Mathematical modelling of fungi-initiated siderophore-iron interactions.

Nearly all life forms require iron to survive and function. Microorganisms utilize a number of mechanisms to acquire iron including the production of siderophores, which are organic compounds that combine with ferric iron into forms that are easily absorbed by the microorganism. There has been significant experimental investigation into the role, distribution and function of siderophores in fungi but until now no predictive tools have been developed to qualify or quantify fungi-initiated siderophore-iron interactions.

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

Various spatial density profiles can develop in partially miscible stratifications when a phase A dissolves with a finite solubility into a host phase containing a dissolved reactant B. We investigate theoretically the impact of an A+B→C reaction on such density profiles in the host phase and classify them in a parameter space spanned by the ratios of relative contributions to density and diffusion coefficients of the chemical species. While the density profile is either monotonically increasing or decreasing in the nonreactive case, reactions combined with differential diffusivity can create eight different types of density profiles featuring up to two extrema in density, at the reaction front or below it.

Buoyancy-driven instabilities around miscible A+B→C reaction fronts: a general classification.

Upon contact between miscible solutions of reactants A and B along a horizontal interface in the gravity field, various buoyancy-driven instabilities can develop when an A+B→C reaction takes place and the density varies with the concentrations of the various chemicals. To classify the possible convective instability scenarios, we analyze the spatial dependence of the large time asymptotic density profiles as a function of the key parameters of the problem, which are the ratios of diffusion coefficients and of solutal expansion coefficients of species A, B, and C. We find that 62 different density profiles can develop in the reactive problem, whereas only 6 of them can be obtained in the nonreactive one.

Thermal effects on the diffusive layer convection instability of an exothermic acid-base reaction front.

A buoyancy-driven hydrodynamic instability appearing when an aqueous acid solution of HCl overlies a denser alkaline aqueous solution of NaOH in a vertically oriented Hele-Shaw cell is studied both experimentally and theoretically. The peculiarity of this reactive convection pattern is its asymmetry with regard to the initial contact line between the two solutions as convective plumes develop in the acidic solution only. We investigate here by a linear stability analysis (LSA) of a reaction-diffusion-convection model of a simple A+B→C reaction the relative role of solutal versus thermal effects in the origin and location of this instability.

Experimental evidence of reaction-driven miscible viscous fingering.

An experimental demonstration of reaction-driven viscous fingering developing when a more viscous solution of a reactant A displaces a less viscous miscible solution of another reactant B is presented. In the absence of reaction, such a displacement of one fluid by another less mobile one is classically stable. However, a simple A+B→C reaction can destabilize this interface if the product C is either more or less viscous than both reactant solutions.

Differential diffusion effects on buoyancy-driven instabilities of acid-base fronts: the case of a color indicator.

Buoyancy-driven hydrodynamic instabilities of acid-base fronts are studied both experimentally and theoretically in the case where an aqueous solution of a strong acid is put above a denser aqueous solution of a color indicator in the gravity field. The neutralization reaction between the acid and the color indicator as well as their differential diffusion modifies the initially stable density profile in the system and can trigger convective motions both above and below the initial contact line. The type of patterns observed as well as their wavelength and the speed of the reaction front are shown to depend on the value of the initial concentrations of the acid and of the color indicator and on their ratio.

Convective mixing induced by acid-base reactions.

When two miscible solutions, each containing a reactive species, are put in contact in the gravity field, local variations in the density due to the reaction can induce convective motion and mixing. We characterize here both experimentally and theoretically such buoyancy-driven instabilities induced by the neutralization of a strong acid by a strong base in aqueous solutions. The diverse patterns obtained are shown to depend on the type of reactants used and on their relative concentrations.

Influence of double diffusive effects on miscible viscous fingering.

Miscible viscous fingering classically occurs when a less viscous fluid displaces a miscible more viscous one in a porous medium. We analyze here how double diffusive effects between a slow diffusing S and a fast diffusing F component, both influencing the viscosity of the fluids at hand, affect such fingering, and, most importantly, can destabilize the classically stable situation of a more viscous fluid displacing a less viscous one. Various instability scenarios are classified in a parameter space spanned by the log-mobility ratios R(s) and R(f) of the slow and fast component, respectively, and parametrized by the ratio of diffusion coefficients δ.

Chemically driven hydrodynamic instabilities.

In the gravity field, density changes triggered by a kinetic scheme as simple as A+B-->C can induce or affect buoyancy-driven instabilities at a horizontal interface between two solutions containing initially the scalars A and B. On the basis of a general reaction-diffusion-convection model, we analyze to what extent the reaction can destabilize otherwise buoyantly stable density stratifications. We furthermore show that, even if the underlying nonreactive system is buoyantly unstable, the reaction breaks the symmetry of the developing patterns.

Analytical small-time asymptotic properties of A+B-->C fronts.

The small-time asymptotic properties of the reaction front formed by a reaction A+B-->C coupled to diffusion are considered. Reactants A and B are initially separately dissolved in two identical solvents. The solvents are brought into contact and the reactants meet through diffusion.

Higher-order large-time asymptotics for a reaction of the form nA+mB-->C.

This study examines the large time asymptotic behavior for the family of reactions of the form nA+mB-->C when the reactants A and B are initially separated. Once the reactants are brought into contact they are assumed to react with a kinetic rate proportional to A;{n}B;{m} . A planar reaction front forms and usually moves away from its initial position to invade one of the reactant solutions.

Analytical asymptotic solutions of nA+mB-->C reaction-diffusion equations in two-layer systems: a general study.

Large time evolution of concentration profiles is studied analytically for reaction-diffusion systems where the reactants A and B are each initially separately contained in two immiscible solutions and react upon contact and transfer across the interface according to a general nA+mB-->C reaction scheme. This study generalizes to immiscible two-layer systems the large time analytical asymptotic limits of concentrations derived by Koza [J. Stat.

Dynamics of A + B --> C reaction fronts in the presence of buoyancy-driven convection.

The dynamics of A+B-->C fronts in horizontal solution layers can be influenced by buoyancy-driven convection as soon as the densities of A, B, and C are not all identical. Such convective motions can lead to front propagation even in the case of equal diffusion coefficients and initial concentration of reactants for which reaction-diffusion (RD) scalings predict a nonmoving front. We show theoretically that the dynamics in the presence of convection can in that case be predicted solely on the basis of the knowledge of the one-dimensional RD density profile across the front.

Free-surface thin-film flows over uniformly heated topography.

The long-wave (lubrication) approximation governing the evolution of a thin film over a uniformly heated topographical substrate is solved numerically. We study the initial-value problem for a variety of governing dimensionless parameters and topographical substrates. We demonstrate that the dynamics is characterized by a slow relaxation process with continuous coarsening of drops up to a large time where coarsening is terminated and the interface organizes into a series of drops each of which is located in a trough in topography.

An analytical, numerical, and experimental comparison of the fluid velocity in the vicinity of an open tank with one and two lateral exhaust slot hoods and a uniform crossdraft.

The objective of this research was to compare mathematical models of the fluid velocity in the vicinity of an open tank with lateral slot exhaust. Two approaches were explored: a numerical solution assuming turbulent flow and an analytical solution assuming potential flow. A numerical simulation of the flow field in and around an open surface tank was performed using the commercial software FLUENT.