Looking at rational mixture theories within the context of a new perspective, this work aims to put forward a proposal for an Eshelbian approach to the nonlinear mechanics of a constrained solid-fluid mixture, made up of an inhomogeneous poroelastic solid and an inviscid compressible fluid, which do not undergo any chemical reaction
We studied the kinetics and mechanism of the dehydration reaction of calcium sulfate dihydrate to hemihydrate under controlled temperature and water vapor partial pressure. From kinetic and reaction rate curves obtained using TGA under isothermal and isobaric conditions, we determined the overall behavior of this dehydration reaction and the effects of the system's intensive variables on its kinetics. We observed that the reactions take place with an initial induction period that decreases with increasing temperature, followed by a sigmoidal mass loss controlled by both nucleation and growth processes. Characterization of our samples at different instants of the reaction allowed us to observe and confirm a surface nucleation process followed by isotropic growth of the nuclei with inward development of the solid product. We then employed the Mampel kinetic model based on the observed experimental results considering the physical nature of the investigated transformation and the real geometry of the particles. Form this model, we obtained sets of kinetic parameters for the nucleation and growth processes and their evolution with temperature. We then proposed physicochemical mechanisms for both processes, and they were considered to interpret the kinetic parameters obtained previously. This mechanistic analysis of the system allowed determining the effects of both temperature and water vapor pressure on the kinetic behavior of the reaction, which corresponds to a novel approach for the dehydration reaction of calcium sulfate dihydrate. The use of this universal kinetic approach to treat this chemical system.The methodology used in this work can be applied for studying the dehydration of other ionic hydrates.
We study the drawing of a Newtonian viscous sheet under the influence of cooling with temperature dependence of the viscosity. Classically this problem has an instability called draw resonance, when the draw ratio Dr, which is the ratio of the outlet velocity relative to the inlet velocity, is beyond a critical value Drc. The heat transfer from the surface compared to the bulk energy advection is conveniently measured by the Stanton number St. Usual descriptions of the problem are one-dimensional and rigorously apply for St ≤ 1. The model presented here accounts for variations of the temperature across the sheet and has therefore no restriction on St. Stability analysis of the model shows two different cooling regimes: the ‘advection-dominated’ cooling for St ≪ 1 and the ‘transfer-dominated’ cooling for St ≫ 1. The transition between those two regimes occurs at St = O(1) where the stabilizing effect due to cooling is most efficient, and for which we propose a mechanism for stabilization, based on phase shifts between the tension and axial-averaged flow quantities. Away from this transition, the sheet is always shown to be unstable at smaller draw ratios. Additionally, in the limit of St → ∞, the heat exchange is such that the temperature of the fluid obtains the far-field temperature, which hence corresponds to a ‘prescribed temperature’ regime. This dynamical situation is comparable to the isothermal regime in the sense that the temperature perturbation has no effect on the stability properties. Nevertheless, in this regime, the critical draw ratio for draw resonance can be below the classical value of Drc = 20.218 obtained in isothermal conditions.
La génération de la forme des tissus biologiques invoque des phénomènes de croissance (variation des longueurs relâchées) et de remodelage (variation des propriétés mécaniques). La modélisation de ces phénomènes est de première importance sur le plan non seulement fondamental mais aussi technologique, pour le secteur de la santé. Dans le cadre d'une approche mécanique macroscopique, nous regardons le tissu osseux comme un milieu continu avec microstructure, dont les caractéristiques mécaniques locales (à cette échelle) se traduisent par un comportement linéairement élastique, anisotrope et évolutif. En particulier, la cinématique proposée est assez riche pour suivre l'évolution de la microstructure du tissu considéré, et en même temps prendre en compte le couplage existant entre contrainte, croissance et remodelage. Nous proposons donc une approche unifiée de la mécanique de la croissance et du remodelage, dans laquelle toutes les lois de bilan dérivent d'un principe des puissances virtuelles. Cette approche a été appliquée, pour le moment, à l'étude du remodelage de la raideur élastique par rotation de la microstructure dans le cas bidimensionnel, en l'absence de phénomènes de croissance volumique et de réponse physiologique aux stimuli (remodelage passif). L'analyse des résultats obtenus achève cette étude.
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