Steady Marangoni flow traveling with chemical fronts

Frontal polymerization in thin layers: Hydrodynamic effects and asymptotic dynamics

Buoyancy-driven convection currents arise from temperature gradients in thermal frontal polymerization (FP) when the spatially localized polymerization reaction travels perpendicularly to the gravity field. We propose a theoretical study of the system dynamics under adiabatic conditions. The polymer and the reactant mixture are considered to be in the same liquid phase, but the viscosity can increase with the degree of polymerization. We find that the reaction zone propagates as a hot spot-like pattern with a broken symmetry in both the vertical and horizontal directions. Furthermore, the system can reach an asymptotic dynamics characterized by a front with a steady shape that propagates at constant speed with a steady vortex surrounding it. As the strength of the vortex is increased, either by decreasing the reactants' viscosity or by increasing the layer's thickness, we observe a transition between (i) a passive regime predicted by pure reaction-diffusion and hydrodynamic models and (ii) an active chemo-hydrodynamic regime where such models separately break down. In the active regime (ii), the front speed decreases as convection intensifies. By means of a scaling analysis, we explain how hydrodynamic currents might lower the velocity of a polymerization wave. As the viscosity of the polymer is enlarged, the flow is shifted ahead of the reaction zone and becomes more symmetrical with respect to the middle of the system, as recently observed in solid-liquid FP experiments [Y. Gao et al., Phys. Rev. Lett. 130, 028101 (2023) and Y. Gao et al., Int. J. Heat Mass Transf. 240, 126622 (2025)].

Exploring buoyancy-driven effects in chemo-hydrodynamic oscillations sustained by bimolecular reactions

Exotic dynamics, previously associated only with reactions involving complex kinetics, have been observed even with simple bimolecular reactions A + B → C, when coupled with hydrodynamical flows. Numerical studies in two-dimensional reactors have shown that oscillatory dynamics can emerge from an antagonistic coupling between chemically-driven buoyancy and Marangoni convective flows, induced by changes in density and surface tension, respectively, as the reaction occurs. Here, we investigate reactions increasing both surface tension and density, leading to a cooperative coupling between the flows and show how, in this configuration, buoyancy-driven contribution dampens spatio-temporal oscillations of concentration. We finally identify the key parameters controlling the onset and persistence of the oscillatory instability, namely the density and surface tension gradients, and the systems height.

Marangoni-driven nonlinear dynamics of bimolecular frontal systems: a general classification for equal diffusion coefficients

When bimolecular fronts form in solutions, their dynamics is likely to be affected by chemically driven convection such as buoyancy- and Marangoni-driven flows. It is known that front dynamics in the presence of buoyancy-driven convection can be predicted solely on the basis of the one-dimensional reaction-diffusion concentration profiles but that those predictions fail for Marangoni-driven convection. With a two-dimensional reaction-diffusion-Marangoni convection model, we analyze here convective effects on the time scalings of the front properties, together with the influence of reaction reversibility and of the ratio of initial reactants' concentrations on the front dynamics. The effect of buoyancy forces is here neglected by assuming the reactive system to be in zero-gravity condition and/or the solution density to be spatially homogenous. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

Anisotropic frontal polymerization in a model resin-copper composite

This work investigates experimentally and numerically frontal polymerization in a thermally anisotropic system with parallel copper strips embedded in 1,6-hexanediol diacrylate resin. Both experiments and multiphysics finite element analyses reveal that the front propagation in the thermally anisotropic system is orientation-dependent, leading to variations in the front shape and the front velocity due to the different front-metal strip interaction mechanisms along and across the metal strips. The parameters entering the cure kinetics model used in this work are chosen to capture the key characteristics of the polymerization front, i.e., the front temperature and velocity. Numerical parametric analyses demonstrate that the front velocity in the directions parallel and perpendicular to the metal strips increases as the system size decreases and approaches the analytical prediction for homogenized systems. A two-dimensional homogenized model for anisotropic frontal polymerization in the metal-resin system is proposed.

Chemo-hydrodynamic pulsations in simple batch A + B → C systems

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 ΔM and ΔR, 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.

Making a Simple A+B→C Reaction Oscillate by Coupling to Hydrodynamic Effect

We present a new mechanism through which chemical oscillations and waves can be induced in batch conditions with a simple A+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.

