Cross-Diffusion in a Water-in-Oil Microemulsion Loaded with Malonic Acid or Ferroin. Taylor Dispersion Method for Four-Component Systems

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.

Nonlinear waves in a quintic FitzHugh-Nagumo model with cross diffusion: Fronts, pulses, and wave trains

We study a tristable piecewise-linear reaction-diffusion system, which approximates a quintic FitzHugh-Nagumo model, with linear cross-diffusion terms of opposite signs. Basic nonlinear waves with oscillatory tails, namely, fronts, pulses, and wave trains, are described. The analytical construction of these waves is based on the results for the bistable case [Zemskov et al., Phys. Rev. E 77, 036219 (2008) and Phys. Rev. E 95, 012203 (2017) for fronts and for pulses and wave trains, respectively]. In addition, these constructions allow us to describe novel waves that are specific to the tristable system. Most interesting is the pulse solution with a zigzag-shaped profile, the bright-dark pulse, in analogy with optical solitons of similar shapes. Numerical simulations indicate that this wave can be stable in the system with asymmetric thresholds; there are no stable bright-dark pulses when the thresholds are symmetric. In the latter case, the pulse splits up into a tristable front and a bistable one that propagate with different speeds. This phenomenon is related to a specific feature of the wave behavior in the tristable system, the multiwave regime of propagation, i.e., the coexistence of several waves with different profile shapes and propagation speeds at the same values of the model parameters.

Energetic and entropic cost due to overlapping of Turing-Hopf instabilities in the presence of cross diffusion

A systematic introduction to nonequilibrium thermodynamics of dynamical instabilities are considered for an open nonlinear system beyond conventional Turing pattern in presence of cross diffusion. An altered condition of Turing instability in presence of cross diffusion is best reflected through a critical control parameter and wave number containing both the self- and cross-diffusion coefficients. Our main focus is on entropic and energetic cost of Turing-Hopf interplay in stationary pattern formation. Depending on the relative dispositions of Turing-Hopf codimensional instabilities from the reaction-diffusion equation it clarifies two aspects: energy cost of pattern formation, especially how Hopf instability can be utilized to dictate a stationary concentration profile, and the possibility of revealing nonequilibrium phase transition. In the Brusselator model, to understand these phenomena, we have analyzed through the relevant complex Ginzberg-Landau equation using multiscale Krylov-Bogolyubov averaging method. Due to Hopf instability it is observed that the cross-diffusion parameters can be a source of huge change in free-energy and concentration profiles.

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.

Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion

We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system with linear cross diffusion. To be specific, we consider a piecewise linear approximation of the FitzHugh-Nagumo model, also known as the Bonhoeffer-van der Pol model. We focus on two types of traveling waves, namely solitary pulses that correspond to a homoclinic solution, and sequences of pulses or wave trains, i.e., a periodic solution. The effect of cross diffusion on wave profiles and speed of propagation is analyzed. We find the intriguing result that both pulses and wave trains occur in the bistable cross-diffusive FitzHugh-Nagumo system, whereas only fronts exist in the standard bistable system without cross diffusion.

Interfacial hydrodynamic instabilities driven by cross-diffusion in reverse microemulsions

When two microemulsions are put in contact in the gravity field along a horizontal contact line, cross-diffusion can trigger the transport of one species in the presence of a gradient in concentration of another species. We show here theoretically that such cross-diffusion effects can induce buoyancy-driven convective instabilities at the interface between two solutions of different compositions even when initially the less dense solution lies on top of the denser one. Two different sources of convective modes are identified depending whether positive or negative cross-diffusion is involved. We evidence the two predicted cross-diffusion driven instabilities experimentally using a two-layer stratification of Aerosol-OT (AOT) water-in-oil microemulsions solutions with different water or AOT composition.

Accelerated dynamics in active media: from Turing patterns to sparkling waves

We report the destabilization of stationary Turing patterns and the subsequent emergence of fast spatiotemporal dynamics due to reactant consumption. The localized hexagonal Turing spots switch from a stationary regime to a dynamics state by exhibiting spatial oscillations with two characteristic wavelengths and one representative temporal period. These oscillatory Turing spots are not temporally stable and evolve into traveling spiral tips that, in addition to the unexpected birth of spots, rapidly transform into target patterns and originate multiple collisions and wave breakups due to their proximity, degenerating into a chaotic scenario.

Cross-diffusion-induced convective patterns in microemulsion systems

Cross-diffusion phenomena are experimentally and theoretically shown to be able to induce convective fingering around an initially stable stratification of two microemulsions with different compositions.

Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane

We present a comprehensive analysis of experimental results obtained for Fickian diffusion in the benchmark ternary liquid mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane (nC12) with equal mass fractions. Isothermal diffusion coefficients have been measured by two independent experimental methods: by Taylor dispersion technique, and by a counter flow cell fitted with an optical interferometry device. The experimental diffusion matrices have been critically analyzed regarding the Onsager reciprocal relations, for which we introduce a matrix asymmetry index s(2) that is independent of the frame of reference and the component order.

Amplitude equations for reaction-diffusion systems with cross diffusion

Using Taylor series expansion, multiscaling, and further expansion in powers of a small parameter, we develop general amplitude equations for two-variable reaction-diffusion systems with cross-diffusion terms in the cases of Hopf and Turing instabilities. We apply this analysis to the Oregonator and Brusselator models and find that inhibitor cross diffusion induced by the activator and activator cross diffusion induced by the inhibitor have opposite effects in the two models as a result of the different structure of their community matrices. Our analysis facilitates finding regions of supercritical and subcritical bifurcations, as well as wave and antiwave domains and domains of turbulent waves in the case of Hopf instability.

Effects of cross diffusion on Turing bifurcations in two-species reaction-transport systems

We study the Turing bifurcation in general two-species reaction-transport systems, where particle dispersal is governed by diffusion, including cross diffusion. By performing a linear stability analysis, we find conditions for the Turing instability and compare the results with the standard Turing conditions. We apply our results to two model systems, the Lengyel-Epstein model and the Brusselator, and find strong effects of cross diffusion on the Turing bifurcation.