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*Thermodynamics of Interfaces and Fluid Mechanics *deals with interfaces that are space areas with a low thickness and which separate environments of different properties. They designate phase separation but also thin flames and waves of discontinuity. At a macroscopic scale, they are associated with material surfaces that possess thermodynamic attributes and their own behavior laws.

The analysis of systems with **interfaces **involves scale changes and the use of specific techniques such as asymptotic developments, the second gradient theory or the phase field model method. Digital simulation is implemented in order to solve the complex systems studied. Testing is an essential step to solve the set problems.

2D varieties of interfaces often coexist with 1D varieties such as ligaments (atomization), contact lines (set drops) or Plateau’s edges (foams).

The articles in the journal deal with all of the mentioned above subjects.

*Thermodynamique des interfaces et mécanique des fluides* traite des interfaces qui sont des zones de l’espace de faible épaisseur séparant des milieux à propriétés différentes. Elles désignent les séparations de phase, mais aussi les flammes minces et les ondes de discontinuité. A l’échelle macroscopique, on les assimile à des surfaces matérielles douées de propriétés thermodynamiques et possédant leurs propres lois de comportement.

L’analyse des systèmes comprenant des **interfaces **implique des changements d’échelle et l’utilisation de techniques spécifiques telles que les développements asymptotiques, la théorie du second gradient ou la méthode des champs de phase. La simulation numérique est mise en œuvre pour résoudre les systèmes complexes étudiés. L’expérimentation est une étape indispensable pour résoudre les problèmes posés.

Les variétés 2D que constituent les interfaces coexistent fréquemment avec des variétés 1D telles les ligaments (atomisation), les lignes de contact (gouttes posées) ou les bords de Plateau (mousses).

Les articles de la revue traitent de l’ensemble des disciplines énumérées plus haut.

Edoh Tossou,
Kwassi Anani,
Roger Prud’homme

*This paper makes a contribution by generalizing the classical series solution for initial boundary value problems of the one-dimensional reaction-diffusion equation on any finite interval of the real line. The general form of the equation is considered on a generic bounded interval and is subjected in the unified way to the three classical boundary conditions, namely the Neumann, Dirichlet, and Robin boundary conditions. The Fourier decomposition method, is used to derive the solution of the resulting homogeneous equation with zero boundary conditions. Subsequently, the solution of the nonhomogeneous equation with homogeneous boundary conditions is obtained using the Duhamel’s principle. Finally, the solution of the general problem is obtained as a convergent series over the considered interval, with the construction of an auxiliary. The Hopf-Cole transformation has facilitated the generalization of the exact solution of the Burger’s equation to generic intervals, as demonstrated by the described method.*

The interest of microgravity for the study of fluid interfaces

Roger Prud’homme,
Kwassi Anani

*We discuss here the interest that experimentation in microgravity can represent for the study of fluid interfaces. First, we must know the situations where gravity is likely to exert an action on the interfaces. We will limit ourselves to two cases: the first is that of capillary interfaces where surface tension is present even at equilibrium, the second is that of thin flames which only exist outside of equilibrium, but which can be considered as generalized interfaces. A quick presentation of the means offered for the experiment is made. Concrete examples are treated by theory, numerical calculation and experimentation.*

Fire-air: a story of flame

Roger Prud’homme,
Mahouton Norbert Hounkonnou,
Guillaume Legros

*We relate how at the end of the 18th century, a discovery linked to combustion, could challenge the idea that we had about constituents of matter and lead to revolutionize chemistry. A correct interpretation of this discovery had to be found and for that to question existing theories and dogmas. It then took a fundamental reflection on experimental work and the importance of quantitative measurements, to invent a scientific way of operating. The innovations and the progress made during the following two centuries in physics and chemistry, but also in thermodynamics and mechanics, brought to the current situation where combustion has found its place as a science in its own right.*

Modelization of partial wetting by macroscopic approach in discrete mechanics

Jean-Paul Caltagirone,
Roger Prud’homme

*The partial wetting is generally defined by a contact angle between the liquid and the surface in the case of a static equilibrium excluding other types of actions such as gravity, inertia, viscosity, etc. When these last effects are no longer negligible, the modeling of two-phase flows governed by capillary forces cannot be reduced to simple geometrical laws on the surface tensions between the phases. The triple line is subject to accelerations that combine in a complex way to fix in time its motion on the surface. The macroscopic approach adopted is based on the representativity of the discrete equation of motion derived from the fundamental law of dynamics expressed in terms of accelerations. The formalism leads to a wave equation whose form corresponds to the two components of a Helmholtz Hodge decomposition, the first to the curl-free and the second to the divergence-free. Like all other contributions, the capillary effects are expressed in two terms of the capillary potential, an energy per unit mass. The longitudinal and transverse surface tensions allow for possible anisotropy effects in the tangent plane at the interface. The assignment of the surface tension values on the triple line related to the contact angle allows to take into account the partial wetting effects in a dynamic context. Two examples illustrate the validity of this approach.*

Numerical simulation of an average flow in an inter-blade channel of a horizontal axis wind mill

Delphin Tomboravo,
Roger Vony,
Francis Raveloson,
Tsialefitry Aly Saandy

*This article states a numerical method of finished differences, making it possible to calculate the variables describing an average flow, no viscous and no heavy, through a mobile wheel of a wind mill with horizontal axis, to deduce its performances from them, by using a grid with irregular steps. Centered space discretization’s diagrams inside the calculation domain and decentered towards the interior for the nodes placed on the borders are used. The temporal discretization uses an explicit diagram with two steps of time, with about two precisions. Calculations are made in two stages: a prediction stage and a correction stage. They preceded to calculations of the three-dimensional flow initial state, realized thereafter in its bypass sections. Boundary conditions are imposed on the borders of the calculation domain. Calculation convergence is ensured by numerical viscosity implicitly introduced by the time discretization’s diagrams. The internal stability is ensured by a constraint on the step of temporal discretization in accordance with CFL condition Initial conditions are calculated while realizing, on the flow bypass sections, characteristic quantities initially imposed in the calculation domain volume.*

Editorial Board

Editor in Chief

Roger PRUD’HOMME

Sorbonne Université – CNRS

roger.prud_homme@upmc.fr

Co-Editors

Kwassi ANANI

Université de Lomé

Togo

kanani@univ-lome.tg

Abdon ATANGANA

IGS- Bloemfontein

Republic of South Africa

AtanganaA@ufs.ac.za

Amine CHADIL

CNRS, MSME

amine.chadil@cnrs.fr

Christian CHAUVEAU

CNRS – ICARE

christian.chauveau@cnrs-orleans.fr

Alain MAILFERT

Université de Lorraine

alain.mailfert@univ-lorraine.fr

Mahouton Norbert HOUNKONNOU

University of Abomey-Calavi

Benin

norbert_hounkonnou@cipma.net

Sébastien TANGUY

IMFT - Toulouse

tanguy@imft.fr

Pierre TRONTIN

LMFA - Université de Lyon 1

pierre.trontin@univ-lyon1.fr

Stéphane VINCENT

Université Paris-Est Marne-La-Vallée

stephane.vincent@u-pem.fr

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