Molecular Communications Pulse-Based Jamming Model for Bacterial Biofilm Suppression

Studies have recently shown that the bacteria survivability within biofilms is responsible for the emergence of superbugs. The combat of bacterial infections, without enhancing its resistance to antibiotics, includes the use of nanoparticles to quench the quorum sensing of these biofilm-forming bacteria. Several sequential and parallel multi-stage communication processes are involved in the formation of biofilms. In this paper, we use proteomic data from a wet lab experiment to identify the communication channels that are vital to these processes. We also identified the main proteins from each channel and propose the use of jamming signals from synthetically engineered bacteria to suppress the production of those proteins. This biocompatible technique is based on synthetic biology and enables the inhibition of biofilm formation. We analyze the communications performance of the jamming process by evaluating the path loss for a number of conditions that include different engineered bacterial population sizes, distances between the populations, and molecular signal power. Our results show that sufficient molecular pulse-based jamming signals are able to prevent the biofilm formation by creating lossy communications channels (almost -3 dB for certain scenarios). From these results, we define the main design parameters to develop a fully operational bacteria-based jamming system.

Interaction of Pure Marangoni Convection with a Propagating Reactive Interface under Microgravity

A reactive interface in the form of an autocatalytic reaction front propagating in a bulk phase can generate a dynamic contact line upon reaching the free surface when a surface tension gradient builds up due to the change in chemical composition. Experiments in microgravity evidence the existence of a self-organized autonomous and localized coupling of a pure Marangoni flow along the surface with the reaction in the bulk. This dynamics results from the advancement of the contact line at the surface that acts as a moving source of the reaction, leading to the reorientation of the front propagation. Microgravity conditions allow one to isolate the transition regime during which the surface propagation is enhanced, whereas diffusion remains the main mode of transport in the bulk with negligible convective mixing, a regime typically concealed on Earth because of buoyancy-driven convection.

Honeycomb-like PLGA- b-PEG Structure Creation with T-Junction Microdroplets

Amphiphilic block copolymers are widely used in science owing to their versatile properties. In this study, amphiphilic block copolymer poly(lactic- co-glycolic acid)- block-poly(ethylene glycol) (PLGA- b-PEG) was used to create microdroplets in a T-junction microfluidic device with a well-defined geometry. To compare interfacial characteristics of microdroplets, dichloromethane (DCM) and chloroform were used to prepare PLGA- b-PEG solution as an oil phase. In the T-junction device, water and oil phases were manipulated at variable flow rates from 50 to 300 μL/min by increments of 50 μL/min. Fabricated microdroplets were directly collected on a glass slide. After a drying period, porous two-dimensional and three-dimensional structures were obtained as honeycomb-like structure. Pore sizes were increased according to increased water/oil flow rate for both DCM and chloroform solutions. Also, it was shown that increasing polymer concentration decreased the pore size of honeycomb-like structures at a constant water/oil flow rate (50:50 μL/min). Additionally, PLGA- b-PEG nanoparticles were also obtained on the struts of honeycomb-like structures according to the water solubility, volatility, and viscosity properties of oil phases, by the aid of Marangoni flow. The resulting structures have a great potential to be used in biomedical applications, especially in drug delivery-related studies, with nanoparticle forming ability and cellular responses in different surface morphologies.

Surface tension- and buoyancy-driven flows across horizontally propagating chemical fronts

Chemical reactions can interplay with hydrodynamic flows to generate various complex phenomena. Because of their relevance in many research areas, chemically-induced hydrodynamic flows have attracted increasing attention in the last decades. In this context, we propose to give a review of the past and recent theoretical and experimental works which have considered the interaction of such flows with chemical fronts, i.e. reactive interfaces, formed between miscible solutions. We focus in particular on the influence of surface tension- (Marangoni) and buoyancy-driven flows on the dynamics of chemical fronts propagating horizontally in the gravity field.

