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Register a new userReactive-infiltration instabilities in rocks. Fracture dissolution
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A reactive fluid dissolving the surface of a uniform fracture will trigger an instability in the dissolution front, leading to spontaneous formation of pronounced well-spaced channels in the surrounding rock matrix. Although the underlying mechanism is similar to the wormhole instability in porous rocks there are significant differences in the physics, due to the absence of a steadily propagating reaction front. In previous work we have described the geophysical implications of this instability in regard to the formation of long conduits in soluble rocks. Here we describe a more general linear stability analysis, including axial diffusion, transport limited dissolution, non-linear kinetics, and a finite length system.
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Recent experiments demonstrate how a soluble body placed in a fluid spontaneously forms a dissolution pinnacle -- a slender, upward pointing shape that resembles naturally occurring karst pinnacles found in stone forests. This unique shape results from the interplay between interface motion and the natural convective flows driven by the descent of relatively heavy solute. Previous investigations suggest these structures to be associated with shock-formation in the underlying evolution equations, with the regularizing Gibbs-Thomson effect required for finite tip curvature. Here, we find a class of exact solutions that act as attractors for the shape dynamics in two and three dimensions. Intriguingly, the solutions exhibit large but finite tip curvature without any regularization, and they agree remarkably well with experimental measurements. The relationship between the dimensions of the initial shape and the final state of dissolution may offer a principle for estimating the age and environmental conditions of geological structures.
We investigate the chemical dissolution of porous media using a network model in which the system is represented as a series of interconnected pipes with the diameter of each segment increasing in proportion to the local reactant consumption. Moreover, the topology of the network is allowed to change dynamically during the simulation: as the diameters of the eroding pores become comparable with the interpore distances, the pores are joined together thus changing the interconnections within the network. With this model, we investigate different growth regimes in an evolving porous medium, identifying the mechanisms responsible for the emergence of specific patterns. We consider both the random and regular network and study the effect of the network geometry on the patterns. Finally, we consider practically important problem of finding an optimum flow rate that gives a maximum increase in permeability for a given amount of reactant.
Chemical reactions can accelerate, slow down or even be at the very origin of the development of dissolution-driven convection in partially miscible stratifications, when they impact the density profile in the host fluid phase. We numerically analyze the dynamics of this reactive convective dissolution in the fully developed non-linear regime for a phase A dissolving into a host layer containing a dissolved reactant B. We show that for a general A+B$rightarrow$C reaction in solution, the dynamics vary with the Rayleigh numbers of the chemical species, i.e. with the nature of the chemicals in the host phase. Depending on whether the reaction slows down, accelerates or is at the origin of the development of convection, the spatial distributions of species A, B or C, the dissolution flux and the reaction rate are different. We show that chemical reactions enhance the steady-state flux as they consume A and can induce more intense convection than in the absence of reactions. This result is important in the context of CO$_2$ geological sequestration where quantifying the storage rate of CO$_2$ dissolving into the host oil or aqueous phase is crucial to assess the efficiency and the safety of the project.
The reactive-infiltration instability, which develops when a porous matrix is dissolved by a flowing fluid, contains two important length scales. Here we outline a linear stability analysis that simultaneously incorporates both scales. We show that the commonly used thin-front model is a limiting case of a more general theory, which also includes convection-dominated dissolution as another special case. The wavelength of the instability is bounded from below, and lies in the range 1mm to 1km for physically reasonable flow rates and reaction rates. We obtain a closed form for the growth rate when the change in porosity is small.
The formation and evolution of immersed surface micro- and nanobubbles are essential in various practical applications, such as the usage of superhydrophobic rematerials, drug delivery, and mineral flotation. In this work, we investigate the entrapment of microbubbles on a hydrophobic surface, structured with microwells, when water flow passes along, and the subsequent microbubble dissolution. At entrapment, the microbubble is initially pinned at the edge of the microwell. At some point, the three-phase contact line detaches from one side of the edge and separates from the wall, after which it further recedes. We systematically investigate the evolution of the footprint diameter and the contact angle of the entrapped microbubbles, which reveals that the dissolution process is in the constant contact angle mode. By varying the gas undersaturation level, we quantify how a high gas undersaturation enhances the dissolution process, and compare with simplified theoretical predictions for dissolving bubbles on a plane surface. We find that geometric partial blockage effects of the diffusive flux out of the microbubble trapped in the microwell lead to reduced dissolution rates.
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