Volume of Mixing Effect on Fluid Counter-Diffusion

The counter-current diffusion-driven mixing process of two miscible fluids is studied in the absence of gravity, assuming that the mixture is non regular, that is its volume is smaller than the sum of the initial volumes of the two components. Two competing effects are present in the mixing region: on one hand, the mass flow rate of each species increases, due to the larger density of the fluid; on the other hand, though, the volumetric flux is retarded by the inward convection due to volume disappearance, which opposes the outward velocity field due to diffusion. This intuition is confirmed by the analytical result of a 1D non-ideal mixing process, showing that, in the presence of the convection induced by a volume decrease, a) the process is self-similar; b) the mass flux of each species at the interface increases by approximately 0.8 e, where e is the maximum relative volume decrease; c) the volume flux of each species decreases by approximately a 0.2 e amount. This result is further confirmed by a perturbation analysis for small e.