Flow development of co-flowing streams in rectangular micro-channels

Abstract

The diffusion and flow development characteristics of two co-flowing, laminar streams in a high aspect ratio rectangular micro-channel have been examined. A long, thin splitter plate initially separates the two streams such that fully developed flow in each of the two channels is established prior to merging. The co-flowing micro-channel has an aspect ratio of 16 with a width of 1006 μm and a height of 63 μm. Micro-Particle Image Velocimetry (μPIV) was utilized to observe the interaction between the streams for a range of flow rate ratios ranging from one to nine, for Reynolds numbers of one and ten. For flow rate ratios greater than one, a cross-stream pressure gradient exists immediately downstream of the splitter plate, which results in a strong lateral flow of the faster moving fluid into the slower moving fluid. Despite this rapid expansion, the fluids in the two streams do not mix. The two streams eventually recover a fully developed velocity profile across the entire channel. A model is presented to predict this development length based on the pressure imbalance between the two streams. The model is expressed in terms of the flow rate ratio between the streams, which is shown to be a function of channel aspect ratio. An asymptotic condition for the development length is found for high flow rate ratios and high aspect ratio channels. It is shown that existing entrance length relationships greatly underpredict this development length.