Effects of constant electric fields on the buoyant stability of reaction fronts

The effects that applying constant electric fields have on the buoyant instability of reaction fronts propagating vertically in a Hele-Shaw cell are investigated for a range of electric field strengths and fluid parameters. The reaction produces a decrease in density across the front such that upwards propagating fronts are buoyantly unstable in the field-free situation. The reaction kinetics are modeled by cubic autocatalysis. A linear stability analysis reveals that a positive electric field increases the stability of a reaction front and can stabilize an otherwise unstable front. A negative field has the opposite effect, making the reaction front more unstable. Numerical simulations of the full nonlinear problem confirm these predictions and show the development of cellular fingers on unstable fronts. These simulations show that the electric field effects on the reaction within the front can alter the fluid density so as to give the possibility of destabilizing an otherwise stable downward propagating front

Etude théorique de l'influence des effets thermiques et d'un champ électrique externe sur la digitation de fronts chimiques

Several types of instability can affect the interface between two fluids. For instance, a Rayleigh-Taylor instability (or density fingering) is encountered when a heavier fluid is placed upon a lighter one in the gravity field and double diffusive instabilities can be triggered by differential diffusivity of the different species present in the fluid. In this context our work aims to understand theoretically in which way a chemical reaction can induce and influence such instabilities in a fluid initially at rest.To understand the dynamics resulting from the coupling between chemical reactions and hydrodynamical instabilities we use chemical fronts as model systems. These fronts result from the coupling between autocatalytical chemical reactions and diffusion and they allow to create a self-organized interface between the products and the reactants. As during a chemical reaction the density may vary due to solutal and thermal effects, the products and the reactants can have different densities which may trigger convection movements leading to the destabilization of the fronts.We have in particular studied the influence of the exothermicity of the reaction on the fingering of chemical fronts, focusing first on the influence of heat losses through the walls of the set-up.These leaks have a marked influence on the dynamics because they affect the temperature profiles and hence the density profiles too. We have also classified the various types of instabilities that may appear dues to solutal and thermal effects. We have found a new type of hydrodynamic instability of statically stable fronts induced by the chemical reaction. We have furthermore analyzed an isothermal model with two chemical species. If they diffuse at different rates the front can be subject to diffusive instabilities as well. We have shown that the coupling between such a diffusive instability and fingering can trigger complex dynamics. We have eventually studied the influence of an external electric field on the diffusive instabilities and on fingering underlying the possibility to destabilize otherwise stable fronts./Différents types d'instabilités hydrodynamiques peuvent affecter les interfaces entre deux fluides comme par exemple, une instabilité de Rayleigh-Taylor (ou digitation de densité) quand un fluide plus dense se trouve placé au-dessus d'un fluide moins dense dans le champ de gravité ou des instabilités de double diffusion induites par des différences entre les diffusivités d'un soluté et de la chaleur contenus dans les fluides. Dans ce contexte, notre thèse s'attache à comprendre de manière théorique comment une réaction chimique peut influencer ces instabilités voire les générer dans un fluide initialement au repos. Pour étudier les dynamiques résultant du couplage entre réactions chimiques et instabilités hydrodynamiques, nous utilisons des systèmes modèles: les fronts chimiques de conversion résultant de la compétition entre réactions chimiques autocatalytiques et diffusion créant une interface auto-organisée entre les réactifs et les produits. Comme au cours d'une réaction chimique la densité peut varier par des effets solutaux et thermiques, les produits et les réactifs de densités différentes peuvent générer des mouvements de convection qui conduisent à la déstabilisation des fronts. Nous avons en particulier étudié l'influence de l'exothermicité de la réaction sur les instabilités de digitation de fronts chimiques, en nous focalisant dans un premier temps sur l'influence des pertes de chaleur par les parois du réacteur.Ces fuites ont un effet marqué sur les instabilitités car elles affectent les profils de température et donc les profils de densité dans le système. Nous avons également classifié les différentes instabilités qui peuvent apparaître via des changements de densité dûs à des effets thermiques et solutaux et mis en évidence un nouveau type de déstabilisation hydrodynamique de fronts statiquement stables induit par une réaction chimique. Nous avons ensuite analysé un modèle isotherme impliquant deux espèces chimiques. Si ces dernières diffusent a des vitesses différentes le front peut être sujet à une instabilité diffusive. Nous avons montré qu'un couplage entre une telle instabilité diffusive et de la digitation peut être à l'origine de dynamiques complexes. Nous avons ensuite considéré l'influence d'un champ électrique sur les instabilité diffusives et de digitation en soulignant la possibilié de déstabiliser via ce champ des fronts initialement stables.Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe

