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

Abstract

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.

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

“…We have shown that the CDD effect can result in the development of a perfectly regular convective pattern [31]. The effect was found primarily for the pair HNO 3 /NaOH, but then it was demonstrated also for other systems, for example, HNO 3 /KOH, HCl/NaOH [32,33].…”

“…In the last years, this simple, irreversible chemical reaction occurring in liquid-liquid miscible systems was extensively studied, to mention but a few [28,29,[31][32][33]. The Rayleigh-Taylor plumes and fingers are commonly observed under gravity when the heavier A overlies the lighter B [28].…”

“…Another mechanism breaking the equilibrium was found to be double diffusion instability and diffusive-layer convection [29]. Recently, we have reported a new type of instability, the CDD convection [31][32][33]. It belongs to the family of double-diffusion phenomena and arises when the diffusion coefficients of species depend on their concentrations.…”

“…The parameter α is estimated to be about α = 10 3 . The Rayleigh numbers can be estimated from experimental data as R A = 1.5 × 10 5 , R B = 1.8 × 10 5 , R S = 2.4 × 10 5 [33].…”

“…Second-order reactions coupled with flows have been attracting the attention of researchers because of their relatively simple but nonlinear kinetics [28][29][30]. Previously, we have found that convection can arise in the presence of gravity due to the effect of concentration-dependent diffusion (CDD) of species [31][32][33]. The CDD convection is used here to demonstrate how to control the mass transfer in the microreactor by manipulating its wall relief.…”