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Henri Gouin

Publications and source records attributed to Henri Gouin.

At least 37 records · Page 2Linked to original sources
arXiv2017

Travelling waves of density for a fourth-gradient model of fluids

In mean-field theory, the non-local state of fluid molecules can be taken into account using a statistical method. The molecular model combined with a density expansion in Taylor series of the fourth order yields an internal energy value relevant to the fourth-gradient model, and the equation of isother-mal motions takes then density's spatial derivatives into account for waves travelling in both liquid and vapour phases. At equilibrium, the equation of the density profile across interfaces is more precise than the Cahn and Hilliard equation, and near the fluid's critical-point, the density profile verifies an Extended Fisher-Kolmogorov equation, allowing kinks, which converges towards the Cahn-Hillard equation when approaching the critical point. Nonetheless, we also get pulse waves oscillating and generating critical opalescence.

physics.flu-dyn↗
arXiv2015

Archimedes' famous-theorem

In his treatise addressed to Dositheus of Pelusium, Archimedes of Syracuse obtained the result of which he was the most proud: a sphere has two-thirds the volume of its circumscribing cylinder. At his request a sculpted sphere and cylinder were placed on his tomb near Syracuse. Usually, it is admitted that to find this formula, Archimedes used a half polygon inscribed in a semicircle; then he performed rotations of these two figures to obtain a set of trunks in a sphere. This set of trunks allowed him to determine the volume. In our opinion, Archimedes was so clever that he found the proof with shorter demonstration. Archimedes did not need to know $π$ to prove the result and the Pythagorean theorem was probably the key to the proof.

math.HO↗
arXiv2015

Dynamical pressure for fluid mixtures with several temperatures

We consider binary mixtures of fluids with components having different temperatures. A new dynamical pressure term is associated with the difference of temperatures between components even if fluid viscosities are null. The non-equilibrium dynamical pressure can be measured and may be convenient in several physical situations as for example in cosmological circumstances where a dynamical pressure played a major role in the evolution of the early universe.

physics.class-ph↗
arXiv2015

Vesicle model with bending energy revisited

The equations governing the conditions of mechanical equilibrium in fluid membranes subject to bending are revisited thanks to the principle of virtual work. The note proposes systematic tools to obtain the shape equation and the line condition instead of Christoffel symbols and the complex calculations they entail. The method seems adequate to investigate all problems involving surface energies.

cond-mat.soft↗
arXiv2015

The watering of tall trees - Embolization and recovery

We can propound a thermo-mechanical understanding of the ascent of sap to the top of tall trees thanks to a comparison between experiments associated with the cohesion-tension theory and the disjoining pressure concept for liquid thin-films. When a segment of xylem is tight-filled with crude sap, the liquid pressure can be negative although the pressure in embolized vessels remains positive. Examples are given that illustrate how embolized vessels can be refilled and why the ascent of sap is possible even in the tallest trees avoiding the problem due to cavitation. However, the maximum height of trees is limited by the stability domain of liquid thin-films.

physics.chem-ph↗
arXiv2013

Motions in liquid-vapour interfaces by using a continuous mechanical model

By using a limit analysis for the motion equations of viscous fluid endowed with internal capillarity, we are able to propose a dynamical expression for the surface tension of moving liquid-vapour interfaces without any phenomenological assumption. The proposed relation extends the static case, yields the Laplace formula in cases of mass transfer across interfacial layers and allows to take the second coefficient of viscosity of compressible fluids into account. We generalize the Maxwell rule in dynamics and directly explain the Marangoni effect.

