Large deformations during the coalescence of fluid interfaces

Surface forces and shape changes were simultaneously measured during the approach and coalescence of two liquid-liquid and liquid-air interfaces. Large normal and lateral deformations were observed that are nevertheless consistent with a simple theoretical analysis of the long-range effects of short-range attractive van der Waals forces. The results imply that two fluidlike structures such as liquid droplets and soft biological cells can sense each other at much larger separations than previously assumed based on criteria taken from the interactions of hard particles.     

Additional attraction between surfactant-coated surfaces

A simple model that shows an additional attraction between solvated surfactant-coated systems is developed. The model simply calculates the van der Waals attraction between the solvated surfactant layers. This attraction was previously neglected as it was expected to have a small energetic contribution. This is indeed the case; however, despite the small energetic contribution the force is large. In other words, although the expression that we get is small in energy, it is large in force. This is particularly important for surface force balance measurements, where using the developed expression, some apparent discrepancies between measured and theoretical values may now have a possible explanation, and especially those associated with surfactant-coated surfaces. We apply the new expression to a given system, and compare with the experimental results.     

$L^1$-Stability and error estimates for approximate Hamilton-Jacobi solutions

Summary.   We study the -stability and error estimates of general approximate solutions for the Cauchy problem associated with multidimensional Hamilton-Jacobi (H-J) equations. For strictly convex Hamiltonians, we obtain a priori error estimates in terms of the truncation errors and the initial perturbation errors. We then demonstrate this general theory for two types of approximations: approximate solutions constructed by the vanishing viscosity method, and by Godunov-type finite difference methods. If we let denote the `small scale' of such approximations (– the viscosity amplitude , the spatial grad-size , etc.), then our -error estimates are of , and are sharper than the classical -results of order one half, . The main building blocks of our theory are the notions of the semi-concave stability condition and -measure of the truncation error. The whole theory could be viewed as a multidimensional extension of the -stability theory for one-dimensional nonlinear conservation laws developed by Tadmor et. al. [34,24,25]. In addition, we construct new Godunov-type schemes for H-J equations which consist of an exact evolution operator and a global projection operator. Here, we restrict our attention to linear projection operators (first-order schemes). We note, however, that our convergence theory applies equally well to nonlinear projections used in the context of modern high-resolution conservation laws. We prove semi-concave stability and obtain -bounds on their associated truncation errors; -convergence of order one then follows. Second-order (central) Godunov-type schemes are also constructed. Numerical experiments are performed; errors and orders are calculated to confirm our -theory. Received April 20, 1998 / Revised version received November 8, 1999 / Published online August 24, 2000     

A first-principles measure for the twinnability of FCC metals

Twinnability is the property describing the ease with which a metal plastically deforms by twinning relative to deforming by dislocation-mediated slip. In this paper a theoretical measure for twinnability in face-centered-cubic (fcc) metals is obtained through homogenization of a recently introduced criterion for deformation twinning (DT) at a crack tip in a single crystal. The DT criterion quantifies the competition between slip and twinning at the crack tip as a function of crack orientation and applied loading. The twinnability of bulk material is obtained by constructing a representative volume element of the material as a polycrystal containing a distribution of microcracks and integrating the DT criterion over all possible grain and microcrack orientations. The resulting integral expression depends weakly on Poisson's ratio and significantly on three interfacial energies: the stacking-fault energy, the unstable-stacking energy and the unstable-twinning energy. All these four quantities can be computed from first principles. The weak dependence on Poisson's ratio is exploited to derive a simple and accurate closed-form approximation for twinnability which clarifies its dependence on the remaining material parameters. To validate the new measure, the twinnability of eight pure fcc metals is computed using parameters obtained from quantum-mechanical tight-binding calculations. The ranking of these materials according to their theoretical twinnability agrees with the available experimental evidence, including the low incidence of DT in Al, and predicts that Pd should twin as easily as Cu.     

Effective refractive index and intermolecular forces associated with a phase of functional groups

Cases in which a functional groups form distinct phases are known in material science in general and specifically in polymer and surfactant sciences. To calculate the van der Waals forces associated with such phases there is a need to evaluate the refractive index of those phases. We expand and generalize a method to estimate the refractive index of such ‘functional group phase’ and discuss how to use the refractive indices to calculate the interaction energies associated with such functional group phases and thereby modify the total theoretically calculated van der Waals forces.     

Drop retention force as a function of resting time

The force, f, required to slide a drop on a surface is shown to be a growing function of the time, t, that the drop waited resting on the surface prior to the commencement of sliding. In this first report on the resting time effect, we demonstrate the existence of this phenomenon in different systems, which suggests that this phenomenon is general. We show that d f/d t is never negative. The shorter the resting times, the higher d f/d t is. As the resting time increases, d f/d t decreases toward zero (plateau) as t --> infinity. The increase in the force, Delta f, due to the resting time effect (i.e., f( t --> infinity) - f( t --> 0)) correlates well with the vertical component of the liquid-vapor surface tension, and we attribute this phenomenon to the corrugation of the surface by the drop due to this unsatisfied normal component of Young's equation.     

Drop retention force as a function of drop size

The force, f, required to slide a drop past a surface is often considered in the literature as linear with the drop width, w, so that f/w = const. Furthermore, according to the Dussan equation for the case that the advancing and receding contact angles are constant with drop size, one can further simplify the above proportionality to f/V(1/3) = const where V is the drop volume. We show, however, that experimentally f/V(1/3) is usually a decaying function of V (rather than constant). The retention force increases with the time the drop rested on the surface prior to sliding. We show that this rested-time effect is similar for different drop sizes, and thus the change of f/V(1/3) with V occurs irrespective of the rested-time effect which suggests that the two effects are induced by different physical phenomena. The time effect is induced by the unsatisfied normal component of the Young equation which slowly deforms the surface with time, while the size effect is induced by time independent properties. According to the Dussan equation, the change of f/V(1/3) with V is also expressed in contact angle variation. Our results, however, show that contact angle variation that is within the scatter suffices to explain the significant force variation. Thus, it is easier to predict contact angle variation based on force variation rather than predicting force variation based on contact angle variation. A decrease of f/V(1/3) with V appears more common in the system studied compared to an increase.     

Interfacial tension and spreading coefficient for thin films

We present a modified mathematical expression for the interfacial tension of very thin films. At large thicknesses the modified expression converges to the classic mathematical expression. We use this modified expression to derive an equation for the spreading coefficient as a function of film thickness. The spreading coefficient equation is then used to calculate the equilibrium thickness of a wetting liquid film for a "pancake drop". Our predictions agree with experimental data. The study is subjected to systems with van der Waals interactions only.