Interfacial hydrodynamic instabilities driven by cross-diffusion in reverse microemulsions

Hydrodynamically-enhanced transfer of dense non-aqueous phase liquids into an aqueous reservoir

The use of surfactants represents a viable strategy to boost the removal yield of Dense Non-Aqueous Phase Liquids (DNAPLs) from groundwater and to shorten the operational timing of the remediation process. Surfactants, in general, help in reducing the interfacial tension at the DNAPL/water interface and enhance the solubility of the pollutant in the water phase through the formation of dispersed systems, such as micelles and emulsions. In this paper, we show that a suitable choice of a surfactant, in this case belonging to the bio-degradable class of ethoxylated alcohols, allows for the formation of hydrodynamic interfacial instabilities that further enhances the dissolution rate of the organic pollutant into the water phase. In a stratified configuration (denser organic phase at the bottom and lighter water phase on top), the instabilities appear as upward-pointing fingers that originate from the inversion of the local density at the interface. This inversion stems from the synergetic coupling of two effects promoted by the ethoxylated surfactant: i) the enhanced co-solubility of the DNAPL into the water (and viceversa), and (ii) the differential diffusion of the DNAPL and the surfactant in the aqueous phase. By dissolving into the DNAPL, the surfactant also reduces locally the surface tension at the liquid-liquid interface, thereby inducing transversal Marangoni flows. In our work, we carefully evaluated the effects of the concentration of different surfactants (two different ethoxylated alcohols, sodium dodecylsulphate, cetyltrimethyl ammonium bromide, N-tetradecyl-N, N-dimethylamine oxide and bis(2-ethylhexyl) sulfosuccinate sodium salt) on the onset of the instabilities in 3 different DNAPLs/water stratifications, namely chloroform, trichloroethylene and tetrachloroethylene, with a special emphasis on the trichloroethylene/water system. By means of a theoretical model and nonlinear simulations, supported by surface tension, density and diffusivity measurements, we could provide a solid explanation to the observed phenomena and we found that the type of the dispersed system, the solubility of the DNAPL into the water phase, the solubility of the surfactant in the organic phase, as well as the relative diffusion and density of the surfactant and the DNAPL in the aqueous phase, are all key parameters for the onset of the instabilities. These results can be exploited in the most common remediation techniques.

Buoyancy-Driven Chemohydrodynamic Patterns in A + B → Oscillator Two-Layer Stratifications

Chemohydrodynamic patterns due to the interplay of buoyancy-driven instabilities and reaction-diffusion patterns are studied experimentally in a vertical quasi-two-dimensional reactor in which two solutions A and B containing separate reactants of the oscillating Belousov-Zhabotinsky system are placed in contact along a horizontal contact line where excitable or oscillating dynamics can develop. Different types of buoyancy-driven instabilities are selectively induced in the reactive zone depending on the initial density jump between the two layers, controlled here by the bromate salt concentration. Starting from a less dense solution above a denser one, two possible differential diffusion instabilities are triggered depending on whether the fast diffusing sulfuric acid is in the upper or lower solution. Specifically, when the solution containing malonic acid and sulfuric acid is stratified above the one containing the slow-diffusing bromate salt, a diffusive layer convection (DLC) instability is observed with localized convective rolls around the interface. In that case, the reaction-diffusion wave patterns remain localized above the initial contact line, scarcely affected by the flow. If, on the contrary, sulfuric acid diffuses upward because it is initially dissolved in the lower layer, then a double-diffusion (DD) convective mode develops. This triggers fingers across the interface that mix the reactants such that oscillatory dynamics and rippled waves develop throughout the whole reactor. If the denser solution is put on top of the other one, then a fast developing Rayleigh-Taylor (RT) instability induces fast mixing of all reactants such that classical reaction-diffusion waves develop later on in the convectively mixed solutions.

Light scattering from mixtures of interacting, nonionic micelles with hydrophobic solutes

Model equations for the Rayleigh ratio and the electric field autocorrelation function are derived using thermodynamic fluctuation theory applied to crowded solute-containing micellar solutions and microemulsions with negligible molecular species and polydispersity. This theory invokes non-equilibrium thermodynamics and enforces local equilibrium between molecular solute, surfactant, and the various micellar species, in order to elucidate the influence of self-assembly on light scattering correlation functions. We find that self-assembly driven variations in the average micelle radius and aggregation number along gradients in concentration, which were previously shown to drive strong multicomponent diffusion effects expressed via the ternary diffusivity matrix [D], do not affect the scattering functions in the limit of zero local polydispersity. Hence, theoretical predictions for the Rayleigh ratio and the field autocorrelation function for ternary mixtures of solute-containing, locally monodisperse micellar solutions are identical to those developed for binary mixtures of monodisperse, colloidal hard spheres. However, self-assembly driven multicomponent diffusion phenomena are predicted to influence the thermodynamic driving forces for diffusion in these mixtures. In support of our theoretical results, measurements for the Rayleigh ratio and the field autocorrelation function for ternary aqueous solutions of decaethylene glycol monododecyl ether (C₁₂E₁₀) with either decane or limonene solute were performed for several molar ratios and volume fractions up to ϕ ≈ 0.25, and for binary mixtures of C₁₂E₁₀/water up to ϕ ≈ 0.5. Excellent agreement between our light scattering theory and experimental data is achieved for low to moderate volume fractions (ϕ < 0.3), and at higher concentrations when our theoretical results are corrected to account for micelle dehydration.

