Displaying similar documents to “Modelling of Miscible Liquids with the Korteweg Stress”

Reaction-Diffusion Equations for Chemically Reacting Gas Mixtures

Marzia Bisi (2008)

Bollettino dell'Unione Matematica Italiana

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In this paper we aim at describing the hydrodynamic limit of a mixture of chemically reacting gases. Starting from kinetic Boltzmann-type equations, we derive Grad's 13-moments equations for single species. Then, after scaling such equations in terms of a suitable Knudsen number, we apply an asymptotic Chapman-Enskog procedure in order to build up hydrodynamic equations of Navier-Stokes type.

Modelling of miscible liquids with the Korteweg stress

Ilya Kostin, Martine Marion, Rozenn Texier-Picard, Vitaly A. Volpert (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the...

Longtime behavior of solutions of a Navier-Stokes/Cahn-Hilliard system

Helmut Abels (2009)

Banach Center Publications

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We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids of the same density in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in the model. Moreover, diffusion of both components is taken into account. This leads to a coupled Navier-Stokes/Cahn-Hilliard system, which can describe the evolution of droplet formation and collision during the flow. We review some...

Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases

Marzia Bisi, Laurent Desvillettes (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in...

An existence proof for the stationary compressible Stokes problem

A. Fettah, T. Gallouët, H. Lakehal (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper, we prove the existence of a solution for a quite general stationary compressible Stokes problem including, in particular, gravity effects. The Equation Of State gives the pressure as an increasing superlinear function of the density. This existence result is obtained by passing to the limit on the solution of a viscous approximation of the continuity equation.

A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation

Emmanuel Audusse, Marie-Odile Bristeau, Benoît Perthame, Jacques Sainte-Marie (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighboring layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic...

On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors

M. A. Budroni, M. Rustici, E. Tiezzi (2010)

Mathematical Modelling of Natural Phenomena

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We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical...