Direct numerical simulation of a single contaminated droplet microextraction in a yield-stress fluid

The present work investigates the extraction of solute from the contaminated micro-droplet suspended in non-Newtonain viscoplastic fluids (Herschel Bulkley). The fluid flow dynamics and interfacial mass transfer phenomena near a contaminated micro-droplet have been investigated prior to the estimation of extraction efficiency. The stagnant-cap model is employed to depict the droplet that has been contaminated. Dispersed droplet systems are commonly observed in diverse facets of our everyday encounters. These systems are found in various industries, encompassing flotation, energy storage, biofuels, printing, airlift reactors, and foam manufacture, among others. The study has focused on a linear thermodynamic equilibrium relationship that exists at the interface between two fluid phases. The momentum and species transport have been solved for a range of dimensionless parameters. These parameters include theta(cap), which varies between 120 degrees and 150 degrees, the Reynolds number (1 <= Re <= 100), the Bingham number (0 <= Bn <= 5), the dispersed to continuous fluid viscosity ratio (0.5 <= mu(ratio) <= 4), and the shear-thinning index (0.4 <= n <= 1). The results have been conveyed in the form of streamlines, contours, and by delineating the regions of deformation and non-deformation. The size of the zone that undergoes yielding tends to diminish as a result of the impact of the yield stress, while the presence of inertia promotes the enlargement of the zone that remains unyielded. The extraction efficiency and Sherwood number were estimated to be a function of theta(cap), Bingham number, Reynolds number, and shear-thinning index.