Marangoni flow traveling with reaction fronts: Eikonal approximation

Chemical reaction fronts traveling in liquids generate gradients of surface tension leading to fluid motion. This surface tension driven flow, known as Marangoni flow, modifies the shape and the speed of the reaction front. We model the front propagation using the Eikonal relation between curvature and normal speed of the front, resulting in a front evolution equation that couples to the fluid velocity. The sharp discontinuity between the reactants and products leads to a surface tension gradient proportional to a delta function. The Stokes equations with the surface tension gradient as part of the boundary conditions provide the corresponding fluid velocity field. Considering stress free boundaries at the bottom of the liquid layer, we find an analytical solution for the fluid vorticity leading to the velocity field. Solving numerically the appropriate no-slip boundary condition, we gain insights into the role of the boundary condition at the bottom layer. We compare our results with results from two other models for front propagation: the deterministic Kardar-Parisi-Zhang equation and a reaction-diffusion equation with cubic autocatalysis, finding good agreement for small differences in surface tension.

Flow-driven pattern formation in the calcium-oxalate system

The precipitation reaction of calcium oxalate is studied experimentally in the presence of spatial gradients by controlled flow of calcium into oxalate solution. The density difference between the reactants leads to strong convection in the form of a gravity current that drives the spatiotemporal pattern formation. The phase diagram of the system is constructed, the evolving precipitate patterns are analyzed and quantitatively characterized by their diameters and the average height of the gravity flow. The compact structures of calcium oxalate monohydrate produced at low flow rates are replaced by the thermodynamically unstable calcium oxalate dihydrate favored in the presence of a strong gravity current.

Maze solving using fatty acid chemistry

This study demonstrates that the Marangoni flow in a channel network can solve maze problems such as exploring and visualizing the shortest path and finding all possible solutions in a parallel fashion. The Marangoni flow is generated by the pH gradient in a maze filled with an alkaline solution of a fatty acid by introducing a hydrogel block soaked with an acid at the exit. The pH gradient changes the protonation rate of fatty acid molecules, which translates into the surface tension gradient at the liquid-air interface through the maze. Fluid flow maintained by the surface tension gradient (Marangoni flow) can drag water-soluble dye particles toward low pH (exit) at the liquid-air interface. Dye particles placed at the entrance of the maze dissolve during this motion, thus exhibiting and finding the shortest path and all possible paths in a maze.

Convective dynamics of traveling autocatalytic fronts in a modulated gravity field

Modulation of the gravity field, spanning from the hyper-gravity to micro-gravity of a parabolic flight, reveals the contribution of Marangoni flow in a propagating reaction front with an open air–liquid interface.

Barriers to front propagation in ordered and disordered vortex flows

We present experiments on reactive front propagation in a two-dimensional (2D) vortex chain flow (both time-independent and time-periodic) and a 2D spatially disordered (time-independent) vortex-dominated flow. The flows are generated using magnetohydrodynamic forcing techniques, and the fronts are produced using the excitable, ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. In both of these flows, front propagation is dominated by the presence of burning invariant manifolds (BIMs) that act as barriers, similar to invariant manifolds that dominate the transport of passive impurities. Convergence of the fronts onto these BIMs is shown experimentally for all of the flows studied. The BIMs are also shown to collapse onto the invariant manifolds for passive transport in the limit of large flow velocities. For the disordered flow, the measured BIMs are compared to those predicted using a measured velocity field and a three-dimensional set of ordinary differential equations that describe the dynamics of front propagation in advection-reaction-diffusion systems.

The heads and tails of buoyant autocatalytic balls

Buoyancy produced by autocatalytic reaction fronts can produce fluid flows that advect the front position, giving rise to interesting feedback between chemical and hydrodynamic effects. In this paper, we numerically investigate the evolution of autocatalytic iodate-arsenous acid reaction fronts initialized in spherical configurations. Deformation of these "autocatalytic balls" is driven by buoyancy produced by the reaction. In our simulations, we have found that depending on the initial ball radius, the reaction front will develop in one of three different ways. In an intermediate range of ball size, the flow can evolve much like an autocatalytic plume: the ball develops a reacting head and tail that is akin to the head and conduit of an autocatalytic plume. In the limit of large autocatalytic balls, however, growth of a reacting tail is suppressed and the resemblance to plumes disappears. Conversely, very small balls of product solution fail to initiate sustained fronts and eventually disappear.