math-ph↗
arXiv2013

Scaling Navier-Stokes Equation in Nanotubes

On one hand, classical Monte Carlo and molecular dynamics (MD) simulations have been very useful in the study of liquids in nanotubes, enabling a wide variety of properties to be calculated in intuitive agreement with experiments. On the other hand, recent studies indicate that the theory of continuum breaks down only at the nanometer level; consequently flows through nanotubes still can be investigated with Navier-Stokes equations if we take suitable boundary conditions into account. The aim of this paper is to study the statics and dynamics of liquids in nanotubes by using methods of non-linear continuum mechanics. We assume that the nanotube is filled with only a liquid phase; by using a second gradient theory the static profile of the liquid density in the tube is analytically obtained and compared with the profile issued from molecular dynamics simulation. Inside the tube there are two domains: a thin layer near the solid wall where the liquid density is non-uniform and a central core where the liquid density is uniform. In the dynamic case a closed form analytic solution seems to be no more possible, but by a scaling argument it is shown that, in the tube, two distinct domains connected at their frontiers still exist. The thin inhomogeneous layer near the solid wall can be interpreted in relation with the Navier length when the liquid slips on the boundary as it is expected by experiments and molecular dynamics calculations.

physics.flu-dyn↗
arXiv2013

Statics and dynamics of fluids in nanotubes

The purpose of this article is to study the statics and dynamics of nanotubes by using the methods of continuum mechanics. The nanotube can be filled with only a liquid or a vapour phase according to the physicochemical characteristics of the wall and to the disjoining pressure associated with the liquid and vapour mother bulks of the fluid, regardless of the nature of the external mother bulk. In dynamics, flows through nanotubes can be much more important than classical Poiseuille flows. When the external mother bulk is of vapour, the flow can be a million times larger than the classical flows when slippage on wall does not exist.

physics.flu-dyn↗
arXiv2013

Interfaces endowed with non-constant surface energies revisited with the d'Alembert-Lagrange principle

The equation of motions and the conditions on surfaces and edges between fluids and solids in presence of non-constant surface energies, as in the case of surfactants attached to the fluid particles at the interfaces, are revisited under the principle of virtual work. We point out that adequate behaviors of surface concentrations may drastically modify the surface tension which naturally appears in the Laplace and the Young-Dupré equations. Thus, the principle of virtual work points out a strong difference between the two revisited concepts of surface energy and surface tension.

cond-mat.soft↗
arXiv2012

On the Müller paradox for thermal-incompressible media

In his monograph Thermodynamics, I. Müller proves that for incompressible media the volume does not change with the temperature. This Müller paradox yields an incompatibility between experimental evidence and the entropy principle. This result has generated much debate within the mathematical and thermodynamical communities as to the basis of Boussinesq approximation in fluid dynamics. The aim of this paper is to prove that for an appropriate definition of incompressibility, as a limiting case of quasi thermal-incompressible body, the entropy principle holds for pressures smaller than a critical pressure value. The main consequence of our result is the physically obvious one, that for very large pressures, no body can be perfectly incompressible. The result is first established in the fluid case. In the case of hyperelastic media subject to large deformations the approach is similar, but with a suitable definition of the pressure associated with convenient stress tensor decomposition.

physics.class-ph↗
arXiv2012

Geometric evolution of the Reynolds stress tensor

The dynamics of the Reynolds stress tensor for turbulent flows is described with an evolution equation coupling both geometric effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are neglected: the Reynolds stress tensor is then expressed as the sum of three tensor products of vector fields which are governed by a distorted gyroscopic equation. Along the mean flow trajectories, the fluctuations of velocity are described by differential equations whose coefficients depend only on the mean flow deformation. If the mean flow vorticity is small enough, an approximate turbulence model is derived, and its application to shear shallow water flows is proposed. Moreover, the approximate turbulence model admits a variational formulation which is similar to the one of capillary fluids.

physics.class-ph↗
arXiv2012

A consistent thermodynamical model of incompressible media as limit case of quasi-thermal-incompressible materials

In this paper we consider the conditions on quasi-thermal-incompressible so that they satisfy all the principles of thermodynamics, including the stability condition associated with the concavity of the chemical potential. We analyze the approximations under which a quasi-thermal-incompressible medium can be considered as incompressible. We find that the pressure cannot exceed a very large critical value and that the compressibility factor must be greater than a lower limit that is very small. The analysis is first done for the case of fluids and then extended to the case of thermoelastic solids.

