Convection-diffusion of solutes in dynamic media

Abstract

We investigate convective-diffusive transport of a solute through a medium with properties that can be externally modulated in space and time. In particular, we focus on the effect of a front—a sharp transition in the convective velocity (v) and diffusivity (D)—on the evolution of the solute concentration profile. Numerical results show that by suitably moving the front during the process an anti-dispersive effect may be realized, in which the solute accumulates in a thin region close to the moving boundary. Our computations take into account the realistic case of a front having a small but finite thickness, and we find that the width of the concentration profile scales as $$\left( {1/\sqrt {Pe} } \right)$$ , where Pe is the Peclet number. This is in sharp contrast to the 1/Pe scaling observed for the ideal case of the singular front assumed in previous work. The effect of the thickness of the front and the magnitude of the drop inv andD, on the solute concentration profile has also been studied. These results are relevant in order to implement and optimize protocols that apply an externally controlled moving boundary for the purpose of separation. We also present experimental results characterizing solute transport across a stationary front, expected to display many features needed in a model for moving fronts. The concentration profile of electrophoretically mobile BSA-FITC within the boundary layer at a polyacrylamde gel-buffer interface were visualized by epifluorescence microscopy. Measured boundary layer thickness exceeded that predicted for even a finite interface, indicating that the length scale associated with real boundaries is relevant to the modeling problem.