Interfacial Mass Transfer in Trichloroethylene/Surfactants/ Water Systems: Implications for Remediation Strategies

The fate of dense non-aqueous phase liquids (DNAPLs) in the environment and the consequential remediation problems have been intensively studied over the last 50 years. However, a scarce literature is present about the mass transfer at the DNAPL/water interface. In this paper, we present a fast method for the evaluation of the mass transfer performance of a surfactant that can easily be employed to support an effective choice for the so-called enhanced remediation strategies. We developed a lab-scale experimental system modelled by means of simple ordinary differential equations to calculate the mass transfer coefficient (K) of trichloroethylene, chosen as representative DNAPL, in the presence and in the absence of two ethoxylated alcohols belonging to the general class of Synperonic surfactants. Our findings revealed that it exists an optimal surfactant concentration range, where K increases up to 40% with respect to pure water.

Multicomponent diffusion of interacting, nonionic micelles with hydrophobic solutes

Ternary diffusion coefficient matrices [D] were measured using the Taylor dispersion method, for crowded aqueous solutions of decaethylene glycol monododecyl ether (C₁₂E₁₀) with either decane or limonene solute. The matrix [D], for both systems, was found to be highly non-diagonal, and concentration dependent, over a broad domain of solute to surfactant molar ratios and micelle volume fractions. A recently developed theoretical model, based on Batchelor's theory for gradient diffusion in dilute, polydisperse mixtures of interacting spheres, was simplified by neglecting local polydispersity, and effectively used to predict [D] with no adjustable parameters. Even though the model originates from dilute theory, the theoretical results were in surprisingly good agreement with experimental data for concentrated mixtures, with volume fractions up to φ≈ 0.47. In addition, the theory predicts eigenvalues D_- and D₊ that correspond to long-time self and gradient diffusion coefficients, respectively, for monodisperse spheres, in reasonable agreement with experimental data.

Fisher-Kolmogorov-Petrovskii-Piskunov wave front as a sensor of perturbed diffusion in concentrated systems

The sensitivity to perturbations of the Fisher and Kolmogorov, Petrovskii, Piskunov front is used to find a quantity revealing perturbations of diffusion in a concentrated solution of two chemical species with different diffusivities. The deterministic dynamics includes cross-diffusion terms due to the deviation from the dilution limit. The behaviors of the front speed, the shift between the concentration profiles of the two species, and the width of the reactive zone are investigated, both analytically and numerically. The shift between the two profiles turns out to be a well-adapted criterion presenting noticeable variations with the deviation from the dilution limit in a wide range of parameter values.

Chemical communication and dynamics of droplet emulsions in networks of Belousov-Zhabotinsky micro-oscillators produced by microfluidics

Chemical communication leading to synchronization and collective behaviour of dynamic elements, such as cell colonies, is a widespread phenomenon with biological, physical and chemical importance. Such synchronization between elements proceeds via chemical communication by emmision, interdiffusion and reception of specific messenger molecules. On a lab scale, these phenomena can be modeled by encapsulating an oscillating chemical reaction, which serves as a signal (information) sender/receiver element, inside microcompartments such as droplet emulsions, liposomes and polymersomes. Droplets can thus be regarded as single units, able to generate chemical messengers that diffuse in the environment and hence can interact with other compartments. The Belousov-Zhabotinsky (BZ) reaction is a well-known chemical oscillator largely used as a model for complex nonlinear phenomena, including chemical, physical and biological examples. When the BZ-reaction is encapsulated inside microcompartments, its chemical intermediates can serve as messengers by diffusing among different microcompartments, to trigger specific reactions leading to a collective behavior between the elements. The geometry and constitution of the diffusion pathways play an important role in governing the collective behaviour of the system. In this context, microfluidics is not only a versatile tool for mastering the encapsulation process of the BZ-reaction in monodisperse microcompartments, but also for creating geometries and networks with well defined boundaries. The individual compartments can be engineered with selected properties using different surfactants in the case of simple emulsions, or with specific membrane properties in the case of liposomes. Furthermore, it enables the arrangement of these microcompartments in various geometric configurations, where the diffusive coupling pathways between individual compartments are both spatially and chemically well-defined. In this tutorial paper, we review a number of articles reporting various approaches to generate networks of compartmentalized Belousov-Zhabotinsky (BZ) chemical oscillators using microfluidics. In contrast to biological cellular networks, the dynamical characteristics of the BZ-reaction is well-known and, when confined in microcompartments arranged in different configurations with a pure interdiffusive coupling, these communicative microreactors can serve to mimic various types of bio-physical networks, aiding to comprehend the concept of chemical communication.

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.

Cross-diffusion-driven hydrodynamic instabilities in a double-layer system: General classification and nonlinear simulations

Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.