Mass transfer around a slender drop in a nonlinear extensional flow

Moshe Favelukis

doi:10.1515/nleng-2018-0019

Abstract

Abstract Mass transfer around a slender drop in a nonlinear extensional and creeping flow is theoretically studied. The fluid mechanics problem is governed by three dimensionless parameters: The capillary number (Ca ≫ 1), the viscosity ratio (λ ≪ 1), and the nonlinear intensity of the flow (|E| ≪ 1). The transfer of mass around such a drop is studied for the two asymptotic cases of large and zero Peclet numbers (Pe). The results show that as the capillary number increases, the drop becomes longer, thinner, its surface area increases, leading to larger mass transfer rates, especially at large Peclet numbers, since then convection contributes to the overall mass transfer as well. Taking a slender inviscid drop (λ = 0) in a linear extensional flow (E = 0) as our reference case, we find that the addition of nonlinear effects to the flow sometimes increases (Eλ−1Ca−2 < 64/9) and sometimes decreases (Eλ−1Ca−2 > 64/9) the rate of mass transfer.

Highlights

Many industrial products such as foods, paints, pharmaceutics and cosmetics are made of emulsions in which a drop is embedded in a liquid
The results show that as the capillary number increases, the drop becomes longer, thinner, its surface area increases, leading to larger mass transfer rates, especially at large Peclet numbers, since convection contributes to the overall mass transfer as well
Mass transfer around slender drops in an axisymmetric linear extensional ow, for the two limits of the Peclet number, are summarized in Favelukis [22, 23]. For both asymptotic limits of the Peclet number, we found that as the elongation rate or the capillary number increases, the drop becomes thinner, longer and it surface area increases, leading to larger mass transfer rates

Summary

Introduction

Many industrial products such as foods, paints, pharmaceutics and cosmetics are made of emulsions in which a drop is embedded in a liquid. Taking a slender inviscid drop (λ = 0) in a linear extensional ow (E = 0) as our reference case, we nd that the addition of nonlinear e ects to the ow sometimes increases (Eλ− Ca− < 64/9) and sometimes decreases (Eλ− Ca− > 64/9) the rate of mass transfer.

Results

Conclusion