Instability of a liquid sheet with viscosity contrast in inertial microfluidics

Flows at moderate Reynolds numbers in inertial microfluidics enable high throughput and inertial focusing of particles and cells with relevance in biomedical applications. In the present work, we consider a viscosity-stratified three-layer flow in the inertial regime. We investigate the interfacial instability of a liquid sheet surrounded by a density-matched but more viscous fluid in a channel flow. We use linear stability analysis based on the Orr-Sommerfeld equation and direct numerical simulations with the lattice Boltzmann method (LBM) to perform an extensive parameter study. Our aim is to contribute to a controlled droplet production in inertial microfluidics. In the first part, on the linear stability analysis we show that the growth rate of the fastest growing mode [Formula: see text] increases with the Reynolds number [Formula: see text] and that its wavelength [Formula: see text] is always smaller than the channel width w for sufficiently small interfacial tension [Formula: see text]. For thin sheets we find the scaling relation [Formula: see text], where m is viscosity ratio and [Formula: see text] the sheet thickness. In contrast, for thicker sheets [Formula: see text] decreases with increasing [Formula: see text] or m due to the nearby channel walls. Examining the eigenvalue spectra, we identify Yih modes at the interface. In the second part on the LBM simulations, the thin liquid sheet develops two distinct dynamic states: waves traveling along the interface and breakup into droplets with bullet shape. For smaller flow rates and larger sheet thicknesses, we also observe ligament formation and the sheet eventually evolves irregularly. Our work gives some indication how droplet formation can be controlled with a suitable parameter set [Formula: see text].