Unraveling dispersion and buoyancy dynamics around radial A + B → C reaction fronts: microgravity experiments and numerical simulations.

Radial Reaction-Diffusion-Advection (RDA) fronts for A + B → C reactions find wide applications in many natural and technological processes. In liquid solutions, their dynamics can be perturbed by buoyancy-driven convection due to concentration gradients across the front. In this context, we conducted microgravity experiments aboard a sounding rocket, in order to disentangle dispersion and buoyancy effects in such fronts. We studied experimentally the dynamics due to the radial injection of A in B at a constant flow rate, in absence of gravity. We compared the obtained results with numerical simulations using either radial one- (1D) or two-dimensional (2D) models. We showed that gravitational acceleration significantly distorts the RDA dynamics on ground, even if the vertical dimension of the reactor and density gradients are small. We further quantified the importance of such buoyant phenomena. Finally, we showed that 1D numerical models with radial symmetry fail to predict the dynamics of RDA fronts in thicker geometries, while 2D radial models are necessary to accurately describe RDA dynamics where Taylor-Aris dispersion is significant.

Measurement of Capillary Forces Using Two Fibers Dynamically Withdrawn from a Liquid: Evidence for an Enhanced Cheerios Effect.

We study the capillary attraction force between two fibers dynamically withdrawn from a bath. We propose an experimental method to measure this force and show that its magnitude strongly increases with the retraction speed by up to a factor of 10 compared to the static case. We show that this remarkable increase stems from the shape of the dynamical meniscus between the two fibers. We first study the dynamical meniscus around one fiber and obtain experimental and numerical scaling of its size increase with the capillary number, which is not captured by the classical Landau-Levich-Derjaguin theory. We then show that the shape of the deformed air-liquid interface around two fibers can be inferred from the linear superposition of the interface around a single fiber. These results yield an analytical expression for the capillary force which compares well with the experimental data. Our study reveals the critical role of the retraction speed to create stronger capillary interactions, with potential applications in industry or biology.

Peeling from a liquid.

We establish the existence of a cusp in the curvature of a solid sheet at its contact with a liquid subphase. We study two configurations in floating sheets where the solid-vapor-liquid contact line is a straight line and a circle, respectively. In the former case, a rectangular sheet is lifted at its one edge, whereas in the latter a gas bubble is injected beneath a floating sheet. We show that in both geometries the derivative of the sheet's curvature is discontinuous. We demonstrate that the boundary condition at the contact is identical in these two geometries, even though the shape of the contact line and the stress distribution in the sheet are very different.

Honey bees switch mechanisms to drink deep nectar efficiently.

The feeding mechanisms of animals constrain the spectrum of resources that they can exploit profitably. For floral nectar eaters, both corolla depth and nectar properties have marked influence on foraging choices. We report the multiple strategies used by honey bees to efficiently extract nectar at the range of sugar concentrations and corolla depths they face in nature. Honey bees can collect nectar by dipping their hairy tongues or capillary loading when lapping it, or they can attach the tongue to the wall of long corollas and directly suck the nectar along the tongue sides. The honey bee feeding apparatus is unveiled as a multifunctional tool that can switch between lapping and sucking nectar according to the instantaneous ingesting efficiency, which is determined by the interplay of nectar-mouth distance and sugar concentration. These versatile feeding mechanisms allow honey bees to extract nectar efficiently from a wider range of floral resources than previously appreciated and endow them with remarkable adaptability to diverse foraging environments.

Effect of external tension on the wetting of an elastic sheet.

Recent studies of elastocapillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupré (YLD) problem: the capillary interaction between a liquid drop and a thin solid sheet of low bending stiffness. Here we consider a two-dimensional model where the sheet is subjected to an external tensile load and the drop is characterized by a well-defined Young's contact angle θ_{Y}. Using a combination of numerical, variational, and asymptotic techniques, we discuss wetting as a function of the applied tension. We find that, for wettable surfaces with 0<θ_{Y}<π/2, complete wetting is possible below a critical applied tension due to the deformation of the sheet in contrast with rigid substrates requiring θ_{Y}=0. Conversely, for very large applied tensions, the sheet becomes flat and the classical YLD situation of partial wetting is recovered. At intermediate tensions, a vesicle forms in the sheet, which encloses most of the fluid, and we provide an accurate asymptotic description of this wetting state in the limit of small bending stiffness. We show that bending stiffness, however small, affects the entire shape of the vesicle. Rich bifurcation diagrams involving partial wetting and "vesicle" solution are found. For moderately small bending stiffnesses, partial wetting can coexist with both the vesicle solution and complete wetting. Finally, we identify a tension-dependent bendocapillary length, λ_{BC}, and find that the shape of the drop is determined by the ratio A/λ_{BC}^{2}, where A is the area of the drop.

