Using dimensionless numbers to understand interfacial mass transfer for parallel flow in a microchannel

Liquid-liquid Extraction has emerged as a major technique for radioisotope extraction in recent years. This technique is particularly advantageous in the microscale as the surface-volume ratio is much larger. Since some of these radioisotopes have short half-lives, parallel flow in the microscale is used to extract them as it eliminates the need for separating the two fluids. Though such a configuration has been experimentally studied, dimensionless numbers have not been employed to understand the mass transfer mechanisms. This study uses three dimensionless numbers-the Biot, Peclet and Damkohler numbers-to delve deeper into mass transfer with a chemical reaction at the interface. Mass transfer simulations are performed using a Finite Difference model to solve the 2D Convection-Diffusion Equation with a first-order reaction at the interface, and these numbers are varied. The Damkohler number was observed to have the maximal impact on the extraction efficiency, and this was confirmed to be the case when the extraction efficiency didn't change much as long as the Damkohler number was kept constant. In general, a higher Damkohler number results in a higher extraction efficiency and a correlation was proposed to quantify this influence.