Contact angles on heterogeneous surfaces; a new look at Cassie's and Wenzel's laws

We consider a three dimensional liquid drop sitting on a rough and chemically heterogeneous substrate. Using a novel minimization technique on the free energy of this system, a generalized Young's equation for the contact angle is found. In certain limits, the Cassie and Wenzel laws, and a new equivalent rule, applicable in general, are derived. We also propose an equation in the same spirit as these results but valid on a more `microscopic' level. Throughout we work under the presence of gravity and keep account of line tension terms.Comment: 10 pages RevTeX, 2 EPS figures. A few minor corrections mad

Wetting between structured surfaces: Liquid bridges and induced forces

Wetting phenomena are theoretically studied for a slab geometry consisting of a wetting phase confined between two chemically patterned substrates. Each of these is decorated by an array of stripes whose composition alternates between two different surface phases. For a single pair of opposing stripes, the wetting phase may either form a bridge spanning from one surface to the other or it may break up into two separate channels. The bridge state induces an effective interaction between the two substrates. This leads to the bridge itself having a preferred contact angle and the substrates having a preferred separation. In the case of many stripes, one has a whole sequence of morphological transitions with the number of bridges decreasing as the surface separation grows

The Influence of Substrate Structure on Membrane Adhesion

We consider a membrane both weakly and strongly adhering to a geometrically structured substrate. The interaction potential is assumed to be local, via the Deryagin approximation, and harmonic. Consequently, we can analytically describe a variety of different geometries: as well as randomly rough self-affine surfaces, smooth substrates interrupted by an isolated cylindrical pit, a single elongated trench or a periodic array of trenches are investigated. We present more general expressions for the adhesion energy and membrane configuration in Fourier space and find that, compared to planar surfaces, the adhesion energy decreases. We also highlight the possibility of overshoots occurring in the membrane profile and look at its degree of penetration into surface indentations.Comment: 41 pages LaTex, 12 EPS figure

Corrugation-Induced First-Order Wetting: An Effective Hamiltonian Study

We consider an effective Hamiltonian description of critical wetting transitions in systems with short-range forces at a corrugated (periodic) wall. We are able to recover the results obtained previously from a `microscopic' density-functional approach in which the system wets in a discontinuous manner when the amplitude of the corrugations reaches a critical size A*. Using the functional renormalization group, we find that A* becomes dependent on the wetting parameter \omega in such a way as to decrease the extent of the first-order regime. Nevertheless, we still expect wetting in the Ising model to proceed in a discontinuous manner for small deviations of the wall from the plane.Comment: 9 pages RevTex with 2 EPS figures. To appear in Eur. Phys. J.

An exact solution for two dimensional wetting with a corrugated wall

An exact solution of a two dimensional RSOS model of wetting at a corrugated (periodic) wall is found using transfer matrix techniques. In contrast to mean-field analysis of the same problem the wetting transition remains second-order and occurs at a lower temperature than that of the planar system. Comparison with numerical studies and other analytical approaches is made.Comment: 11 pages LaTex with 1 eps figure. To appear in J.Phys.

Coupled Hamiltonians and Three Dimensional Short-Range Wetting Transitions

We address three problems faced by effective interfacial Hamiltonian models of wetting based on a single collective coordinate \ell representing the position of the unbinding fluid interface. Problems (P1) and (P2) refer to the predictions of non-universality at the upper critical dimension d=3 at critical and complete wetting respectively which are not borne out by Ising model simulation studies. (P3) relates to mean-field correlation function structure in the underlying continuum Landau model. We investigate the hypothesis that these concerns arise due to the coupling of order parameter fluctuations near the unbinding interface and wall. For quite general choices of collective coordinates X_i we show that arbitrary two-field models H[X_1,X_2] can recover the required anomalous structure of mean-field correlation functions (P3). To go beyond mean-field theory we introduce a set of Hamiltonians based on proper collective coordinates s near the wall which have both interfacial and spin-like components. We argue that an optimum model H[s,\ell] in which the degree of coupling is controlled by an angle-like variable, best describes the non-universality of the Ising model and investigate its critical behaviour. For critical wetting the appropriate Ginzburg criterion shows that the true asymptotic critical regime for the local susceptibility \chi_1 is dramatically reduced consistent with observations of mean-field behaviour in simulations (P1). For complete wetting the model yields a precise expression for the temperature dependence of the renormalized critical amplitude \theta in good agreement with simulations (P2). We highlight the importance of a new wetting parameter which describes the physics that emerges due to the coupling effects.Comment: 34 pages, RevTex, 8 eps figures. To appear in Physica

Food Security, Gender and Occupational Choice among Urban Low-Income Households

Rising urban poverty and food insecurity are serious concerns in developing countries today. Urban livelihoods and coping strategies remain poorly understood however. This paperexamines the response of female and male household members in marginalized urban (predominantly squatter) areas to the risk of food shortage in terms of occupational choice. More specifically, we use probit analyses to investigate whether household vulnerability or the need to provide self-insurance for food security, alongside gender roles, influence a worker's choice of enterprise activity. We focus our investigation on self-employed women and men using a data set drawn from the 1496 individual sample in 14 urban squatter communities in Bolivia, Ecuador, Philippines and Thailand. Our findings show that selfemployed women in households facing higher risk of food insecurity are likely to engage in food-related enterprise activities and this is especially true in Philippines and Thailand. This suggests the role of occupational choice in in helping urban squatter households in mitigating the risk of food shortage through the selection of an income-generating activity that allows the direct use of unsold inventories for food consumption.food security, self-employment, occupational choice, urban informal secto

Fractal Propagators in QED and QCD and Implications for the Problem of Confinement

We show that QED radiative corrections change the propagator of a charged Dirac particle so that it acquires a fractional anomalous exponent connected with the fine structure constant. The result is a nonlocal object which represents a particle with a roughened trajectory whose fractal dimension can be calculated. This represents a significant shift from the traditional Wigner notions of asymptotic states with sharp well-defined masses. Non-abelian long-range fields are more difficult to handle, but we are able to calculate the effects due to Newtonian gravitational corrections. We suggest a new approach to confinement in QCD based on a particle trajectory acquiring a fractal dimension which goes to zero in the infrared as a consequence of self-interaction, representing a particle which, in the infrared limit, cannot propagate.Comment: To appear in Brazilian Journal of Physics, special edition for the proceedings of IRQCD, Rio de Janeiro, 5-9 June 200