of flow development would aid in the design of devices using microchannels in particular, since they involve low Reynolds numbers and are often oscillatory. In this study a microfluidic device was developed to generate controllable oscillatory flow together with a modular interface system to allow a reliable connection to a syringe pump so as to generate steady and pulsatile flows. The flow of de-ionised water from a large planar plenum into a square channel, nominally 50 by 50 micrometres, was studied under steady, oscillatory and pulsatile flow conditions. Time and phase averaged velocity fields were measured using micro-Particle Image Velocimetry.

Steady flow was studied in the entrance region of the microchannel for Reynolds numbers, 1<Re<60. Entrance lengths were calculated from the measured centerline velocities. The expected non-linear relationship between entrance length with Re, for low Reynolds numbers was found, and the flow was shown to develop much faster than predicted by existing correlations due to the planar entry. An entrance length correlation is proposed for steady flow under these conditions.

Oscillatory flow (zero net flow) was examined with Stokes number, S, <2.45. Time varying entrance lengths were calculated and these varied significantly over an oscillation cycle. Pulsatile flow (a mean flow superimposed on the oscillatory flow) for S=2.45 was examined for a range of oscillatory to steady flow ratios, 0.9<A<3.73. The entrance length was found to vary in time about the steady flow value. For both oscillatory and pulsatile conditions, the maximum entrance length was accurately described by the proposed steady flow correlation for entrance length, based on Re at peak flow. These results represent the first systematic experimental study into oscillatory entrance flows.