Rotational instabilities in microchannel flows

Abstract

Mixing in numerous medical and chemical applications, involving overly long microchannels, can be enhanced by inducing flow instabilities. The channel length is thus shortened in the inertial microfluidics regime due to the enhanced mixing, thereby making the device compact and portable. Motivated by the emerging applications of a lab on a compact disk based microfluidic devices, we analyze the linear stability of rotationally actuated microchannel flows commonly deployed for biochemical and biomedical applications. The solution of the coupled system of Orr-Sommerfeld and Squire equations yields the growth rate and the neutral curves for the Coriolis force-driven instability. We report on the existence of four different types of unstable modes (Type-I to Type-IV) at low rotation numbers. Furthermore, Types-I and II exhibit competing characteristics, signifying that Type-II can play an important role in the transition to turbulence. Type-III and Type-IV modes have relatively lower growth rates, but the associated normal velocity has an oscillatory nature near the center of the channel. Thus, we infer that Types-III and IV might cause strong mixing locally by virtue of strong velocity perturbation in proximity to the various point depths. Moreover, the situation is reliable if the channel is too short to allow for the amplification of Types-I and II. We quantify the potential of all the unstable modes to induce such localized mixing near an imaginary interface (near a hyphothetical interface) inside the flow using the notion of penetration depth. This study also presents an instability regime diagram obtained from the parametric study over a range of Reynolds numbers, rotation numbers, and streamwise and spanwise wavenumbers to assist the design of efficient microchannels. Further insight into the mechanism of energy transfer, drawn from the evaluation of the kinetic-energy budget, reveals how the Reynolds stress first transfers energy from the mean flow to the streamwise velocity fluctuations. The Coriolis force, thereafter, redistributes the axial momentum into spanwise and wall-normal directions, generating the frequently observed roll-cell structures. A qualitative comparison of our predictions with the reported experiments on roll-cells indicates a good agreement.