Cross-diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger unconventional buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications [1,2,3]. Here a cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion to the Stokes equations . In order to isolate the effect of cross-diffusion in the destabilization of a double-layer system, we impose in the bottom layer a starting concentration gap in one of the species while the other is homogeneously distributed over the spatial domain. We show that, depending upon which species features the initial concentration gap, we can selectively activate different cross-diffusion feedback and promote two possible types of hydrodynamic scenarios (negative cross-diffusion convection, NCC, and positive cross-diffusion convection, PCC) corresponding to the sign of the operational cross-diffusion term. The study of the space-time density profiles along the gravitational axis allows to obtain analytical conditions for the onset of convection in terms of two important parameters: the dominating cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in this restricted parameter space is supported and complemented by numerical simulations of the fully nonlinear CDC problem. The resulting spatio-temporal convective dynamics excellently compare with experiments performed with AOT water-in-oil reverse microemulsions (ME) , in which initially stable stratifications between two ME are studied in a Hele-Shaw cell by just imposing a gradient in water or AOT concentration. ME are shown to be a convenient model system for inducing both convective modes predicted and, while PCC scenarios have been already identified experimentally in previous works , NCC modes are isolated, for the first time, with ME. Our approach constitutes a reference framework for future studies on pattern formation arising from the interplay between cross-diffusion convection and chemical reactions.
|Titolo:||Classification of cross-diffusion-driven convection in 2-component double-layer systems: Theory and Experiments|
|Citazione:||Budroni, M.A., Carballido Landeira, J., Wit, A.D., & Rossi, F. (2015). Classification of cross-diffusion-driven convection in 2-component double-layer systems: Theory and Experiments. In 8th International Conference Engineering of Chemical Complexity (pp.58-58).|
|Appare nelle tipologie:||4.2 Abstract in Atti di convegno|
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