Buoyancy-driven pattern formation in reactive immiscible two-layer systems

Nonlinear development of convective patterns driven by a neutralization reaction in immiscible two-layer systems

This article provides the results of a theoretical and experimental study of buoyancy-driven instabilities triggered by a neutralization reaction in an immiscible two-layer system placed in a vertical Hele-Shaw cell. Flow patterns are predicted by a reaction-induced buoyancy number [Formula: see text], which we define as the ratio of densities of the reaction zone and the lower layer. In experiments, we observed the development of cellular convection ([Formula: see text]), the fingering process with an aligned line of fingertips at a slightly denser reaction zone ([Formula: see text]) and the typical Rayleigh-Taylor convection for [Formula: see text]. A mathematical model includes a set of reaction-diffusion-convection equations written in the Hele-Shaw approximation. The model's novelty is that it accounts for the water produced during the reaction, a commonly neglected effect. The persisting regularity of the fingering during the collapse of the reaction zone is explained by the dynamic release of water, which compensates for the heavy fluid falling and stabilizes the pattern. Finally, we present a stability map on the plane of the initial concentrations of solutions. Good agreement between the experimental data and theoretical results is observed. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

Spatial analog of the two-frequency torus breakup in a nonlinear system of reactive miscible fluids

We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction A+B→C in a vertical Hele-Shaw cell under constant gravity. We have recently reported that the concentration-dependent diffusion of species coupled with a frontal neutralization reaction can produce a multilayer system where low-density depleted zones could be embedded between the denser layers. This leads to the excitation of chemoconvective modes spatially separated from each other by a motionless fluid. In this Rapid Communication, we show that the layers can interact via a diffusion mechanism. Since diffusively coupled instabilities initially have different wavelengths, this causes a long-wave modulation of one pattern by another. We have developed a mathematical model which includes a system of reaction-diffusion-convection equations. The linear stability of a transient base state is studied by calculating the growth rate of the Lyapunov exponent for each unstable layer. Numerical simulations supported by phase portrait reconstruction and Fourier spectra calculation have revealed that nonlinear dynamics consistently passes through (i) a perfect spatially periodic system of chemoconvective cells, (ii) a quasiperiodic system of the same cells, and (iii) a disordered fingering structure. We show that in this system, the coordinate codirected to the reaction front paradoxically plays the role of time, time itself acts as a bifurcation parameter, and a complete spatial analog of the two-frequency torus breakup is observed.

Adaptive Micromixer Based on the Solutocapillary Marangoni Effect in a Continuous-Flow Microreactor

Continuous-flow microreactors are an important development in chemical engineering technology, since pharmaceutical production needs flexibility in reconfiguring the synthesis system rather than large volumes of product yield. Microreactors of this type have a special vessel, in which the convective vortices are organized to mix the reagents to increase the product output. We propose a new type of micromixer based on the intensive relaxation oscillations induced by a fundamental effect discovered recently. The mechanism of these oscillations was found to be a coupling of the solutal Marangoni effect, buoyancy and diffusion. The phenomenon can be observed in the vicinity of an air⁻liquid (or liquid⁻liquid) interface with inhomogeneous concentration of a surface-active solute. Important features of the oscillations are demonstrated experimentally and numerically. The periodicity of the oscillations is a result of the repeated regeneration of the Marangoni driving force. This feature is used in our design of a micromixer with a single air bubble inside the reaction zone. We show that the micromixer does not consume external energy and adapts to the medium state due to feedback. It switches on automatically each time when a concentration inhomogeneity in the reaction zone occurs, and stops mixing when the solution becomes sufficiently uniform.

Shock-wave-like structures induced by an exothermic neutralization reaction in miscible fluids

We report shock-wave-like structures that are strikingly different from previously observed fingering instabilities, which occur in a two-layer system of miscible fluids reacting by a second-order reaction A+B→S in a vertical Hele-Shaw cell. While the traditional analysis expects the occurrence of a diffusion-controlled convection, we show both experimentally and theoretically that the exothermic neutralization reaction can also trigger a wave with a perfectly planar front and nearly discontinuous change in density across the front. This wave propagates fast compared with the characteristic diffusion times and separates the motionless fluid and the area with anomalously intense convective mixing. We explain its mechanism and introduce a new dimensionless parameter, which allows to predict the appearance of such a pattern in other systems. Moreover, we show that our governing equations, taken in the inviscid limit, are formally analogous to well-known shallow-water equations and adiabatic gas flow equations. Based on this analogy, we define the critical velocity for the onset of the shock wave which is found to be in the perfect agreement with the experiments.

Concentration-dependent diffusion instability in reactive miscible fluids

We report on chemoconvective pattern formation phenomena observed in a two-layer system of miscible fluids filling a vertical Hele-Shaw cell. We show both experimentally and theoretically that the concentration-dependent diffusion coupled with frontal acid-base neutralization can give rise to the formation of a local unstable zone low in density, resulting in a perfectly regular cell-type convective pattern. The described effect gives an example of yet another powerful mechanism which allows the reaction-diffusion processes to govern the flow of reacting fluids under gravity conditions.

Chemical convection in the methylene-blue-glucose system: Optimal perturbations and three-dimensional simulations

A case of convection driven by chemical reactions is studied by linear stability theory and direct numerical simulations. In a plane aqueous layer of glucose, the methylene-blue-enabled catalytic oxidation of glucose produces heavier gluconic acid. As the oxygen is supplied through the top surface, the production of gluconic acid leads to an overturning instability. Our results complement earlier experimental and numerical work by Pons et al. First, we extend the model by including the top air layer with diffusive transport and Henry's law for the oxygen concentration at the interface to provide a more realistic oxygen boundary condition. Second, a linear stability analysis of the diffusive basic state in the layers is performed using an optimal perturbation approach. This method is appropriate for the unsteady basic state and determines the onset time of convection and the associated wavelength. Third, the nonlinear evolution is studied by the use of three-dimensional numerical simulations. Three typical parameters sets are explored in detail showing significant differences in pattern formation. One parameter set for which the flow is dominated by viscous forces, displays persistently growing convection cells. The other set with increased reaction rate displays a different flow regime marked by local chaotic plume emission. The simulated patterns are then compared to experimental observations.

Thermal effects on the diffusive layer convection instability of an exothermic acid-base reaction front

A buoyancy-driven hydrodynamic instability appearing when an aqueous acid solution of HCl overlies a denser alkaline aqueous solution of NaOH in a vertically oriented Hele-Shaw cell is studied both experimentally and theoretically. The peculiarity of this reactive convection pattern is its asymmetry with regard to the initial contact line between the two solutions as convective plumes develop in the acidic solution only. We investigate here by a linear stability analysis (LSA) of a reaction-diffusion-convection model of a simple A+B→C reaction the relative role of solutal versus thermal effects in the origin and location of this instability. We show that heat effects are much weaker than concentration-related ones such that the heat of reaction only plays a minor role on the dynamics. Computation of density profiles and of the stability analysis eigenfunctions confirm that the convective motions result from a diffusive layer convection mechanism whereby a locally unstable density stratification develops in the upper acidic layer because of the difference in the diffusion coefficients of the chemical species. The growth rate and wavelength of the pattern are determined experimentally as a function of the Brinkman parameter of the problem and compare favorably with the theoretical predictions of both LSA and nonlinear simulations.