Chemo-Marangoni convection driven by an interfacial reaction: pattern formation and kinetics

A combined study devoted to chemo-Marangoni convection and the underlying kinetics is presented for a biphasic system in which surfactants are produced in situ by an interfacial reaction. The pattern formation studied in a Hele-Shaw cell in both microgravity and terrestrial environments initially shows an ensemble of chemo-Marangoni cells along a nearly planar interface. Soon, a crossover occurs to periodic large-scale interfacial deformations which coexist with the Marangoni cells. This crossover can be correlated with the autocatalytic nature of the interfacial reaction identified in the kinetic studies. The drastic increase in the product concentration is associated with an enhanced aggregate-assisted transfer after the critical micellar concentration is approached. In this context, it was possible to conclusively explain the changes in the periodicity of the interfacial deformations depending on the reactant concentration ratio.

Marangoni-driven convection around exothermic autocatalytic chemical fronts in free-surface solution layers

Gradients of concentration and temperature across exothermic chemical fronts propagating in free-surface solution layers can initiate Marangoni-driven convection. We investigate here the dynamics arising from such a coupling between exothermic autocatalytic reactions, diffusion, and Marangoni-driven flows. To this end, we numerically integrate the incompressible Navier-Stokes equations coupled through the tangential stress balance to evolution equations for the concentration of the autocatalytic product and for the temperature. A solutal and a thermal Marangoni numbers measure the coupling between reaction-diffusion processes and surface-driven convection. In the case of an isothermal system, the asymptotic dynamics is characterized by a steady fluid vortex traveling at a constant speed with the front, deforming and accelerating it [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)]. We analyze here the influence of the reaction exothermicity on the dynamics of the system in both cases of cooperative and competitive solutal and thermal effects. We show that exothermic fronts can exhibit new unsteady spatio-temporal dynamics when the solutal and thermal effects are antagonistic. The influence of the solutal and thermal Marangoni numbers, of the Lewis number (ratio of thermal diffusivity over molecular diffusivity), and of the height of the liquid layer on the spatio-temporal front evolution are investigated.

Buoyancy-driven convection may switch between reactive states in three-dimensional chemical waves

Traveling waves in an extended reactor, whose width cannot be neglected, represent a three-dimensional (3D) reaction-diffusion-convection system. We investigate the effects of buoyancy-driven convection in such a setting. The 3D waves traveled through horizontal layers of the iodate-arsenous acid (IAA) reaction solution containing excess of arsenous acid. The depth of the reaction solution was the examined parameter. An increase in the intensity of buoyancy-driven flow caused an increase of the traveling wave velocities. Convection distorted the front of the chemical waves. For layers deeper than h>13 mm, heat release became smaller than heat production causing the emergence of Rayleigh-Bénard convection cells. At the interface, a dependency of wave shape on solution depth was observed. For h<7 mm, the waves adopted a stable V-like shape, while for h>13 mm a parabolic shape dominated. For 7<h<13 mm, both shapes were realized with the same probability. Finally, an intermittent switch between stoichiometric regimes is observed as an unexpected effect of the buoyancy-driven convection. The switch is expressed by iodine enrichment in the product. Hence, the experiments demonstrate that the buoyancy-driven convective flow can cause long-lived, but nevertheless transient, changes in the chemical composition by inducing a local transition between different regimes of the IAA reaction.

Chemical activity induces dynamical force with global structure in a reaction-diffusion-convection system

We found a rotating global structure induced by the dynamical force of local chemical activity in a thin solution layer of excitable Belousov-Zhabotinsky reaction coupled with diffusion. The surface flow and deformation associated with chemical spiral waves (wavelength about 1 mm) represents a global unidirectional structure and a global tilt in the entire Petri dish (100 mm in diameter), respectively. For these observations, we scanned the condition of hierarchal pattern selection. From this result, the bromomalonic acid has an important role to induce the rotating global structure. An interaction between a reaction-diffusion process and a surface-tension-driven effect leads to such hierarchal pattern with different scales.

Lattice Boltzmann study of convective drop motion driven by nonlinear chemical kinetics

We model a reaction-diffusion-convection system which comprises a liquid drop containing solutes that undergo an Oregonator reaction producing chemical waves. The reactants are taken to have surfactant properties so that the variation in their concentrations induces Marangoni flows at the drop interface which lead to a displacement of the drop. We discuss the mechanism by which the chemical-mechanical coupling leads to drop motion and the way in which the net displacement of the drop depends on the strength of the surfactant action. The equations of motion are solved using a lattice Boltzmann approach.

