(230k) Structure of Internal Circulations in Slug Flow through a Rectangular Micro-Channel

Mixing in the commonly observed slug flow regime in a liquid-liquid system in micro-channels is enhanced by internal circulations induced by shear. This helps improve mass transfer in this flow regime. In this work we exploit the low Re characteristic of the flow and seek a semi analytical solution to understand the structure of the vortex patterns formed in the two phases in the slug flow regime. The system is analysed in a moving reference frame under both creeping flow and the low Re flow-regimes which prevail in micro-channels. To get an analytical solution we assume the slugs to be rectangular. The governing equations of the model are solved using two approaches: 1) primitive variable formulation with the Chebyshev collocation method, 2) a stream function vorticity formulation based on finite differences. Results obtained from the two approaches are validated with each other. Specifically we focus on formation of vortex structures in the different phases and understanding the role of viscosity of the fluids. The system is analysed for two cases (i) when there is no thin film surrounding the slug and (ii) there is a thin film surrounding the slug. In the former secondary vortices are always induced in the fluid with the lower viscosity. In the latter the secondary vortices are always induced in the slug phase or discrete phase.