The line of contact of three fluid phases

Abstract

Articles you may be interested inFluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theoryWe study the variation of density or chemical composition in the neighborhood of tbe line in which three phases meet and we determine the associated line tension. Three models are considered: a phenomenological model based on a primitive approximation to the excess free-energy density that arises from the inhomogeneities at tbe two-phase interfaces and at tbe three-phase line; a generalized van der Waals approximation. in which the excess free-energy density is the sum of an analytic function of the densities and a quadratic form in the density gradients; and a microscopic model of a three-component, three-phase fluid. for which the properties of the interfaces and of the three-phase line are determined in mean-field approximation as solutions of nonlocal functional equations. Both positive and negative line tensions are found. In the third model. when the nonlocal functional equations for the composition profiles of the twophase interfaces are approximated by gradient expansions truncated in second order (van der Waals approximation). the resulting profiles are fairly accurate but the surface tensions are not.

Contact-Angle Hysteresis Caused by a Random Distribution of Weak Heterogeneities on a Solid Surface

“…[23] are satisfied for 1 ≤ |n| ≤ M a solution point. We shall need an estimate of the mathematical expectation of the total number of those solution points for which E (2) , as given by [21], is positive definite.…”

“…Substitution of this expression into [23], which is valid only for n = 0, gives an expression for α n ; using it in [11], and using also [10], we find that at equilibrium the shape of the contact line is given by…”

“…To make them easier to understand, we may think of a onedimensional problem: suppose there is just one equation of the type [23], say…”

“…Expression for the Expected Number of Solutions to the Equilibrium Equations [23] Suppose that in the expansions [11], [17], and [18] we include all terms for which |n| ≤ M. Since α −n = α * n , we see from [11] and [10] that the function ζ (x) − z 0 is determined (in our approximation) by the value of the 2M-dimensional vector α whose components are the real quantities α n and α n , n = 1, 2, . .…”

Laboring in the Vineyard of Physical Chemistry

“…The objects of our theoretical studies have then been σ , τ b , τ , wetting and prewetting transitions, and the structures (density and composition profiles) of the interfaces, boundaries, and contact lines in the several phase equilibria (44)(45)(46)(47)(48)(49)(50). The framework for our calculations has almost always been some version or adaptation of the century-old mean-field free-energy-density model of van der Waals (51).…”