Modelling of mass transfer from falling droplets

Abstract

The prediction of mass transfer rates to and from moving drops has traditionally used the Whitman two-film theory approach in which the resistances to mass transfer on each side of the interface are described by film mass transfer coefficients. These are correlated in terms of the hydrodynamic conditions, the physical properties of the fluids, and the geometry of the system. The performance of liquid–liquid contactors in which mass transfer occurs between swarms of moving droplets of one phase and the other liquid phase as the continuous phase, has similarly been correlated in terms of mass transfer coefficients. These lump together the combined effects of interfacial mass transfer resistances and those associated with the bulk phases, the effects of interfacial disturbances, coalescence and break-up phenomena, specific surface area, and the effects of axial mixing. In this paper we build upon earlier work and other published research which uses finite element methods to quantitatively calculate flow field data and trajectory predictions for single particles and drops in a two phase system. The differential equations were discretised using the finite element approach employing a procedure based on the Lagrangian framework developed earlier. Here we extend the approach to calculate mass transfer rates between single aqueous drops and a continuous immiscible solvent phase. The calculated values of drop velocity and mass transfer rates are compared with experimental values determined for single drops of ethanol/water mixtures extracting into a continuous phase of n-decanol. Good agreement between the experimental and predicted values was obtained, thus demonstrating that in this case, interfacial mass transfer in liquid–liquid systems can be predicted from the fundamental transport equations. The results of the work indicate the potential of further development of this approach for swarming drops and hence quantitative prediction of the behaviour of liquid–liquid contactors.