Unsteady conjugate mass and heat transfer from/to a prolate spheroidal droplet in uniaxial extensional creeping flow

Abstract

The unsteady conjugate mass/heat transfer from/to a prolate droplet suspended in uniaxial extensional creeping flow was numerically investigated. Based on the Stokes velocity field of a prolate droplet at small Reynolds numbers, a numerical algorithm combined with the finite difference method, the concentration transformation method and the level set approach was adopted to solve the convection-diffusion transport equations. The effects of Peclet number (1 ≤ Pe ≤ 1000), capillary number (0 ≤ Ca ≤ 0.1), viscosity ratio (0.01 ≤ λ ≤ 1), diffusivity ratio (0.1 ≤ K ≤ 10) and distribution coefficient (0.1 ≤ m ≤ 10) on interphase transport process were examined in terms of numerical simulation. The results show that the conjugate mass transfer from/to a single prolate droplet in the uniaxial extensional flow is significantly influenced by these five parameters, and the local and total mass transfer rates of a deformable droplet are slightly different from that of a spherical one. Given Pe, Ca, λ, K and m, an empirical correlation with an average relative deviation of 12.01% was proposed to predict Sh1,∞ of the prolate and spherical droplets suspended in uniaxial extensional creeping flow.