On Non-Monotonic Variation of Hydrodynamically Focused Width in a Rectangular Microchannel

This article presents a comprehensive theoretical model and limited experimental results for describing two-dimensional hydrodynamic focusing in microchannels involving immiscible fluids. It is shown that the normalized focused sample width depends on three non-dimensional parameters - the flow rate ratio, viscosity ratio and aspect ratio. A theory encompassing the effects of all these parameters is developed. Whereas the effects of flow rate ratio and viscosity ratio on the focused sample width are monotonic in nature, those of aspect ratio can be non-monotonic. We report existence of a viscosity ratio beyond which the normalized width decreases with an increase in the aspect ratio, and for viscosity ratio less than a critical value the normalized width increases with increase in the aspect ratio. This parameter range where the minimum sample width is obtained is further analysed. The effect of aspect ratio and flow rate ratio have been validated experimentally using oil and water based systems. A physical explanation of the variation of sample width with aspect ratio along with microchannel-design guidelines are also provided in this study. We demonstrate that the derived results are more general than the available theoretical models. This comprehensive theory can eventually be employed for predicting hydrodynamically focused width in microdevices and for employing optimal aspect ratio microchannels, without incurring the cost of experiments and human effort.