We present a new mechanism through which chemical oscillations and waves can be induced in batch conditions with a simple A þ B → C reaction in the absence of any nonlinear chemical feedback or external trigger. Two reactants A and B, initially separated in space, react upon diffusive contact and the product actively fuels in situ convective Marangoni flows by locally increasing the surface tension at the mixing interface. These flows combine in turn with the reaction-diffusion dynamics, inducing damped spatiotemporal oscillations of the chemical concentrations and the velocity field. By means of numerical simulations, we single out the detailed mechanism and minimal conditions for the onset of this periodic behavior. We show how the antagonistic coupling with buoyancy convection, due to concurrent chemically induced density changes, can control the oscillation properties, sustaining or suppressing this phenomenon depending on the relative strength of buoyancy-and surface-tension-driven forces. The oscillatory instability is characterized in the relevant parametric space spanned by the reactor height, the Marangoni (Ma i ) and the Rayleigh (Ra i ) numbers of the ith chemical species, the latter ruling the surface tension and buoyancy contributions to convection, respectively.

Dissolution of fractured rocks is often accompanied by the formation of highly localized flow paths. While the fluid flow follows existing fractures in the rock, these fissures do not, in general, open uniformly. Simulations and laboratory experiments have shown that distinct channels or “wormholes” develop within the fracture, from which a single highly localized flow path eventually emerges. The aim of the present work is to investigate how these emerging flow paths are influenced by the initial aperture field. We have simulated the dissolution of a single fracture starting from a spatially correlated aperture distribution. Our results indicate a surprising insensitivity of the evolving dissolution patterns and flow rates to the amplitude and correlation length characterizing the imposed aperture field. We connect the similarity in outcomes to the self‐organization of the flow into a small number of wormholes, with the spacing determined by the length of the longest wormholes. We have also investigated the effect of a localized region of increased aperture on the developing dissolution patterns. A competition was observed between the tendency of the high‐permeability region to develop the dominant wormhole and the tendency of wormholes to spontaneously nucleate throughout the rest of the fracture. We consider the consequences of these results for the modeling of dissolution in fractured and porous rocks.

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.

We consider a simple model of infiltration‐driven mineral replacement, in which the chemical coupling between precipitation and dissolution leads to the appearance of a reaction front advancing into the system. Such fronts are usually accompanied by a local increase of porosity. We analyze the linear stability of the replacement front to establish whether such a localized porosity increase can lead to global instability and pattern formation in these systems. We find that for a wide range of control parameters such fronts are unstable. However, both short‐ and long‐wavelength perturbations are stabilized, whereas in a purely dissolutional instability only short wavelengths are stable. We analyze the morphologies of the dissolution patterns emerging in the later stages of the evolution of the system, when the dynamics are beyond the linear regime. Implications of these results for the natural systems are discussed, particularly in the context of karst formation in terra rossa‐covered carbonate bedrock.