Effect of radial advection on autocatalytic reaction-diffusion fronts.

The reaction-diffusion-advection properties of autocatalytic fronts are studied both theoretically and experimentally in the case where the autocatalytic species is injected radially into the reactant at a constant flow rate. The theoretical part analyzes both polar and spherical cases. At long times or equivalently large radius from the injection point, the well-known properties of one-dimensional reaction-diffusion autocatalytic fronts are logically recovered as the influence of the advection field decreases radially. At earlier times however, the radial advection impacts the dynamics of the front. We characterize numerically the influence in this transient regime of the injection flow rate and of the ratio of initial concentration of reactant and autocatalytic product on the position of the front, the reaction rate and the amount of product generated. We confirm experimentally the theoretical predictions in polar geometries using the autocatalytic chlorite-tetrathionate reaction.

Bioinspired shape shifting of liquid-infused ribbed sheets.

The recent emergence of stimuli-responsive, shape-shifting materials offers promising applications in fields as different as soft robotics, aeronautics, or biomedical engineering. Targeted shapes or movements are achieved from the advantageous coupling between some stimulus and various materials such as liquid crystalline elastomers, magnetically responsive soft materials, swelling hydrogels, etc. However, despite the large variety of strategies, they are strongly material dependent and do not offer the possibility to choose between reversible and irreversible transformations. Here, we introduce a strategy applicable to a wide range of materials yielding systematically reversible or irreversible shape transformations of soft ribbed sheets with precise control over the local curvature. Our approach-inspired by the spore-releasing mechanism of the fern sporangium-relies on the capillary deformation of an architected elastic sheet impregnated by an evaporating liquid. We develop an analytical model combining sheet geometry, material stiffness, and capillary forces to rationalize the onset of such deformations and develop a geometric procedure to inverse program target shapes requiring fine control over the curvature gradient. We finally demonstrate the potential irreversibility of the transformation by UV-curing a photosensitive evaporating solution and show that the obtained shells exhibit enhanced mechanical stiffness.

Trade-off mechanism of honey bee sucking and lapping.

Animals have developed various drinking strategies in capturing liquid to feed or to stay hydrated. In contrast with most animals, honey bees Apis mellifera that capture nectar with their tongue, can deliberately switch between sucking and lapping methods. They preferentially suck diluted nectar whereas they are prone to lap concentrated nectar. In vivo observations have shown that bees select the feeding method yielding the highest efficiency at a given sugar concentration. In this combined experimental and theoretical investigation, we propose two physical models for suction and lapping mode of capture that explain the transition between these two feeding strategy. The critical viscosity, µ*, at which the transition occurs, is derived from these models, and agrees well with in vivo measurements. The trade-off mechanism of honey bee sucking and lapping may further inspire microfluidics devices with higher capability of transporting liquids across a large range of viscosities.

Dynamics of A+B→C reaction fronts under radial advection in a Poiseuille flow.

A+B→C reaction fronts describe a wide variety of natural and engineered dynamics, according to the specific nature of reactants and product. Recent works have shown that the properties of such reaction fronts depend on the system geometry, by focusing on one-dimensional plug flow radial injection. Here, we extend the theoretical formulation to radial deformation in two-dimensional systems. Specifically, we study the effect of a Poiseuille advective velocity profile on A+B→C fronts when A is injected radially into B at a constant flow rate in a confined axisymmetric system consisting of two parallel impermeable plates separated by a thin gap. We analyze the front dynamics by computing the temporal evolution of the average over the gap of the front position, the maximum production rate, and the front width. We further quantify the effects of the nonuniform flow on the total amount of product, as well as on its radial concentration profile. Through analytical and numerical analyses, we identify three distinct temporal regimes, namely (i) the early-time regime where the front dynamics is independent of the reaction, (ii) the transient regime where the front properties result from the interplay of reaction, diffusion that smooths the concentration gradients and advection, which stretches the spatial distribution of the chemicals, and (iii) the long-time regime where Taylor dispersion occurs and the system becomes equivalent to the one-dimensional plug flow case.

Essential role of papillae flexibility in nectar capture by bees.

