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

Henri Gouin (1) , Giuseppe Saccomandi (2)

1 IUSTI - Institut universitaire des systèmes thermiques industriels
2 Dipartimento di Ingegneria Industriale

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.

Mots clés: Capillary fluids; Phases transition; Lagrangian methods; Gradient theories; Travelling waves; Extended Fisher-Kolmogorov equation

Domaines: Mécanique des fluides [physics.class-ph]; Vibrations [physics.class-ph]; Matière Molle [cond-mat.soft]; Physique mathématique [math-ph]

Henri Gouin, Giuseppe Saccomandi. Travelling waves of density for a fourth-gradient model of fluids. Continuum Mechanics and Thermodynamics, 2016, 28 (5), pp.1511 - 1523. ⟨10.1007/s00161-016-0492-3⟩. ⟨hal-01480940⟩