Abstract

We investigate the convective mass transfer of dilute passive tracers contained in small viscous drops into a submerging falling liquid film. This problem has applications in industrial cleaning, domestic dishwashers, and decontamination of hazardous material. The film Peclet number is very high, whereas the drop Peclet number varies from 0.1 to 1. We model the mass transfer using an analogy with Newton’s law of cooling. This empirical model is supported by an analytical model solving the quasi-steady two-dimensional advection—diffusion equation in the film that is coupled with a time-dependent one-dimensional diffusion equation in the drop. We find excellent agreement between our experimental data and the two models. The transport characteristic time is related to the drop diffusion time scale, as diffusion within the drop is the limiting process. Our theoretical model not only predicts the well-known relationship between the Sherwood number and the external Reynolds number in the case of a well-mixed drop Sh ~ Re^(1/3), it also predicts a correction in the case of a non-uniform drop concentration. We compare and discuss this correction with experimental data. This material is based upon work supported by the Defense Threat Reduction Agency under Contract No. HDTRA1 -12-D-0003-0001.