arXiv subjects

Henri Gouin

Publications and source records attributed to Henri Gouin.

At least 19 recordsLinked to original sources

arXiv2026

Laplace's law for sharp and diffuse interfaces

We study both diffuse and sharp liquid-vapor interfaces. The equilibrium equation of fluids is derived by using the principle of virtual work in a domain including the interfaces. For diffuse interfaces, the surface tension coefficient depends on the density profile across the interface. For sharp interfaces, the liquid-vapor layer is mathematically represented by a geometric surface and its specific energy is a Dirac delta function at the surface. We compare the both approaches and find relations between the surface tension coefficient and parameters of the models.

math-ph↗

arXiv2026

Mechanics and thermodynamics: A link between the two theories

In this note, we analyze the relationships that should govern the use of thermodynamics in fluid mechanics in a way that we believe is understandable to mathematicians. We also aim to better define the reasons why mechanics and thermodynamics must be correctly linked by showing that the principle of virtual work expressed using a specific internal energy is perfectly suited to fluid mechanics problems, provided that a well-chosen internal energy is proposed.

physics.class-ph↗

arXiv2025

Climbing plants -- Wrapping elastic plant stems around a cylindrical stake

Since Charles Darwin's time, the study of climbing plants on a cylindrical stake has been the subject of numerous articles in plant biology. One of the main ideas for studying the coiling of an elastic plant stem is to consider the growth of the plant stem in terms of evolution over time. However, as this development takes place over a long time scale, the static study alone has not been studied independently. Our static approach requires us to take into account elasticity, turgor pressure and gravity forces in a first analysis. The aim of this article is to present a simplified model demonstrating why plant stems climb mainly on their circular helix-shaped stakes, with the diameter of the stake playing an important role in plant stem ascent, as does the fineness of the stem. To perform this calculation, for a given mass density, we consider the variational principle of minimum energy. For thin plant stems, we can see, in first approximation, that the effect of gravity and turgor pressure can be neglected with respect to the energy of elasticity, and that the bulk of the calculation concerns elasticity terms.

physics.bio-ph↗

arXiv2024

Principle of virtual action in continuum mechanics

We present the principle of virtual action as a foundation of continuum mechanics. Used mainly in relativity, the method has a useful application in classical mechanics and places the notion of action as the basic concept of dynamics. The principle is an extension of virtual work to space-time. It extends the efforts made by d'Alembert and Lagrange. Unlike the classical case of equilibrium, the principle of virtual action becomes a postulate for the formulation of models in dynamics. It allows to use a minimal set of clear conjectures and is extended to the case of media with dissipation; it can be used for more complex systems.

physics.class-ph↗

arXiv2023

Noether theorem in fluid mechanics

Invariance theorems in analytical mechanics, such as Noether's theorem, can be adapted to continuum mechanics. For this purpose, it is useful to give a functional representation of the motion and to interpret the groups of invariance with respect to the space of reference associated with Lagrangian variables. A convenient method of calculus uses the Lie derivative. For instance, Kelvin theorems can be obtained by such a method.

physics.class-ph↗

arXiv2023

Remarks on the Lie derivative in fluid mechanics

The invariance theorems obtained in analytical mechanics and derived from Noether's theorems can be adapted to fluid mechanics. For this purpose, it is useful to give a functional representation of the fluid motion and to interpret the invariance group with respect to time in the quadri-dimensional reference space of Lagrangian variables. A powerful method of calculation uses Lie's derivative, and many invariance theorems and conservation laws can be obtained in fluid mechanics.

math-ph↗

arXiv2022

Theoretical model of the Leidenfrost temperature

The Leidenfrost effect is a phenomenon in which a liquid, poured onto a surface significantly hotter than the liquid's boiling point, produces a layer of vapor that prevents the liquid from rapid evaporation. Rather than making physical contact, a drop of water levitates above the surface. The temperature above which the phenomenon occurs is called the Leidenfrost temperature. The reason for the existence of the Leidenfrost temperature, which is much higher than the boiling point of the liquid, is not fully understood and predicted. Here we prove that the Leidenfrost temperature corresponds to a bifurcation in the solutions of equations describing evaporation of a nonequilibrium liquid-vapor interface. For water, the theoretical values of obtained Leidenfrost temperature, and that of the liquid bulk which is smaller than the boiling point of liquid, fit the experimental results found in the literature.

