Liquid-solid interface inertia

Abstract

2014 Nous remarquons que, lors de la fusion ou de la croissance d'un cristal, les atomes se réarrangent à l'interface à cause de la différence de structure entre liquide et solide. Il en résulte une énergie « cinétique » de surface. Nous étudions les conséquences de ce terme dans le cas de 4He où l'interface est très mobile. La relation de dispersion des ondes de cristallisation devient linéaire : 03C9 = c0 k. La transmission, à travers l'interface, des phonons est augmentée. La résistance de Kapitza est donc diminuée, mais presente toujours le comportement anormal RK ~ T-5 prédit par Marchenko et Parshin sur d'autres bases. Abstract. 2014 We remark that, during crystallization or melting, due to the structural difference between solid and liquid, the atoms have to rearrange themselves at the interface. This results in a supplementary surface « kinetic » energy. We examine the consequence of this term in the case of 4He where the interface is very mobile. The dispersion relation for crystallization waves becomes linear : 03C9 = c0 k. The phonon transmission through the interface is enhanced. The Kapitza resistance is thus decreased, but presents always the anomalous dependence RK ~ T-5 predicted by Marchenko and Parshin on other grounds. B

Viscoelastic surface waves and the surface structure of liquids

“…At the intermediate frequencies between the elastic (equation (6.12)) and the hydrodynamic (equation (6.16)) regime the viscoelastic equations (6.8) and (6.9) should be investigated numerically. where vt ~ r144/rnp 9 As a side-remark we notice that the real part of equation (6.23) reduces to the result [12] obtained recently for surfaces which acquire some inertia (~ r 0) because of the prevailing non-equilibrium conditions. In the present context the equilibrium surface is most conveniently localized with Gibbs condition ~ = 0 in which case we recover the standard Kelvin result [1] coa = q3er / mp.…”

Sound propagation in a superleak covered with solid 4He

“…Experimental conditions for grafoil superleaks are considered. [1][2][3] and this causes various interesting phenomena at the interface between solid and liquid such as crystallization waves [3][4][5][6][7][8], a striking decrease in sound transmission [9,10] and anomalous temperature dependence of the Kapitza resistance [11][12][13][14]7]. The fast crystal growth can affect some bulk properties of superfluid 4He if the ratio of the interface area to the volume is sufficiently large.…”

“…Melting or crystallization will produce a tangential force on the solid, which will be transmitted directly to the substrate as we have assumed that the solid is rigid. The interfacial tension and the interfacial inertia [7] are not included for the following reasons : the ratio of the pressure change due to the surface tension to the compression is very small :…”

“…where the quantities with a prime indicate the deviations from the equilibrium, and a is the interfacial tension, co the first sound velocity of liquid, and a the atomic distance. The inertia of the interface [7] Q would appear in (3) as a term and the ratio of this term to the first term of (3) is we suppose that this value is much smaller than unity (see 4).…”

“…The two-phase equilibrium condition for chemical potentials with the steady flow vo is given by When there is a small perturbation, (6) becomes where we have used the equilibrium condition to relate the pressure to the substrate potential. Substituting (7) into (3), we obtain the system of linearized equations :…”