Mathematical Modelling of Liquid –Liquid Extraction in the Slug Flow Regime in a Microchannel

Slug flow is a commonly observed flow regime in the microchannel. Mixing in the slug flow regime is enhanced by internal circulations induced by shearing due to wall. This helps improve mass transfer in this flow regime.

In this work, we exploit the low Reynold's number characteristic of the flow and seek a numerical solution to understand the structure of the vortex patterns formed in the two phases in the slug flow regime. Further, we study liquid-liquid extraction in the system and determine the improvement in mass transfer performance. A Lagrangian approach where we analyze the behaviour of a unit cell in the channel in a moving reference frame is adopted for the analysis. The system is analysed for two cases when there is (i) no film surrounding the slug (ii) a thin film surrounding the slug. The 2D governing equations for fluid flow are solved using two approaches: a) a stream function formulation based on finite differences, b) primitive variable formulation with the Chebyshev collocation method. Results obtained from the two methods are validated with each other. Then, the species balance equation is solved numerically using a finite volume code. The extraction performance is analysed in terms of extraction efficiency and mass transfer coefficient. It is believed that the enhancement in mass transfer is due to the mixing induced by the strong internal circulation set up due to the channel wall. The model is validated with published experimental results.