cond-mat.stat-mech↗

arXiv2020

Rankine-Hugoniot conditions obtained by using the space-time Hamilton action

In the quadri-dimensional space-time, the variation of Hamilton's action is a powerful tool to study the process equations for conservative fluid media. In this framework, Hamilton's principle allows to obtain equation of motions, equation of energy but also Rankine-Hugoniot conditions. The varia-tional method may be a versatile key to obtain the shock-wave conditions for complex media when the equations of processes are not expressed by linear or quasi-linear differential equations.

math-ph↗

arXiv2020

Influence of lunisolar tides on plants. Parametric resonance induced by periodic variations of gravity

Recent experiments conducted in the International Space Station highlight the apparent periodicity of leaf oscillations and other biological phenomena associated with rhythmic variations of lunisolar forces. These events are similar to those occurring on Earth, but with greater effects over a shorter period of time. Among the possible disturbances, other than forced or self-existing oscillations, parametric resonances appear caused by a small periodic term; such is the case of fluids subjected to small periodic variations in gravitational forces in microscopic or mesoscopic plant channels filled with sap and air-vapor. The interface instabilities verify a Mathieu's second order differential equation resulting from a Rayleigh-Taylor stability model. These instabilities appear during the Moon's rotation around the Earth and during the revolution of the International Space Station. They create impulses of pressure and sap movements in the network of roots, stems and leaves. The model can explain the effects of the lunar tide on plant growth. The eccentricity of the lunar orbit around the Earth creates an important difference between the apogee and perigee of the Moon's trajectory and therefore the tidal effects can depend on the distance between the Moon and the Earth.

physics.class-ph↗

arXiv2020

Rankine--Hugoniot conditions for fluids whose energy depends on space and time derivatives of density

By using the Hamilton principle of stationary action, we derive the governing equations and Rankine-Hugoniot conditions for continuous media where the specific energy depends on the space and time density derivatives. The governing system of equations is a time reversible dispersive system of conservation laws for the mass, momentum and energy. We obtain additional relations to the Rankine-Hugoniot conditions coming from the conservation laws and discuss the well-founded of shock wave discontinuities for dispersive systems.

physics.flu-dyn↗

arXiv2019

Variational formulation for models of shear shallow water flows and ideal turbulence

The shallow water equations without shear effects are similar to the gas dynamics equations with a polytropic equation of state. When the shear effects are taken into account, the equations contain additional evolution equations mathematically analogous to those of the Reynolds stresses in turbulent flows of compressible fluids when the source terms are neglected (ideal turbulence). We show that the non-dissipative model of shear shallow water flows and the model of ideal turbulence admit a similar variational formulation where, in the both cases, the equations for the Reynolds stress tensor evolution are considered as non-holonomic constraints.

physics.class-ph↗

arXiv2019

Dynamic boundary conditions for membranes whose surface energy depends on the mean and Gaussian curvatures

Membranes are an important subject of study in physical chemistry and biology. They can be considered as material surfaces with a surface energy depending on the curvature tensor. Usually, mathematical models developed in the literature consider the dependence of surface energy only on mean curvature with an added linear term for Gauss curvature. Therefore, for closed surfaces the Gauss curvature term can be eliminated because of the Gauss-Bonnet theorem. In [18], the dependence on the mean and Gaussian curvatures was considered in statics. The authors derived the shape equation as well as two scalar boundary conditions on the contact line. In this paper-thanks to the principle of virtual working-the equations of motion and boundary conditions governing the fluid membranes subject to general dynamical bending are derived. We obtain the dynamic 'shape equa-tion' (equation for the membrane surface) and the dynamic conditions on the contact line generalizing the classical Young-Dupr{é} condition.

physics.class-ph↗

arXiv2018

Symmetric forms for hyperbolic-parabolic systems of multi-gradient fluids

We consider multi-gradient fluids endowed with a volumetric internal energy which is a function of mass density, volumetric entropy and their successive gradients. We obtained the thermodynamic forms of equation of motions and equation of energy, and the motions are compatible with the two laws of thermodynamics. The equations of multi-gradient fluids belong to the class of dispersive systems. In the conservative case, we can replace the set of equations by a quasi-linear system written in a divergence form. Near an equilibrium position, we obtain a symmetric-Hermitian system of equations in the form of Godunov's systems. The equilibrium positions are proved to be stable when the total volume energy of the fluids is a convex function with respect to convenient conjugated variables-called main field-of mass density, volumetric entropy, their successive gradients, and velocity.

