Interfacial hydrodynamic instabilities driven by cross-diffusion in reverse microemulsions

Abstract

When two microemulsions are put in contact in the gravity field along a horizontal contact line, cross-diffusion can trigger the transport of one species in the presence of a gradient in concentration of another species. We show here theoretically that such cross-diffusion effects can induce buoyancy-driven convective instabilities at the interface between two solutions of different compositions even when initially the less dense solution lies on top of the denser one. Two different sources of convective modes are identified depending whether positive or negative cross-diffusion is involved. We evidence the two predicted cross-diffusion driven instabilities experimentally using a two-layer stratification of Aerosol-OT (AOT) water-in-oil microemulsions solutions with different water or AOT composition.

Interfacial Mass Transfer in Trichloroethylene/Surfactants/ Water Systems: Implications for Remediation Strategies

“…Mass transfer at the interface of two miscible and/or slightly miscible liquids is in general a complex mechanism that involves diffusive and advective phenomena [21]. Molecular diffusion, double diffusion [22] and cross-diffusion [23][24][25] can trigger hydrodynamic instabilities (fingers, plumes, waves, etc.) that generally enhance the mixing of the liquids but are difficult to decouple in order to understand the single contributions to the global dynamics.…”

Stochastic approach to Fisher and Kolmogorov, Petrovskii, and Piskunov wave fronts for species with different diffusivities in dilute and concentrated solutions

“…Eqs. (18) and (19) and replacing ∂ x X by (N X (i+1)−N X (i))/Ω∆x for X = A, B, we assign well-chosen terms of the flux j X (i+ 1 /2) to the transition rates to the left and to the right…”

“…The effect of non standard diffusion on the speed of FKPP front is currently investigated [8,9,10,11] and we recently considered the propagation of a wave front in a concentrated solution in which cross-diffusion cannot be neglected [12]. Experimental evidence of cross-diffusion has been given in systems involving ions, micelles, surface, or polymer reactions and its implication in hydrodynamic instabilities has been demonstrated [13,14,15,16,17,18]. In parallel, cross-diffusion is becoming an active field of research in applied mathematics [19,20,21,22,23,24].…”

Introduction to Focus Issue: Oscillations and Dynamic Instabilities in Chemical Systems: Dedicated to Irving R. Epstein on occasion of his 70th birthday

“…50 Budroni et al report that cross-diffusion effects in AOT water-in-oil microemulsion solution with different water or AOT compositions can induce buoyancy-driven convective instabilities at the interface between the two solutions. 51 Microscale encapsulation of the BZ reaction was developed by the group of Irv Epstein with microfluidic droplet technology. 52,53 The system displayed rich in and anti-phase synchronization patterns and was recently used to confirm all predictions of Turing for a ring of six coupled drops, in particular, related to the differential growth of the droplets due to the formation of the spatial pattern.…”