Density profiles around A+B→C reaction-diffusion fronts in partially miscible systems: A general classification

CO2 Microbubbles in Silicone Oil (Part II: Henry's Constant and Anomalous Diffusion)

This work demonstrates the utility of microfluidic devices for characterizing diffusion mechanisms. We determined Henry's constant and characterized the diffusion process of gaseous CO2 in silicone oil. Using microfluidic techniques, we analyzed the evolution of the CO2 bubble size in a solvent flowing through a microchannel system. The reduction in bubble size due to the mass transfer of gaseous CO2 into the solvent fluid primarily affects their length. A microfluidic device was used to produce bubbles, consisting of a pressure-driven injection system for the gas and a flow-driven system for the liquid. Additionally, an optical device was coupled for tracking and studying the bubbles in the microchannels, enabling us to study their spatial and temporal evolution using image analysis. From this study, we found two diffusion regimes. The first is a superdiffusive process for short times. In this regime, due to the high concentration gradient values at the gas-liquid interface, we observed a higher rate of carbon dioxide transfer to the silicone oil. At longer times, we see that the gas transfer rate significantly decreases compared to the previous regime, leading to a subdiffusive process. In this latter regime, it was found that if we increase the gas pressure, the system approaches a normal diffusive process that coincides with previously conducted studies by other researchers. It is suggested that the subdiffusion could be due to the high degree of confinement of the bubbles within the microchannel, similar to what occurs in porous media, the high viscosity of the fluid, and the low gas pressure used in the tests. The microfluidic device proved to be a very efficient method for determining the diffusion process and Henry's constant in this case. Its easy fabrication and low cost make this type of device appropriate for substance characterization.

Effect of variable solubility on reactive dissolution in partially miscible systems

When two partially miscible systems are put in contact, one phase, A, can dissolve into the other one with a given solubility. Chemical reactions in the host phase can impact this dissolution by consuming A and by generating products that impact the solubility of A. Here, we study theoretically the optimal conditions for transfer of a reactant A in a host phase containing a species B when a bimolecular A + B → C reaction generates a product C that linearly decreases the solubility of A. We have quantified numerically the influence of this variable solubility on the reaction-diffusion (RD) concentration profiles of all species in the host phase, on the temporal evolution of the position of the reaction front, and on the flux of A through the interface. We have also computed the analytical asymptotic concentration profiles, solutions at long times of the RD governing equations. For a fixed negative effect of C on the solubility of A, an increase in the initial concentration of reactant B or an increase in the diffusion rate of species B and C results in a larger flux of A and hence a larger amount of A dissolved in the host solution at a given time. However, when the influence of C on the solubility increases, the mass transfer decreases. Our results help understand to what extent a chemical reaction can optimize the reactive transfer of a solute to a host phase with application to, among other things, the geological sequestration of carbon dioxide in an aquifer.

Investigation of chemoconvection in vibration fields

This study is devoted to the investigation of the chemoconvection in a two-layer miscible system caused by the neutralisation reaction proceeding in the convective-controlled (CC) regime under the influence of vertical vibrations. The CC regime without vibrational influence is characterized by the development of a density wave and vigorous convection in the upper layer, ensuring a high reaction rate and forcing the reaction front to move downwards more rapidly than in the well-known diffusive-controlled (DC) regime. It is shown that vibrations lead to some deceleration of the convection that depends both on the magnitude of the vibrational acceleration and on the initial concentrations of the reagents. Analysis of the system behaviour depending on the dimensionless parameters is carried out. It is demonstrated that the theory of thermal vibrational convection may be applied for reacting systems on quasi-steady time intervals.

Diffusion-controlled annihilation A+B→0: Coalescence, fragmentation, and collapse of nonidentical A-particle islands submerged in the B-particle sea

We present a systematic analysis of diffusion-controlled interaction and collapse of two nonidentical spatially separated d-dimensional A-particle islands in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. We show that at a sufficiently large initial distance between the centers of islands 2ℓ and a relatively large initial ratio of island-to-sea concentrations, the evolution dynamics of the island-sea-island system demonstrates remarkable universality and, depending on the system dimension, is determined unambiguously by two dimensionless parameters Λ=N_{0}^{+}/N_{Ω} and q=N_{0}^{-}/N_{0}^{+}, where N_{0}^{+} and N_{0}^{-} are the initial particle numbers in the larger and smaller of the islands, respectively, and N_{Ω} is the initial number of sea particles in the volume Ω=(2ℓ)^{d}. We find that at each fixed 0<q≤1, there are threshold values Λ_{★}(q) and Λ_{s}(q)≥Λ_{★}(q) that depend on the dimension and separate the domains of individual death of each of the islands Λ<Λ_{★}(q), coalescence and subsequent fragmentation (division) of a two-centered island Λ_{★}(q)<Λ<Λ_{s}(q), and collapse of a single-centered island formed by coalescence Λ>Λ_{s}(q). We demonstrate that regardless of d, the trajectories of the island centers are determined unambiguously by the parameter q, and we reveal a detailed picture of the evolution of islands and front trajectories with an increase in Λ, focusing on the scaling laws of evolution at the final collapse stage and in the vicinity of starting coalescence and fragmentation points.

