Zeitschrift f¨ ur Angewandte Mathematik und Mechanik, 1 February 2013 Propagation of linear compression waves through plane interfacial lay- ers and mass adsorption in second gradient fluids Giuseppe Rosi 1, ∗ , Ivan Giorgio 1,2, ∗∗ , and Victor A. Eremeyev 3, ∗∗∗ 1 International Research Center for the Mathematics and Mechanics of Complex Systems (M&MoCS), Universit` a dell’Aquila, Palazzo Caetani, 04012 Cisterna di Latina, Italia 2 Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Universit` a di Roma, Via Eudossiana, 18, 00184 - Roma, Italia 3 Institut f¨ ur Mechanik, Otto-von-Guericke-Universit¨ at Magdeburg, 39106 Magdeburg, Germany, and South Scientific Center of RASci & South Federal University, Rostov on Don, Russia Received XXXX, revised XXXX, accepted XXXX Published online XXXX Key words Linear waves, interfacial layer, gradient elasticity, second gradient, capillary fluid, Cahn-Hilliard fluid, mass adsorption This paper addresses the problem of reflection and transmission of compression waves at the phase transition layer between the vapour and liquid phases of the same fluid. Within the framework of second gradient fluid modeling, we use a non- convex free energy in order to describe the phase transition phenomenon. A stationary solution for the fluid density is found for an infinite domain, and an analytical expression for the phase transition is presented. Then the propagation of linear waves superposed to this stationary solution is discussed, with particular attention to the behaviour in correspondence of the interfacial layer. The reflection and transmission of waves is studied and analized with the aid of numerical simulations, and an interesting phenomenon of mass adsorption at the interface is observed and discussed. Copyright line will be provided by the publisher Introduction Modelling of phase transitions (PT) in solids and fluids is one of the most important problems of continuum physics and mechanics of materials. Its actuality is determined by the fact that the majority of materials used in modern engineering undergoes PT during manufacturing or exploitation. The crucial point in mechanics of PT is proper description of a phase interface. Fluid/Solid, Fluid/Fluid and Fluid/Vapour interfaces in PT phenomena can be modelled using different points of view. Depending on the length scale which is to be assumed as the most relevant one it is possible to describe then by means of • molecular models, where the physical system is described as a discrete set of interacting particles, see e.g. [9, 11, 12, 22, 23, 63, 93]; • 3D and 2D continuum models in which the interface is modelled as a 2D or 1D continua, respectively, carrying material properties, see e.g. [1, 2, 4–7, 24, 29, 32, 34, 44–47, 53, 56, 66, 68, 80, 88, 89, 92, 98, 99, 107, 111]. In this approach one assumes explicit existence of a so-called sharp phase interface being a sufficiently regular surface or curve separating different material phases. The position and motion of the phase interface itself are among the most discussed issues in the field analyzed theoretically, numerically and experimentally. The compatibility conditions on the phase interface may be obtained by the variational approach, by using the integral balance laws, etc.; • continuum models in which both phases and the interface are modelled by means of a unique continuum model, with a free energy density depending on the deformation gradient and on its higher gradients (the mass density and on its spatial gradients in the case of fluids). Such models are related to the original works by Grioli [67], Mindlin [81–84], Toupin [108], Germain [59,60], Eringen [48–50]. Nowadays known as the gradient elasticity and the gradient plasticity this approach is widely used in the mechanics of solids, see e.g. [3, 31, 36–38, 51, 55, 69, 71, 73, 86], as well as in hydrodynamics, see e.g. [15–20,26,57,58,62,64,65,100,103,105]. Here one do not use the explicit introduction of the * Corresponding author, e-mail: rosi@me.com. Phone: 06.90286784, Fax: 0773.1871016 ** e-mail: ivan.giorgio@uniroma1.it. *** e-mail: eremeyev.victor@gmail.com. Copyright line will be provided by the publisher