s, EURADH 2004, Vol. 1, DECHEMA, Frankfurt, pp. 319–324. 402j References

Spinodal decomposition can be observed only in systems whose dynamics are slow enough to quench through the metastable region where the phase transition occurs by nucleation. We discuss the capillary rise of a fluid in a cone inserted into a bulk fluid, with the wide end down. The rise displays a first-order phase transition with a spinodal and is easily accessible both theoretically and experimentally.

Small capillaries can provide strong binding to fluids confined within them. We analyze this behavior with a simple microscopic theory, considering two geometries, a slit pore and a cylindrical pore. A goal is to achieve the maximum possible capillary rise (H) within each type of pore. The attraction for very small capillaries can result in a large value of H, exceeding 100 km in a number of cases (e. g., hydrogen, methane and water in cylindrical graphitic pores). The specific value of H depends on the details of the pore and the fluid-surface interaction. It is maximized in the case of small cylindrical pores, strong interactions and small adsorbate mass. Explicit calculations are presented for graphite and MgO substrates. Experimental tests are possible with an ultracentrifuge, where the high effective gravitational field reduces H. Copyright (c) EPLA, 2008.

The relationship between continuous-time dynamics and the corresponding discrete schemes, and its generally limited validity, is an important and widely acknowledged field within numerical analysis. In this paper, we propose another, more physical, viewpoint on this topic in order to understand the possible failure of discretisation procedures and the way to fix it. Three basic examples, the logistic equation, the Lotka–Volterra predator–prey model and Newton's law for planetary motion, are worked out. They illustrate the deep difference between continuous-time evolutions and discrete-time mappings, hence shedding some light on the more general duality between continuous descriptions of natural phenomena and discrete numerical computations.

Discrete autonomous dynamical systems in dimension 1 can exhibit chaotic behavior, whereas the corresponding continuous evolution equations rule it out, and cannot even possess a nontrivial periodic solution. Therefore the passage from discrete to continuous equations (and conversely) is all but harmless. We address this issue and evidence some caveats on the paradigmatic Verhulst logistic equation, investigating in particular the status and influence of the actual size of the unit time step in discrete modelings, rooted in well-known numerical analysis.

Presently available experimental data on neutron diffraction, elastic properties, specific heat, high temperature susceptibility for solid helium films adsorbed on Grafoil and theoretical calculations of the energy of the fluid are used to give an estimate of first and second solid layer densities as a function of total coverage. Important information on the second layer phase diagram is deduced from this analysis. In3He films, the knowledge of the second-layer-solid density ρ2(x) as a function of total coverage x is essential to elucidate the origin of ferromagnetism for two solid films in the presence of a fluid third layer.

The surprising discovery, in 1991, that liquid helium does not wet a cesium surface at low temperature has triggered an important activity both theoretical and experimental: helium has become a model system for the study of wetting transitions. After summarizing the main theme of helium wetting, I will focus on more recent studies, such as the structure and excitations of helium interfaces, experiments on the capillary rise, the “surfactant effect” of helium-3 impurities on liquid helium-4 and the “quantum prewetting transition” of pure helium-3. Unexpected consequences on the phase separation of3He−4He mixtures in restricted geometry will be drawn.

3He atoms dissolved in super fluid4He may form aimers (3He)2 in twodimensional (2D) geometries. We study dimer formation in films of dilute3He-4He mixture. After designing a schematic3He-4He interaction potential we calculate the dimer binding energy for various substrates. It is shown that3He impurity states localized near the substrate give rise to the largest magnitudes of the binding energies.

A simple model based on interfacial description is used to calculate the line tension of liquid helium at prewetting transitions, i.e. the energy associated with the region which joins the two phases in equilibrium, as a function of the amplitude of the prewetting jump d. The values are typically one order of magnitude smaller than σd, where σ is the surface tension.

The various effects determining quantitatively the reentrant wetting phase diagram of helium mixtures on Cs are discussed. Particularly crucial is the temperature dependence of the helium surface tension, for which different interpretations exist in the literature. Recent experiments by the Irvine group are compatible with the predicted existence of a bound state at the helium/Cs interface, but more direct confirmation is clearly needed.

3He atoms dissolved in superfluid 4He may form dimers (3He)2 in two-dimensional geometries. We study dimer formation in films of dilute 3He-4He mixture. After designing a schematic 3He-3He interaction potential we calculate the dimer binding energy for various substrates. It is shown that 3He impurity states localized near the substrate give rise to the largest magnitudes of the binding energies.

Recent calculations of the surface excitations of liquid4He show that besides the ripplon branch, a second branch of excitations, with one node in the transition density, exists at higher energy. Back-flow effects are essential for a quantitative description. Inclusion of both branches in the thermodynamics of the surface provides good agreement with experiment for the temperature dependence of the surface tension σ(T) up to the λ-transition. Above Tλ, the variation of σ(T) is mainly governed by the difference between the liquid and vapor densities.

Multilayer He-3 film growth on weak-binding alkali substrates is investigated with a nonlocal density functional theory. Although He-3 wets all substrates down to zero temperature, prewetting transitions are predicted to occur on Cs, Rb, and K. Continuous wetting is recovered with increasing strength of substrate potential. Emphasis is put on the role played by the Fermi statistics. The heat capacity and the magnetization of the films exhibits steps associated with the occupation of two-dimensional Fermi disks.