Abstract
We study a two-layer system of initially separated aqueous solutions of an acid and a base placed in a vertically oriented Hele–Shaw cell. After the reactants, a second-order neutralization reaction begins, which is accompanied by the release of salt. Recently, we found that, contrary to expectations of the occurrence of fingering convection, a density wave pattern may occur in this system at some values of initial concentrations of acid and base. This wave has a perfectly planar front with a nearly discontinuous change in density across the front and propagates fast compared with the characteristic diffusion times. The shock wavefront separates the domains of a motionless fluid and intense convective mixing. In this work, we study, both theoretically and experimentally, the influence of the cavity geometry on the dynamics of the density wave. Specifically, we consider the following cases: when (a) the aspect ratio of the cavity changes, (b) the gap width of the Hele–Shaw cell is locally varied, and (c) the oblique obstacle is placed inside the cell. The set of governing equations includes the equation of motion based on Darcy’s law as well as the transfer equations for species. The experimental observations presented for the wave bending around the obstacle are in good agreement with the numerical simulation.
Highlights
In recent years, the problems of reaction–diffusion–convection have attracted the interest of researchers for their fundamental aspects and many technological applications, such as oil refining,1,2 photochemical polymerization,3–5 utilization of carbon dioxide to combat the greenhouse effect,6–8 chemical reactor design,9,10 pharmaceutical production in continuous-flow microreactors,11–13 and so on
We study the influence of the Hele–Shaw cell geometry on the shock wave pattern induced jointly by a secondorder chemical reaction, chemoconvection, and gravity
We investigate the influence of the Hele–Shaw cell aspect ratio on the properties of the wave
Summary
The problems of reaction–diffusion–convection have attracted the interest of researchers for their fundamental aspects and many technological applications, such as oil refining, photochemical polymerization, utilization of carbon dioxide to combat the greenhouse effect, chemical reactor design, pharmaceutical production in continuous-flow microreactors, and so on. The first one is a concentration-dependent diffusion (CDD) instability, emphasizing the sensitivity of the diffusion coefficient of a given substance to its concentration.28 In this case, the final pattern is a periodic system of chemoconvective cells formed parallel to the reaction front and perpendicular to the direction of gravity.. The final pattern is a periodic system of chemoconvective cells formed parallel to the reaction front and perpendicular to the direction of gravity.29 Another instability is a shock-like density wave appearing when the densities of the upper and bottom layers are approximately equal. The HS cell is a versatile experimental and numerical configuration in chemical engineering studies.35–39 This geometry greatly simplifies the theoretical analysis and expands the possibilities for external control of the mixing process.
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