Henri Gouin, Pierre Seppecher. Temperature profile in a liquid-vapor interface near the critical point. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 2017, 473 (20170229), pp.1-13. ⟨10.1098/rspa.2017.0229⟩. ⟨hal-01492802v2⟩ Plus de détails...
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 account of 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.
Henri Gouin, Pierre Seppecher. Temperature profile in a liquid-vapor interface near the critical point. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 2017, 473 (20170229), pp.1-13. ⟨10.1098/rspa.2017.0229⟩. ⟨hal-01492802v2⟩
Journal: Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences
Henri Gouin, Tommaso Ruggeri. Symmetric form for the hyperbolic-parabolic system of fourth-gradient fluid model. Ricerche di matematica, 2017, 66 (2), pp.491-508. ⟨10.1007/s11587-016-0315-7⟩. ⟨hal-01573721⟩ Plus de détails...
The fourth-gradient model for fluids-associated with an extended molecular mean-field theory of capillarity-is considered. By producing fluctuations of density near the critical point like in computational molecular dynamics, the model is more realistic and richer than van der Waals' one and other models associated with a second order expansion. The aim of the paper is to prove-with a fourth-gradient internal energy already obtained by the mean field theory-that the quasi-linear system of conservation laws can be written in an Hermitian symmetric form implying the stability of constant solutions. The result extends the symmetric hyperbolicity property of governing-equations' systems when an equation of energy associated with high order deformation of a continuum medium is taken into account.
Henri Gouin, Tommaso Ruggeri. Symmetric form for the hyperbolic-parabolic system of fourth-gradient fluid model. Ricerche di matematica, 2017, 66 (2), pp.491-508. ⟨10.1007/s11587-016-0315-7⟩. ⟨hal-01573721⟩
Henri Gouin. Continuum mechanics at nanoscale. A tool to study trees' watering and recovery. Rendiconti Lincei. Matematica e Applicazioni, 2017, 28, pp.415-449. ⟨10.4171/RLM/769⟩. ⟨hal-01540964⟩ Plus de détails...
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.
Henri Gouin. Continuum mechanics at nanoscale. A tool to study trees' watering and recovery. Rendiconti Lincei. Matematica e Applicazioni, 2017, 28, pp.415-449. ⟨10.4171/RLM/769⟩. ⟨hal-01540964⟩
Journal: Rendiconti Lincei. Matematica e Applicazioni
Henri Gouin. Interfaces endowed with nonconstant surface energies revisited with the d'Alembert–Lagrange principle. Mathematics and Mechanics of Complex Systems, 2014, 2 (1), pp.23-43. ⟨hal-01152429⟩ Plus de détails...
The equation of motion and the conditions on surfaces and edges between fluids and solids in the presence of nonconstant surface energies, as in the case of surfactants attached to 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.
Henri Gouin. Interfaces endowed with nonconstant surface energies revisited with the d'Alembert–Lagrange principle. Mathematics and Mechanics of Complex Systems, 2014, 2 (1), pp.23-43. ⟨hal-01152429⟩
Journal: Mathematics and Mechanics of Complex Systems