Many bees possess a tongue resembling a brush composed of a central rod (glossa) covered by elongated papillae, which is dipped periodically into nectar to collect this primary source of energy. In vivo measurements show that the amount of nectar collected per lap remains essentially constant for sugar concentrations lower than 50% but drops significantly for a concentration around 70%. To understand this variation of the ingestion rate with the sugar content of nectar, we investigate the dynamics of fluid capture by Bombus terrestris as a model system. During the dipping process, the papillae, which initially adhere to the glossa, unfold when immersed in the nectar. Combining in vivo investigations, macroscopic experiments with flexible rods, and an elastoviscous theoretical model, we show that the capture mechanism is governed by the relaxation dynamics of the bent papillae, driven by their elastic recoil slowed down through viscous dissipation. At low sugar concentrations, the papillae completely open before the tongue retracts out of nectar and thus, fully contribute to the fluid capture. In contrast, at larger concentrations corresponding to the drop of the ingestion rate, the viscous dissipation strongly hinders the papillae opening, reducing considerably the amount of nectar captured. This study shows the crucial role of flexible papillae, whose aspect ratio determines the optimal nectar concentration, to understand quantitatively the capture of nectar by bees and how physics can shed some light on the degree of adaptation of a specific morphological trait.

Oscillatory budding dynamics of a chemical garden within a co-flow of reactants.

The oscillatory growth of chemical gardens is studied experimentally in the budding regime using a co-flow of two reactant solutions within a microfluidic reactor. The confined environment of the reactor tames the erratic budding growth and the oscillations leave their imprint with the formation of orderly spaced membranes on the precipitate surface. The average wavelength of the spacing between membranes, the growth velocity of the chemical garden and the oscillations period are measured as a function of the velocity of each reactant. By means of materials characterization techniques, the micro-morphology and the chemical composition of the precipitate are explored. A mathematical model is developed to explain the periodic rupture of droplets delimitated by a shell of precipitate and growing when one reactant is injected into the other. The predictions of this model are in good agreement with the experimental data.

Effects of radial injection and solution thickness on the dynamics of confined A + B → C chemical fronts.

The spatio-temporal dynamics of an A + B → C front subjected to radial advection is investigated experimentally in a thin solution layer confined between two horizontal plates by radially injecting a solution of potassium thiocyanate (A) into a solution of iron(iii) nitrate (B). The total amount and spatial distribution of the product FeSCN2+ (C) are measured for various flow rates Q and solution thicknesses h. The long-time evolution of the total amount of product, nC, is compared to a scaling obtained theoretically from a one-dimensional reaction-diffusion-advection model with passive advection along the radial coordinate r. We show that, in the experiments, nC is significantly affected when varying either Q or h but scales as nC∼Q-1/2V where V is the volume of injected reactant A provided the solution thickness h between the two confining plates is sufficiently small, in agreement with the theoretical prediction. Our experimental results also evidence that the temporal evolution of the width of the product zone, WC, follows a power law, the exponent of which varies with both Q and h, in disagreement with the one-dimensional model that predicts WC∼t1/2. We show that this experimental observation can be rationalized by taking into account the non-uniform profile of the velocity field of the injected reactant within the cell gap.

Influence of rectilinear vs radial advection on the yield of A + B → C reaction fronts: A comparison.

In the presence of advection at a constant flow rate in a rectilinear geometry, the properties of planar A + B → C reaction fronts feature the same temporal scalings as in the pure reaction-diffusion case. In a radial injection geometry where A is injected into B radially at a constant flow rate Q, temporal scalings are conserved, but the related coefficients depend on the injection flow rate Q and on the ratio γ of initial concentrations of the reactants. We show here that this dependence of the front properties on the radial velocity allows us to tune the amount of product obtained in the course of time by varying the flow rate. We compare theoretically the efficiency of the rectilinear and radial geometries by computing the amount of product C generated in the course of time or per volume of reactant injected. We show that a curve γc(Q) can be defined in the parameter space (γ, Q) below which, for similar experimental conditions, the total amount of C is larger in the radial case. In addition, another curve γ*(Q) < γc(Q) can be defined such that for γ < γ*, the total amount of C produced is larger in the radial geometry, even if the production of C per unit area of the contact interface between the two reactants is larger in the rectilinear case. This comes from the fact that the length of the contact zone increases with the radius in the radial case, which allows us to produce in fine more product C for a same injected volume of reactant or in reactors of a same volume than in the rectilinear case. These results pave the way to the geometrical optimization of the properties of chemical fronts.

Dynamics of A+B → C reaction fronts under radial advection in three dimensions.