Diffusion-controlled coalescence, fragmentation, and collapse of d-dimensional A-particle islands in the B-particle sea

We present a systematic analysis of diffusion-controlled interaction and collapse of two identical spatially separated d-dimensional A-particle islands in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. We show that at a sufficiently large initial distance between the centers of islands 2ℓ compared to their characteristic initial size and a relatively large initial ratio of island to sea concentrations, the evolution dynamics of the island-sea-island system is determined unambiguously by the dimensionless parameter Λ=N_{0}/N_{Ω}, where N_{0} is the initial particle number in the island and N_{Ω} is the initial number of sea particles in the volume Ω=(2ℓ)^{d}. It is established that (a) there is a d-dependent critical value Λ_{★} above which island coalescence occurs; (b) regardless of d the centers of each of the islands move toward each other along a universal trajectory merging in a united center at the d-dependent critical value Λ_{s}≥Λ_{★}; (c) in one-dimensional systems Λ_{★}=Λ_{s}, therefore, at Λ<Λ_{★} each of the islands dies individually, whereas at Λ>Λ_{★} coalescence is completed by collapse of a single-centered island in the system center; (d) in two- and three-dimensional systems in the range Λ_{★}<Λ<Λ_{s} coalescence is accompanied by subsequent fragmentation of a two-centered island and is completed by individual collapse of each of the islands. We discuss a detailed picture of coalescence, fragmentation, and collapse of islands focusing on evolution of their shape and on behavior of the relative width of the reaction front at the final collapse stage and in the vicinity of starting coalescence and fragmentation points. We demonstrate that in a wide range of parameters, the front remains sharp up to a narrow vicinity of the coalescence, fragmentation, and collapse points.

Chemically-driven convective dissolution

When a solute A dissolves in a host phase with a given solubility, the resulting density stratification is stable towards convection if the density profile increases monotonically along the gravity field. We theoretically and numerically study the convective destabilization by reaction of this dissolution when A reacts with a solute B present in the host phase to produce C via an A + B→C type of reaction. In this reactive case, composition changes can give rise to non-monotonic density profiles with a local maximum. A convective instability can then be triggered locally in the zone where the denser product overlies the less dense bulk solution. First, we perform a linear stability analysis to identify the critical conditions for this reaction-driven convective instability. Second, we perform nonlinear simulations and compare the critical values of the control parameters for the onset of convection in these simulations with those predicted by linear stability analysis. We further show that the asymptotic dissolution flux of A can be increased in the convective regime by increasing the difference ΔR_CB = R_C-R_B between the Rayleigh numbers of the product C and reactant B above a critical value and by increasing the ratio β = B₀/A₀ between the initial concentration B₀ of reactant B and the solubility A₀ of A. Our results indicate that chemical reactions can not only initiate convective mixing but can also give rise to large dissolution fluxes, which is advantageous for various geological applications.

Enhanced convective dissolution due to an A + B → C reaction: control of the non-linear dynamics via solutal density contributions

Chemical reactions can have a significant impact on convective dissolution in partially miscible stratifications in porous media and are able to enhance the asymptotic flux with respect to the non-reactive case. We numerically study such reactive convective dissolution when the dissolving species A increases the density of the host phase upon dissolution and reacts with a reactant B present in the host phase to produce C by an A + B → C reaction. Upon varying the difference ΔR_CB = R_C-R_B between the Rayleigh numbers of the product C and the reactant B, we identify four regimes with distinct dynamics when the diffusion coefficients are the same. When ΔR_CB < 0, the density profiles are non-monotonic and the non-linear dynamics are seen to depend on the relative values of the density at the interface and the initial density of the host phase. For ΔR_CB > 0, the monotonic density profiles are destabilizing with respect to the non-reactive case above a certain critical value ΔR_cr. We analyze quantitatively the influence of varying ΔR_CB and the ratio β = B₀/A₀ of the initial concentration of B and the solubility of A on the asymptotic steady flux, the wavelength of the fingers and the position of the reaction front. In the context of CO₂ geological sequestration, understanding how such reactions can enhance the dissolution flux is crucial for improving the efficiency and safety of the process.

Differential Diffusivity Effects in Reactive Convective Dissolution

When a solute A dissolves into a host fluid containing a reactant B, an A + B → C reaction can influence the convection developing because of unstable density gradients in the gravity field. When A increases density and all three chemical species A, B and C diffuse at the same rate, the reactive case can lead to two different types of density profiles, i.e., a monotonically decreasing one from the interface to the bulk and a non-monotonic profile with a minimum. We study numerically here the nonlinear reactive convective dissolution dynamics in the more general case where the three solutes can diffuse at different rates. We show that differential diffusion can add new dynamic effects like the simultaneous presence of two different convection zones in the host phase when a non-monotonic profile with both a minimum and a maximum develops. Double diffusive instabilities can moreover affect the morphology of the convective fingers. Analysis of the mixing zone, the reaction rate, the total amount of stored A and the dissolution flux further shows that varying the diffusion coefficients of the various species has a quantitative effect on convection.

Enhanced steady-state dissolution flux in reactive convective dissolution

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 for a general A + B → C reaction in solution, that 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 can enhance the steady-state flux as they consume A and can induce more intense convection than in the non-reactive case. This result is important in the context of CO₂ geological sequestration where quantifying the storage rate of CO₂ dissolving into the host oil or aqueous phase is crucial to assess the efficiency and the safety of the project.

Chemical control of dissolution-driven convection in partially miscible systems: nonlinear simulations and experiments

Numerical simulations combined with experimental results from two laboratory-scale model systems show how to control convective dissolution by chemical reactions.