The line tension values of n-octane and 1-octene on a hexadecyltrichlorosilane coated silicon wafer, are determined by contact angle measurements at temperatures near a first-order wetting transition T(w). It is shown experimentally that the line tension changes sign as the temperature increases toward T(w) in agreement with a number of theoretical predictions. A simple phenomenological model possessing a repulsive barrier at l(0)=5.1+/-0.2 nm and a scale factor of B=78+/-6 provides a quantitative description of the experiments.

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The behavior of the line tension for n-octane or 1-octene droplets on a hexadecyltrichlorosilane coated Si wafer, near a first-order wetting transition, qualitatively agrees with the theoretical predictions of Indekeu [Physica (Amsterdam) 183A, 439 (1992)] and the calculations of a number of other groups. A simple phenomenological model possessing a repulsive barrier at l 0 ͑5.1 6 0.2͒ nm and a horizontal correlation length j ͑0.40 6 0.03͒ mm provides a quantitative description of the experiments. PACS numbers: 68.45.Gd, 68.10.Cr, 82.65.Dp An understanding of surface phase transitions and the wettability of surfaces has been of much recent interest due to the desire to engineer surfaces with specific characteristics. Undoubtably the most widely studied surface phase transition is the wetting transition which can be either first [1] or second order [2]. In first-order wetting transitions, a macroscopic droplet of contact angle u`situated on a solid surface is in mechanical equilibrium with an adsorbed film of microscopic thickness l 1 [Fig. 2, inset (below)]. As the temperature is increased towards the wetting temperature T w , the contact angle uà pproaches zero, however, the thickness l 1 remains finite until T w whereupon it increases discontinuously to a large (and perhaps macroscopic) value. For second-order wetting transitions, as the temperature is increased towards T w , the thickness l 1 increases continuously to a large and perhaps macroscopic value above T w . The difference in behavior for first-and second-order wetting transitions is governed by the shape of the free energy per unit area V ͑l͒ as a function of the film thickness l as T w is approached [3]. In this paper, we are interested in firstorder wetting transitions which are the most common in nature. For temperatures T , T w , the potential V ͑l͒ has the generic shape depicted in Fig. 1 (inset). The surface energy of the adsorbed film s sy of thickness l 1 is less than that of a thick film (or droplet) of energy s sl 1 s ly (for l !`) and an energy barrier exists between the global minimum at l 1 and the local minimum at l !`. As the temperature is increased towards T w , the surface energies s sy and s sl 1 s ly become more similar in magnitude until at T w , where u` 0 ± , Antonow's rule holds [4] and s sy s sl 1 s ly so that the two minima now have identical energies. For T . T w , the surface energy s sy . s sl 1 s ly and the minimum at l 1 is now a local rather than a global minimum. This type of transition is conveniently expressed in terms of the spreading coefficient S s sy 2 s sl 2 s ly which is negative for T , T w and becomes equal to zero at T w .Unfortunately very little is known about the precise shape of V ͑l͒ at small l except that it is expected to possess the generic form displayed in Fig. 1 (inset). Our understanding of V ͑l͒ is improved at large l where the shape is governed by long-range dispersion interactions with V ͑l͒ ϳ W͞l ͑s21͒ where the Hamaker constant W (.0 for first-order wetting) depends upon the materials pr...

We present a theory that enables us to construct heteroclinic connections in closed form for 2u xx = W u (u), where x ∈ R, u(x) ∈ R 2 and W is a smooth potential with multiple global minima. In particular, multiple connections between global minima are constructed for a class of potentials. With these potentials, numerical simulations for the vector Allen-Cahn equation u t = 2 2 ∆u − W u (u) in two space dimensions with small > 0, show that between any fixed pair of phase regions, interfaces are partitioned into segments of different energy densities, where the proportions of the length of these segments are changing with time. Our results imply that for the case of triple-well potentials the usual Plateau angle conditions at the triple junction are generally violated.

We study the evolution of charged droplets of a conducting viscous liquid. The flow is driven by electrostatic repulsion and capillarity. These droplets are known to be linearly unstable when the electric charge is above the Rayleigh critical value. Here we investigate the nonlinear evolution that develops after the linear regime. Using a boundary elements method, we find that a perturbed sphere with critical charge evolves into a fusiform shape with conical tips at time t0, and that the velocity at the tips blows up as (t0 − t) α , with α close to −1/2. In the neighborhood of the singularity, the shape of the surface is self-similar, and the asymptotic angle of the tips is smaller than the opening angle in Taylor cones.One of the leading problems in fluid dynamics is the formation of singularities on charged masses of fluid. These problems are relevant in a variety of 1

We study a heavy-heavy-light three-body system confined to one space dimension. Both binding energies and corresponding wave functions are obtained for (i) the zero-range, and (ii) two finiterange attractive heavy-light interaction potentials. In case of the zero-range potential, we apply the method of Skorniakov and Ter-Martirosian to explore the accuracy of the Born-Oppenheimer approach. For the finite-range potentials, we solve the Schrödinger equation numerically using a pseudospectral method. We demonstrate that when the two-body ground state energy approaches zero, the three-body bound states display a universal behavior, independent of the shape of the interaction potential.

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We investigate an unsteady plane viscous gravity current of silicone oil on a horizontal glass substrate. Within the lubrication approximation with gravity as the dominant force, this current is described by the nonlinear diffusion equation t ϭ( m x ) x ( is proportional to the liquid thickness h and mϭ3Ͼ0), which is of interest in many other physical processes. The solutions of this equation display a fine example of the competition between diffusive smoothening and nonlinear steepening. This work concerns the so-called waiting-time solutions, whose distinctive character is the presence of an interface or front, separating regions with h 0 and hϭ0, that remains motionless for a finite time interval t w meanwhile a redistribution of h takes place behind the interface. We start the experiments from an initial wedge-shape configuration ͓h(x)Ϸ␣Ј(x 0 Ϫx)͔ with a small angle (␣Јр0.12 rad͒. In this situation, the tip of the wedge, situated at x 0 from the rear wall ͑15 cmрx 0 р75 cm͒, waits at least several seconds before moving. During this waiting stage, a region characterized by a strong variation of the free surface slope ͑corner layer͒ develops and propagates toward the front while it gradually narrows and ‫ץ‬ 2 h/‫ץ‬x 2 peaks. The stage ends when the corner layer overtakes the front. At this point, the liquid begins to spread over the uncovered substrate. We measure the slope of the free surface in a range Ϸ10 cm around x 0 , and, by integration, we determine the fluid thickness h(x) there. We find that the flow tends to a self-similar behavior when the corner layer position tends to x 0 ; however, near the end of the waiting stage, it is perturbed by capillarity. Even if some significant effects are not included in the above equation, the main properties of its solutions are well displayed in the experiments ͓S1063-651X͑96͒13309-2͔