physics.class-ph↗

arXiv2018

Fluid mixtures in nanotubes

The aim of the paper is the study of fluid mixtures in nanotubes by the methods of continuum mechanics. The model starts from a statistical distribution in mean-field molecular theory and uses a density expansion of Taylor series. We get a continuous expression of the volume free energy with density's spatial-derivatives limited at the second order. The nanotubes can be filled with liquid or vapor according to the chemical characteristics of the walls and of liquid or vapor mixture-bulks. An example of two-fluid mixture constituted of water and ethanol inside carbon nanotubes at 20{\textdegree} C is considered. When diameters are small enough, nanotubes are filled with liquid-mixture whatever are the liquid or vapor mixture-bulks. The carbon wall influences the ratio of the fluid components in favor of ethanol. The fluid-mixture flows across nanotubes can be much more important than classical ones and if the external bulk is vapor, the flow can be several hundred thousand times larger than Poiseuille flow.

physics.flu-dyn↗

arXiv2018

Multi-gradient fluids

An internal energy function of the mass density, the volumetric entropy and their gradients at n-order generates the representation of multi-gradient fluids. Thanks to Hamilton's principle, we obtain a thermodynamical form of the equation of motion which generalizes the case of perfect compressible fluids. First integrals of flows are extended cases of perfect compressible fluids. The equation of motion and the equation of energy are written for dissipative cases, and are compatible with the second law of thermodynamics.

physics.flu-dyn↗

arXiv2017

Temperature profile in a liquid-vapor interface near the critical point

Thanks to an expansion with respect to densities of energy, mass and entropy, we discuss the concept of thermocapillary fluid for inhomogeneous fluids. The non-convex state law valid for homogeneous fluids is modified by adding terms taking into account the gradients of these densities. This seems more realistic than Cahn and Hilliard's model which uses a density expansion in mass-density gradient only. Indeed, through liquid-vapor interfaces, realistic potentials in molecular theories show that entropy density and temperature do not vary with the mass density as it would do in bulk phases. In this paper, we prove using a rescaling process near the critical point that liquid-vapor interfaces behave essentially in the same way as in Cahn and Hilliard's model.

cond-mat.stat-mech↗

arXiv2017

Continuum mechanics at nanoscale. A tool to study trees' watering and recovery

The cohesion-tension theory expounds the crude sap ascent thanks to the negative pressure generated by evaporation of water from leaves. Nevertheless, trees pose multiple challenges and seem to live in unphysical conditions: the negative pressure increases cavitation; it is possible to obtain a water equilibrium between connected parts where one is at a positive pressure and the other one is at negative pressure; no theory is able to satisfactorily account for the refilling of vessels after embolism events. A theoretical form of our paper in the Journal of Theoretical Biology is proposed together with new results: a continuum mechanics model of the disjoining pressure concept refers to the Derjaguin School of physical chemistry. A comparison between liquid behaviour both in tight-filled microtubes and in liquid thin-films is offered when the pressure is negative in liquid bulks and is positive in liquid thin-films and vapour bulks. In embolized xylem microtubes, when the air-vapour pocket pressure is greater than the air-vapour bulk pressure, a refilling flow occurs between the air-vapour domains to empty the air-vapour pockets although the liquid-bulk pressure remains negative. The model has a limit of validity taking the maximal size of trees into account. These results drop inkling that the disjoining pressure is an efficient tool to study biological liquids in contact with substrates at a nanoscale range.

cond-mat.soft↗

arXiv2017

Properties of thermocapillary fluids and symmetrization of motion equations

The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is not necessary uniform. In this new general representation writes in symmetric form with respect to the mass and entropy densities. For conservative motions of perfect thermocapillary fluids, Kelvin's circulation theorems are always valid. Dissipative cases are also considered; we obtain the balance of energy and we prove that equations are compatible with the second law of thermodynamics. The internal energy form allows to obtain a Legendre transformation inducing a quasi-linear system of conservation laws which can be written in a divergence form and the stability near equilibrium positions can be deduced. The result extends classical hyperbolicity theory for governing-equations' systems in hydrodynamics, but symmetric matrices are replaced by Hermitian matrices.

physics.flu-dyn↗