Internal mass and heat transfer between a single deformable droplet and simple extensional creeping flow

This work studied numerically the internal mass/heat transfer of a deformable droplet immersed in a simple extensional flow. The droplet would deform gradually from prolate spheroid to 'peanut' in uniaxial extensional flow, or from oblate spheriod to 'red-blood-cell' in biaxial extensional flow. Based on the analytical solution of Stokes flow over a deformable droplet, the convection-diffusion transport equation was numerically solved by the finite difference method. The results show that the heat/mass transfer behaviors of a deformable droplet were different when compared with that of a spherical one. The effects of Pe (1  ≤  Pe  ≤  10000), capillary number Ca (0  ≤  Ca  ≤ 0.5), viscosity ratio λ (0.01 ≤ λ ≤ 100) and the extensional flow direction on the Sh and mean concentration were numerically investigated. It shows that the internal mass/heat transfer rate was always enhanced with the increased degree of drop deformation in the diffusion-dominated case in both uniaxial/biaxial extensional flows. However, in the convection-dominated case, the flow direction has opposite influence on transport rates of mass/heat transfer with different deformation rates. The stabilized mass transfer rate decreased for droplets with different deformation in the order: 'red-blood-cell' shaped droplet, oblate droplet, prolate droplet and 'peanut' shaped droplet. At last, we proposed the empirical correlations to predict the internal mass/heat transfer rate of a deformable droplet (by adding the parameter Ca to represent the deformation of a droplet) in simple extensional flow.