Influence of heat losses on nonlinear fingering dynamics of exothermic autocatalytic fronts

Across traveling exothermic autocatalytic fronts, a density jump can be observed due to changes in composition and temperature. These density changes are prone to induce buoyancy-driven convection around the front when the propagation takes place in absence of gel within the gravity field. Most recent experiments devoted to studying such reaction-diffusion-convection dynamics are performed in Hele-Shaw cells, two glass plates separated by a thin gap width and filled by the chemical solutions. We investigate here the influence of heat losses through the walls of such cells on the nonlinear fingering dynamics of exothermic autocatalytic fronts propagating in vertical Hele-Shaw cells. We show that these heat losses increase tip splittings and modify the properties of the flow field. A comparison of the differences between the dynamics in reactors with respectively insulating and conducting walls is performed as a function of the Lewis number L e, the Newton cooling coefficient α quantifying the amplitude of heat losses and the width of the system. We find that tip splitting is enhanced for intermediate values of α while coarsening towards one single finger dominates for insulated systems or large values of α leading to situations equivalent to isothermal ones. © 2009 Elsevier B.V. All rights reserved.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

The not so dark side of trust: does trust increase the size of the shadow economy?

This paper studies the relationship between the size of the shadow economy and generalized trust, on a cross-section of countries, both developed and developing, and finds that it is significantly negative. That relationship is robust to controlling for a large set of economic, policy, and institutional variables, to changing the estimate of the shadow economy and the estimation period, and to controlling for endogeneity. It is independent from trust in institutions. We provide evidence that it is mainly present in the sample of developing countries. Latest version, September 2011: http://www.solvay.edu/sites/upload/files/CEB_WorkingPapers/LastUpdate/wp08030.pdfinfo:eu-repo/semantics/publishe

The not so dark side of trust: Does trust increase the size of the shadow economy?

This paper reports a negative relationship between the size of the shadow economy and generalized trust, in a sample of countries, both developed and developing. That relationship is robust to controlling for a large set of economic, policy, and institutional variables, to changing the estimate of the shadow economy and the estimation period, and to controlling for endogeneity. It is independent from trust in institutions and from income inequality, and is mainly present in the sample of developing countries. Those findings suggest that the tax compliance effect of trust dominates its role as a substitute for the formal legal system.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Stability of exothermic autocatalytic fronts with regard to buoyancy-driven instabilities in presence of heat losses

Across traveling autocatalytic fronts, density differences due to composition and temperature changes can lead to buoyancy-driven hydrodynamic instabilities deforming the front by convective motions. We study here the influence of heat losses through the walls of the reactor on the stability of such exothermic fronts in the gravity field. The stability domain is computed numerically in a parameter space spanned by the solutal R c and thermal R T Rayleigh numbers of the problem for various values of the Newton's coefficient α quantifying the intensity of heat losses. © 2011 Elsevier B.V.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

The not so dark side of trust: does trust increase the size of the shadow economy?

This paper studies the relationship between the size of the shadow economy and generalized trust, on a cross-section of countries, both developed and developing, and finds that it is significantly negative. That relationship is robust to controlling for a large set of economic, policy, and institutional variables, to changing the estimate of the shadow economy and the estimation period, and to controlling for endogeneity. It is independent from trust in institutions. We provide evidence that it is mainly present in the sample of developing countries. Latest version, September 2011: http://www.solvay.edu/sites/upload/files/CEB_WorkingPapers/LastUpdate/wp08030.pdfShadow economy; informal sector; trust.

Fingering of exothermic reaction-diffusion fronts in Hele-Shaw cells with conducting walls

We consider the influence of heat losses through the walls of a Hele-Shaw cell on the linear stability and nonlinear dynamics of exothermic chemical fronts whose solutal and thermal contributions to density changes have the same signs. Our analysis is based on the reaction-diffusion-convection equations obtained from the Darcy-Boussinesq approximation. The parameters governing the equations are the Damköhler number, a kinetic parameter d, the Lewis number Le, the thermal-expansion coefficient γT, and a heat-transfer coefficient α which measures heat losses through the walls. We show that for thermally insulating walls, the temperature profile is a front that follows the concentration profile, while in the presence of heat losses, the temperature profile becomes a pulse that leads to a nonmonotonic density profile which in turn may lead to a destabilization of an otherwise stable front. © 2005 American Institute of Physics.SCOPUS: ar.jinfo:eu-repo/semantics/publishe