Chemo-hydrodynamic pulsations in simple batch A + B → C systems

Abstract

Spatio-temporal oscillations can be induced under batch conditions with ubiquitous bimolecular reactions in the absence of any nonlinear chemical feedback, thanks to an active interplay between the chemical process and chemically driven hydrodynamic flows. When two reactants A and B, initially separated in space, react upon diffusive contact, they can power convective flows by inducing a localized variation of surface tension and density at the mixing interface. These flows feedback with the reaction-diffusion dynamics, bearing damped or sustained spatio-temporal oscillations of the concentrations and flow field. By means of numerical simulations, we detail the mechanism underlying these chemohydrodynamic oscillations and classify the main dynamical scenarios in the relevant space drawn by parameters Δ M and Δ R, which rule the surface tension- and buoyancy-driven contributions to convection, respectively. The reactor height is found to play a critical role in the control of the dynamics. The analysis reveals the intimate nature of these oscillatory phenomena and the hierarchy among the different phenomena at play: oscillations are essentially hydrodynamic and the chemical process features the localized trigger for Marangoni flows unstable toward oscillatory instabilities. The characteristic size of Marangoni convective rolls mainly determines the critical conditions and properties of the oscillations, which can be further tuned or suppressed by the buoyancy competition. We finally discuss the possible experimental implementation of such a class of chemo-hydrodynamic oscillator and its implications in fundamental and applied terms.

From Transport Phenomena to Systems Chemistry: Chemohydrodynamic Oscillations in A+B→C Systems

“…When chemically‐induced surface tension gradients are beyond a critical threshold, the resulting flows undergo an oscillatory instability which entrains the dynamics of the chemical fields. As a whole, the phenomenon presents then an intrinsic hydrodynamic nature, [57] similar to the well‐known cases where Marangoni flows and related oscillations are promoted through an external fixed spatial gradient of temperature [16] …”

“…This idea of chemo‐hydrodynamic scenarios as a further example of rudimentary mechanisms for the emergence of functional and evolutionary behaviours has to be substantiated through experiments, starting from proof‐of‐concept systems where these dynamics can be isolated by taking into account the minimal ingredients described in previous sections, i. e., the localisation of the reactive source, that has to sustain a large surface‐tension gradient. In a recent paper, [57] we have suggested that labscale model systems may rely on hydrolysis, dissolution or photochemical processes that might also include thermal contributions. In particular, chemo‐Marangoni‐driven oscillations could be obtained in very shallow quasi‐2D reactors (or in microgravity flights) through endothermic processes such as the endothermic alkyl‐formate hydrolysis [70] or dissolution of salts like NH 4 NO 3 , since decreasing temperature is normally associated with an increase in the surface tension.…”

“…We have recently shown [18,57] that chemically-driven transport phenomena can introduce a nonlinear feedback, resulting in oscillatory dynamics of such systems that we will revisit below.…”

“…The resulting nonlinear dynamics is governed by a set of partial differential Reaction-Diffusion-Convection (RDC) equations discussed at length in refs. [18,57], where the bimolecular kinetics is coupled with Fickian diffusion and incompressible Navier-Stokes equations [Eqs. [1][2][3][4]]:…”

“…The global dynamics and phenomenology of these waves are extensively described in Refs. [18,57] and illustrated in Figure 3. Briefly, the reactants A and B meet at the reactor centre, x 0 , where the product C forms in the reaction zone.…”