Towards more predictive correlations for conjugated mass transfer across a droplet interface

Abstract

Most studies of heat or mass transfer in dispersed, two-phase flows are either analytical or empirical, and therefore limited to simplified or specific operating conditions. In this frame, Direct Numerical Simulations (DNS) can be a powerful tool to address the needs arising from the development of new liquid–liquid solvent extraction processes, involving e.g., more viscous solvents or different hydrodynamic conditions. In this study, a large parametric study, in the range: Reynolds number Re∈[1,500], Péclet number Pee∈[10,1000], viscosity ratio μ∗∈[0.05,20] and a thermodynamic equilibrium coefficient k∈[0.1,10] , of mass transfer from an isolated droplet is achieved by DNS to propose a physically based correlation of the apparent Sherwood number, Sh, that is sufficiently generic to apply to emerging and future applications. The updated correlations derive first from a solid analysis of the features, in terms of concentration fields inside and outside the droplet and interface properties, to challenge the validity of the assumptions of mass transfer correlations. Then, we propose proper modifications in the formulation of existing models. In a second step, the accuracy and the robustness of the new models have been assessed by comparison with Sh obtained from DNS. The proposed correlations are applicable for mass transfer as well as for heat transfer problems, in most configurations encountered in chemical plants.