physics.class-ph↗
arXiv2012

The nanofluidics can explain ascent of water in tallest trees

In Amazing numbers in biology, Flindt reports a giant, 128 meter-tall eucalyptus, and a 135 meter-tall sequoia. However, the explanation of the maximum altitude of the crude sap ascent and consequently the main reason of the maximum size that trees can reach is not well understood. According to tree species, the crude sap is driven in xylem microtubes with diameters ranging between 50 and 400 micrometers. The sap contains diluted salts but its physical properties are roughly those of water; consequently, hydrodynamic, capillarity and osmotic pressure yield a crude sap ascent of a few tens of meters only. Today, we can propound a new understanding of the ascent of sap to the top of very tall trees thanks to a new comparison between experiments associated with the cohesion-tension theory and the disjoining pressure concept. Here we show that the pressure in the water-storing tracheids of leaves can be strongly negative whereas the pressure in the xylem microtubes of stems may remain positive when, at high level, inhomogeneous liquid nanolayers wet the xylem walls of microtubes. The nanofluidic model of crude sap in tall trees discloses a stable sap layer up to an altitude where the pancake layer thickness coexists with the dry xylem wall and corresponds to the maximum size of tallest trees. In very thin layers, sap flows are widely more significant than those obtained with classical Navier-Stokes models and consequently are able to refill stomatic cells when phloem embolisms supervene. These results drop an inkling that the disjoining pressure is an efficient tool to study biological liquids in contact with substrates at a nanoscale range.

physics.flu-dyn↗
arXiv2011

Travelling waves near a critical point of a binary fluid mixture

Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal form of the free energy near critical conditions and can be integrated by a rescaling process where the binary mixture is similar to a single fluid. Nevertheless, density solution profiles obtained are not necessarily monotonic. As indicated in Appendix, the results might be extended to other topics like finance or biology.

physics.class-ph↗
arXiv2011

Utilization of the second gradient theory in continuum mechanics to study motions and thermodynamics of liquid-vapor interfaces

A thermomechanical model of continuous fluid media based on second gradient theory is used to study motions in liquid-vapor interfaces. At equilibrium, the model is shown to be equivalent to mean-field molecular theories of capillarity. In such fluids, conservative motions verify first integrals that lead to Kelvin circulation theorems and potential equations. The dynamical surface tension of liquid-vapor interfaces is deduced from viscous fluid equations. The result provides and explains the Marangoni effect.

physics.flu-dyn↗
arXiv2011

Liquid-solid interaction at nanoscale and its application in vegetal biology

The water ascent in tall trees is subject to controversy: the vegetal biologists debate on the validity of the cohesion-tension theory which considers strong negative pressures in microtubes of xylem carrying the crude sap. This article aims to point out that liquids are submitted at the walls to intermolecular forces inferring density gradients making heterogeneous liquid layers and therefore disqualifying the Navier-Stokes equations for nanofilms. The crude sap motion takes the disjoining pressure gradient into account and the sap flow dramatically increases such that the watering of nanolayers may be analogous to a microscopic flow. Application to microtubes of xylem avoids the problem of cavitation and enables us to understand why the ascent of sap is possible for very high trees.

physics.bio-ph↗
arXiv2009

Nucleation of spherical shell-like interfaces by second gradient theory: numerical simulations

The theory of second gradient fluids (which are able to exert shear stresses also in equilibrium conditions) allows us: (i) to describe both the thermodynamical and the mechanical behavior of systems in which an interface is present; (ii) to express the surface tension and the radius of microscopic bubbles in terms of a functional of the chemical potential; (iii) to predict the existence of a (minimal) nucleation radius for bubbles. Moreover, the above theory supplies a 3D-continuum model which is endowed with sufficient structure to allow the construction of a 2D-shell-like continuum representing a consistent approximate 2D-model for the interface between phases. In this paper we use numerical simulations in the framework of second gradient theory to obtain explicit relationships for the surface quantities typical of 2D-models. In particular, for some of the most general two-parameter equations of state, it is possible to obtain the curves describing the relationship between the surface tension, the thickness, the surface mass density and the radius of the spherical interfaces between fluid phases of the same substance. These results allow us to predict the (minimal) nucleation radii for this class of equations of state.

physics.class-ph↗