Thermodynamics of free and of interacting curved interfaces in liquid films

Abstract

We present a method of calculating emitted intensities of angular resolved emission, based on the so-called 'chain method' of Pendry and Gard. All final state lattice scattering effects are included in the formalism. The method is expected to have application particularly at emission energies above the normal'Low Energy'range(O-250 eV). The methodis illustrated by application to angularly resolved x-ray core level emission.

Capillary channels in a gravitational field

“…At r = 0, C u (0) = κu 0 = C u (1) (0) and Σ (1) has constant curvature. Because u(0) = u (1) (0), we conclude then…”

“…Now, we bound the center height u 0 and the outher height u(a). Consider a lower circular arc Σ (1) : u (1) (r), centered on the u-axis, with u (1) (0) = u 0 and of radius R 1 = 1/(κu 0 ). Let also Σ (2) : u (2) (r) be a lower circular arc, centered on the u-axis, with u (2) (0) = u 0 , and such that…”

“…A κ-cylindrical surface is a cylindrical ruled surface that locally satisfies the capillary equation (1).…”

“…So, in the literature, the capillary problem studied here it has been considered in the study of the shape of a meniscus facing a vertical plate. As we will see, in the one-dimensional problem, a first integration of (1) is obtained in such way that the solutions can be expressed in terms of elliptic integrals and some estimates of the height of the meniscus have been obtained from these integrals or as limit case of the two-dimensional case [1,2,8,9,11,12,13]. Our interest in this work is twofold.…”

“…Let the height of this capillary free surface S with respect to Π, assumed nonparametric over Ω, be given by the scalar function u = u(x, y), (x, y) ∈ Ω. When the capillary and gravity forces are in equilibrium, u satisfies the partial differential equation div T u = κu (1) in Ω where…”