External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow

Abstract

This work systematically simulates the external mass transfer from/to a spherical drop and solid particle suspended in a nonlinear uniaxial extensional creeping flow. The mass transfer problem is governed by three dimensionless parameters: the viscosity ratio ( λ ), the Peclet number ( Pe ), and the nonlinear intensity of the flow ( E ). The existing mass transfer theory, valid for very large Peclet numbers only, is expanded, by numerical simulations, to include a much larger range of Peclet numbers (1 ≤ Pe ≤ 10 5 ). The simulation results show that the dimensionless mass transfer rate, expressed as the Sherwood number ( Sh ), agrees well with the theoretical results at the convection-dominated regime ( P e > 10 3 ). Only when E > 5/4, the simulated Sh for a solid sphere in the nonlinear uniaxial extensional flow is larger than theoretical results because the theory neglects the effect of the vortex formed outside the particle on the rate of mass transfer. Empirical correlations are proposed to predict the influence of the dimensionless governing parameters ( λ , Pe , E ) on the Sherwood number ( Sh ). The maximum deviations of all empirical correlations are less than 15% when compared to the numerical simulated results.