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

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'.

Investigation of chemoconvection in vibration fields

This study is devoted to the investigation of the chemoconvection in a two-layer miscible system caused by the neutralisation reaction proceeding in the convective-controlled (CC) regime under the influence of vertical vibrations. The CC regime without vibrational influence is characterized by the development of a density wave and vigorous convection in the upper layer, ensuring a high reaction rate and forcing the reaction front to move downwards more rapidly than in the well-known diffusive-controlled (DC) regime. It is shown that vibrations lead to some deceleration of the convection that depends both on the magnitude of the vibrational acceleration and on the initial concentrations of the reagents. Analysis of the system behaviour depending on the dimensionless parameters is carried out. It is demonstrated that the theory of thermal vibrational convection may be applied for reacting systems on quasi-steady time intervals.

Switching Modes of Mixing Due to an Adjustable Gap in a Continuous-Flow Microreactor

Microreactors are an important development in chemical engineering since the pharmaceutical industry needs flexible production rather than a large amount of product yield. The size of the microreactor may be so small that it requires the development of non-mechanical methods for reagent mixing. In this paper, we propose the design of a continuous-flow microreactor in the form of a narrow cell with a variable gap. By tuning the gap width in time and space, one can control the reaction rate and regulate the product yield. We show that the governing equation for the fluid flow can be reduced to the Darcy equation with permeability varying in space and time. As a test reaction, we consider the neutralization of nitric acid with sodium hydroxide resulting in the solutal convection in the presence of gravity. We show numerically that the prototyping spatially-distributed relief of the reactor walls can successfully separate the incoming and outgoing flows of reagents, control the mixing intensity, increase or decrease the product yield. We demonstrate also the dynamic control of the reactor efficiency via real-time local changes in the gap width.

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.

Experimental methods for visualization of hydrodynamic instability caused by the neutralization reaction in a miscible two-layer system

This paper focuses on experimental investigations of the spatio-temporal distributions of fluid velocity and temperature and the concentration of reagents and reaction products. We study concentration-dependent diffusion (CDD) convection driven by the neutralization reaction in a two-layer miscible system in a vertical Hele-Shaw cell using the original experimental complex. A comprehensive understanding of the physical mechanisms of convective motion and instabilities requires employing various experimental methods simultaneously. The proposed experimental complex provides simultaneous visualization and facilitates identification of the location of the reaction front, which is of importance to the study of its characteristics.