Mass Transfer from Ensembles of Newtonian Fluid Spheres at Moderate Reynolds and Peclet Numbers

In this work, the rate of mass transfer from an ensemble of mono-size spherical Newtonian droplets (free from surfactants) to a Newtonian continuous phase has been numerically studied at moderate Reynolds and Peclet numbers. A simple spherical cell model (so-called free surface cell model) has been used to account for inter-drop hydrodynamic interactions. Extensive numerical results have been obtained to elucidate the effects of the Reynolds number (Reo), the ratio of internal to external fluid viscosity (k), the volume fraction of the dispersed phase (ɛ) and the Schmidt number (Sc) on the local and average Sherwood number (Sh) over the ranges of conditions: 1 ≤ Reo ≤ 200, 0.2 ≤ ɛ ≤ 0.6, 0.1 ≤ k≤ 50 and 1 ≤ Sc ≤ 10 000. It has been observed that the effects of viscosity ratio on the local and average Sherwood number is less significant for small values of the Peclet number (Pe) for all values of dispersed phase concentration. As the value of the viscosity ratio increases, the average Sherwood number decreases for all values of the droplet concentration and the Reynolds number. Based on the present numerical results, a simple predictive correlation is proposed which can be used to estimate the rate of inter-phase mass transfer in a liquid–liquid system in a new application. However, it is also appropriate to add here that at higher concentrations, fluid spheres interact significantly, deform and coalesce. All these effects are neglected in this study. Therefore, the present results are valid only for dilute to moderate concentration of the dispersed phase.