In the gravity field, density changes triggered by a kinetic scheme as simple as A+B$\rightarrow${}C can induce or affect buoyancy-driven instabilities at a horizontal interface between two solutions containing initially the scalars A and B. On the basis of a general reaction-diffusion-convection model, we analyze to what extent the reaction can destabilize otherwise buoyantly stable density stratifications. We furthermore show that, even if the underlying nonreactive system is buoyantly unstable, the reaction breaks the symmetry of the developing patterns. This is demonstrated both numerically and experimentally on the specific example of a simple acid-base neutralization reaction.

Buoyancy-driven instabilities of a horizontal interface between two miscible solutions in the gravity field are theoretically studied in porous media and Hele-Shaw cells (two glass plates separated by a thin gap). Beyond the classical Rayleigh–Taylor (RT) and double diffusive (DD) instabilities that can affect such two-layer stratifications right at the initial time of contact, diffusive-layer convection (DLC) as well as delayed-double diffusive (DDD) instabilities can set in at a later time when differential diffusion effects act upon the evolving density profile starting from an initial step-function profile between the two miscible solutions. The conditions for these instabilities to occur can therefore be obtained only by considering time evolving base-state profiles. To do so, we perform a linear stability analysis based on a quasi-steady-state approximation (QSSA) as well as nonlinear simulations of a diffusion–convection model to classify and analyse all possible buoyancy-driven instabilities of a stratification of a solution of a given solute A on top of another miscible solution of a species B. Our theoretical model couples Darcy's law to evolution equations for the concentration of species A and B ruling the density of the miscible solutions. The parameters of the problem are a buoyancy ratio R quantifying the ratio of the relative contribution of B and A to the density as well as δ, the ratio of diffusion coefficients of these two species. We classify the region of RT, DD, DDD and DLC instabilities in the (R, δ) plane as a function of the elapsed time and show that, asymptotically, the unstable domain is much larger than the one captured on the basis of linear base-state profiles which can only obtain stability thresholds for the RT and DD instabilities. In addition the QSSA allows one to determine the critical time at which an initially stable stratification of A above B can become unstable with regard to a DDD or DLC mechanism when starting from initial step function profiles. Nonlinear dynamics are also analysed by a numerical integration of the full nonlinear model in order to understand the influence of R and δ on the dynamics.

When one solution of reactant A is displacing another miscible solution of reactant B, a miscible product C can be generated in the contact zone if a simple A + B → C chemical reaction takes place. Depending on the relative effect of A, B and C on the viscosity, different viscous fingering (VF) instabilities can be observed. In this context, a linear stability analysis of this reaction–diffusion–convection problem under the quasi-steady-state approximation is performed to classify the various possible instability scenarios. To do so, we determine the criteria for an instability, obtain dispersion curves both at initial contact time using an analytical implicit solution and at later times via numerical stability analysis. Along with recovering known results for non-reactive systems where the displacement of a more viscous fluid by a less viscous one leads to a VF instability, it is found that in the presence of a chemical reaction, injecting a more viscous fluid into a less viscous fluid can also lead to instabilities. This occurs when the chemical reaction leads to the build up of non-monotonic viscosity profiles. Various instability scenarios are classified in a parameter plane spanned by R_b and R_c representing the log-mobility ratios of the viscosities of the B and C solution respectively with respect to that of the injected solution of A. A parametric study of the influence on stability of the Damköhler number and of the time elapsed after contact of the two reactive solutions is also conducted.

We present new insights and results for the problem of a film falling down a heated wall: (i) treatment of a mixed heat flux boundary condition on the substrate; (ii) development of a long-wave theory for large Péclet numbers; (iii) refined treatment of the energy equation based on a high-order Galerkin projection in terms of polynomial test functions which satisfy all boundary conditions; (iv) time-dependent computations for the free-surface height and interfacial temperature; (v) numerical solution of the full energy equation; (vi) demonstration of the existence of a thermal boundary layer at the front stagnation point of a solitary pulse; (vii) development of models that prevent negative temperatures and are in good agreement with the numerical solution of the full energy equation.

Miscible viscous fingering classically occurs when a less viscous fluid displaces a miscible more viscous one in a porous medium. We analyze here how double diffusive effects between a slow diffusing S and a fast diffusing F component, both influencing the viscosity of the fluids at hand, affect such fingering, and, most importantly, can destabilize the classically stable situation of a more viscous fluid displacing a less viscous one. Various instability scenarios are classified in a parameter space spanned by the log-mobility ratios Rs and Rf of the slow and fast component, respectively, and parametrized by the ratio of diffusion coefficients $\delta${}. Numerical simulations of the full nonlinear problem confirm the existence of the predicted instability scenarios and highlight the influence of differential diffusion effects on the nonlinear fingering dynamics.

An experimental demonstration of reaction-driven viscous fingering developing when a more viscous solution of a reactant A displaces a less viscous miscible solution of another reactant B is presented. In the absence of reaction, such a displacement of one fluid by another less mobile one is classically stable. However, a simple A+B$\rightarrow${}C reaction can destabilize this interface if the product C is either more or less viscous than both reactant solutions. Using the pH dependence of the viscosity of some polymer solutions, we provide experimental evidence of both scenarios. We demonstrate quantitatively that reactive viscous fingering results from the buildup in time of nonmonotonic viscosity profiles with patterns behind or ahead of the reaction zone, depending on whether the product is more or less viscous than the reactants. The experimental findings are backed up by numerical simulations.