The dynamics of A+B→C reaction fronts is studied both analytically and numerically in three-dimensional systems when A is injected radially into B at a constant flow rate. The front dynamics is characterized in terms of the temporal evolution of the reaction front position, r_{f}, of its width, w, of the maximum local production rate, R^{max}, and of the total amount of product generated by the reaction, n_{C}. We show that r_{f}, w, and R^{max} exhibit the same temporal scalings as observed in rectilinear and two-dimensional radial geometries both in the early-time limit controlled by diffusion, and in the longer time reaction-diffusion-advection regime. However, unlike the two-dimensional cases, the three-dimensional problem admits an asymptotic stationary solution for the reactant concentration profiles where n_{C} grows linearly in time. The timescales at which the transition between the regimes arise, as well as the properties of each regime, are determined in terms of the injection flow rate and reactant initial concentration ratio.

Filiform corrosion as a pressure-driven delamination process.

Filiform corrosion produces long and narrow trails on various coated metals through the detachment of the coating layer from the substrate. In this work, we present a combined experimental and theoretical analysis of this process with the aim to describe quantitatively the shape of the cross-section, perpendicular to the direction of propagation, of the filaments produced. For this purpose, we introduce a delamination model of filiform corrosion dynamics and show its compatibility with experimental data where the coating thickness has been varied systematically.

Filament dynamics in confined chemical gardens and in filiform corrosion.

Two reaction systems that are at first sight very different produce similar macroscopic filamentary product trails. The systems are chemical gardens confined to a Hele-Shaw cell and corroding metal plates that undergo filiform corrosion. We show that the two systems are in fact very much alike. Our experiments and analysis show that filament dynamics obey similar scaling laws in both instances: filament motion is nearly ballistic and fully self-avoiding, which creates self-trapping events.

Flow Control of A+B→C Fronts by Radial Injection.

The dynamics of A+B→C fronts is analyzed theoretically in the presence of passive advection when A is injected radially into B at a constant inlet flow rate Q. We compute the long-time evolution of the front position, r_{f}, of its width, w, and of the local production rate R of the product C at r_{f}. We show that, while advection does not change the well-known scaling exponents of the evolution of corresponding reaction-diffusion fronts, their dynamics is however significantly influenced by the injection. In particular, the total amount of product varies as Q^{-1/2} for a given volume of injected reactant and the front position as Q^{1/2} for a given time, paving the way to a flow control of the amount and spatial distribution of the reaction front product. This control strategy compares well with calcium carbonate precipitation experiments for which the amount of solid product generated in flow conditions at fixed concentrations of reactants and the front position can be tuned by varying the flow rate.

Flow-driven control of calcium carbonate precipitation patterns in a confined geometry.

Upon injection of an aqueous solution of carbonate into a solution of calcium ions in the confined geometry of a Hele-Shaw cell, various calcium carbonate precipitation patterns are observed. We discuss here the properties of these precipitation structures as a function of the injection flow rate and concentrations of the reactants. We show that such flow-controlled conditions can be used to influence the total amount and the spatial distribution of the solid phase produced as well as the reaction efficiency defined here as the amount of product formed for a given initial concentration of the injected solution.

From Cylindrical to Stretching Ridges and Wrinkles in Twisted Ribbons.

Twisted ribbons under tension exhibit a remarkably rich morphology, from smooth and wrinkled helicoids, to cylindrical or faceted patterns. This complexity emanates from the instability of the natural, helicoidal symmetry of the system, which generates both longitudinal and transverse stresses, thereby leading to buckling of the ribbon. Here, we focus on the tessellation patterns made of triangular facets. Our experimental observations are described within an "asymptotic isometry" approach that brings together geometry and elasticity. The geometry consists of parametrized families of surfaces, isometric to the undeformed ribbon in the singular limit of vanishing thickness and tensile load. The energy, whose minimization selects the favored structure among those families, is governed by the tensile work and bending cost of the pattern. This framework describes the coexistence lines in a morphological phase diagram, and determines the domain of existence of faceted structures.

Wrinkles and folds in a fluid-supported sheet of finite size.

A laterally confined thin elastic sheet lying on a liquid substrate displays regular undulations, called wrinkles, characterized by a spatially extended energy distribution and a well-defined wavelength λ. As the confinement increases, the deformation energy is progressively localized into a single narrow fold. An exact solution for the deformation of an infinite sheet was previously found, indicating that wrinkles in an infinite sheet are unstable against localization for arbitrarily small confinement. We present an extension of the theory to sheets of finite length L, accounting for the experimentally observed wrinkle-to-fold transition. We derive an exact solution for the periodic deformation in the wrinkled state, and an approximate solution for the localized, folded state. We find that a second-order transition between these two states occurs at a critical confinement Δ(F)=λ(2)/L.