Solitary Marangoni-driven convective structures in bistable chemical systems

Bistable chemical fronts can be deformed by Marangoni-driven convective flows induced by gradients of surface tension across the front. We investigate here the nonlinear dynamics of such a system by simulations of two-dimensional Navier-Stokes equations coupled to a reaction-diffusion-convection equation for a surface-active chemical species present in the bulk of the solution and involved in a bistable kinetics. We show that Marangoni flows cannot only alter the shape and speed of the front but also change the relative stability of the two stable steady states, reversing in some cases the direction of propagation of the front with regard to the pure reaction-diffusion situation. A detailed parametric study discusses the properties of the asymptotic dynamics as a function of the Marangoni number M and of a kinetic parameter d.

Front propagation in a laminar cellular flow: shapes, velocities, and least time criterion

We experimentally investigate the propagation of chemical fronts in steady laminar cellular flows at large Péclet numbers and large Damköhler numbers. Fronts are generated in an aqueous solution by an autocatalytic oxydoreduction reaction. They propagate in a channel in which a chain of counter-rotative parallel vortices is induced by electroconvection. We first accurately determine the form, the dynamics and the mean velocity of these fronts in the whole Hele-Shaw regime of the flow. We then address the modeling of the evolution of their mean velocity with the flow amplitude. The structure of the front wakes yields us to reject an effective reaction-diffusion wave as a relevant model for large-scale front propagation. On the other hand, analysis of the role of front heads brings us to introduce a kinematic model at the vortex scale for uncovering the front dynamics. This model addresses the propagation of the front leading point in a chain of vortices whose field is modeled by a two-dimensional solid rotation complemented by a boundary layer. Interestingly, it sensitively relies on the effective trajectory followed by the front leading point. To account for this, a competition is worked out among a one-parameter family of potential trajectories. The actual trajectory is then selected as the fastest one with quite a good agreement with measurements and observations. In particular, the measured effective front velocities are well recovered from the model, including their intrinsic dependence on the boundary layer width. Accordingly, effective front propagation in a laminar steadily stirred medium is thus understood from an optimization principle similar to the Fermat principle of ray propagation in heterogeneous media.

Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers

Density differences across an autocatalytic chemical front traveling horizontally in covered thin layers of solution trigger hydrodynamic flows which can alter the concentration profile. We theoretically investigate the spatiotemporal evolution and asymptotic dynamics resulting from such an interplay between isothermal chemical reactions, diffusion, and buoyancy-driven convection. The studied model couples the reaction-diffusion-convection evolution equation for the concentration of an autocatalytic species to the incompressible Stokes equations ruling the evolution of the flow velocity in a two-dimensional geometry. The dimensionless parameter of the problem is a solutal Rayleigh number constructed upon the characteristic reaction-diffusion length scale. We show numerically that the asymptotic dynamics is one steady vortex surrounding, deforming, and accelerating the chemical front. This chemohydrodynamic structure propagating at a constant speed is quite different from the one obtained in the case of a pure hydrodynamic flow resulting from the contact between two solutions of different density or from the pure reaction-diffusion planar traveling front. The dynamics is symmetric with regard to the middle of the layer thickness for positive and negative Rayleigh numbers corresponding to products, respectively, lighter or heavier than the reactants. A parametric study shows that the intensity of the flow, the propagation speed, and the deformation of the front are increasing functions of the Rayleigh number and of the layer thickness. In particular, the asymptotic mixing length and reaction-diffusion-convection speed both scale as square root Ra for Ra>5. The velocity and concentration fields in the asymptotic dynamics are also found to exhibit self-similar properties with Ra. A comparison of the dynamics in the case of a monostable versus bistable kinetics is provided. Good agreement is obtained with experimental data on the speed of iodate-arsenous acid fronts propagating in horizontal capillaries. We furthermore compare the buoyancy-driven dynamics studied here to Marangoni-driven deformation of traveling chemical fronts in solution open to the air in the absence of gravity previously studied in the same geometry [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)].