Thermodynamics of Interfaces and Fluid Mechanics

TIMF - ISSN 2514-4642 - © ISTE Ltd

Journal issues

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Recent articles

Series solution method for the reaction-diffusion equation over finite intervals

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.

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The interest of microgravity for the study of fluid interfaces

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.

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Fire-air: a story of flame

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.

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Modelization of partial wetting by macroscopic approach in discrete mechanics

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.

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

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.