Contact angle hysteresis on nonwetting microstructured surfaces: Effect of randomly distributed pillars or holes.

We present a numerical study of the advancing and receding apparent contact angles for a liquid meniscus in contact with an ultrahydrophobic surface with randomly distributed microsized pillars or holes in the Cassie's wetting regime. We study the Wilhelmy plate system in the framework of the full capillary model to obtain these angles using the heterogeneous surface approximation model for a broad interval of values of pillar or hole concentration and for both square and circular shapes of the pillars or holes cross-section. Three types of random placing of defects on the plate are investigated, i.

Phase diagram of generalized totally asymmetric simple exclusion process on an open chain: Liggett-like boundary conditions.

The totally asymmetric simple exclusion process with generalized update is a version of the discrete time totally asymmetric exclusion process with an additional interparticle interaction that controls the degree of particle clustering. Though the model was shown to be integrable on the ring and on the infinite lattice, on the open chain it was studied mainly numerically, while no analytic results existed even for its phase diagram. In this paper, we introduce boundary conditions associated with the infinite translation invariant stationary states of the model, which allow us to obtain the exact phase diagram analytically.

Contact angle hysteresis on random self-affine rough surfaces in Wenzel's wetting regime: Numerical study.

We present a numerical study of the advancing and receding apparent contact angles for a liquid meniscus in contact with random self-affine rough surfaces in Wenzel's wetting regime. Within the framework of the Wilhelmy plate geometry, we use the full capillary model to obtain these global angles for a wide range of local equilibrium contact angles and for different parameters that determine the self-affine solid surfaces: Hurst exponent, wave vector domain, and root-mean-square roughness. We find that the advancing and receding contact angles are single-valued functions that depend only on the roughness factor determined by the set of values of the parameters of the self-affine solid surface.

Dependence of the contact line roughness exponent on the contact angle on substrates with dilute mesa defects: numerical study.

We compute the roughness exponent of the averaged contact line width of a liquid on heterogeneous substrates with randomly distributed dilute defects in statics. We study the case of circular "mesa"-type defects placed on homogeneous base. The shape of the liquid meniscus and the contact line are obtained numerically, using the full capillary model when a vertical solid plate, partially dipped in a tank of liquid, is slowly withdrawing from the liquid.

Depinning regimes and contact angle hysteresis of a drop on doubly periodic microtextured surfaces.

We investigate numerically the drop shape evolution under quasistatic drop volume change on doubly periodic microtextured surfaces in the framework of the capillary model. Taking into account the symmetries of the periodic lattice of defects, we study the drop contact line (CL) motion along all lines of symmetry, allowing us to get a more complete view of the CL behavior. Four CL depinning regimes for a liquid drop are distinguished related to the stick, slip, and jump motion of the CL.

Contact angle hysteresis on doubly periodic smooth rough surfaces in Wenzel's regime: The role of the contact line depinning mechanism.

We report here on the contact angle hysteresis, appearing when a liquid meniscus is in contact with doubly sinusoidal wavelike patterned surfaces in Wenzel's wetting regime. Using the full capillary model we obtain numerically the contact angle hysteresis as a function of the surface roughness factor and the equilibrium contact angle for a block case and a kink case contact line depinning mechanism. We find that the dependencies of the contact angle hysteresis on the surface roughness factor are different for the different contact line depinning mechanisms.

Contact-angle hysteresis on periodic microtextured surfaces: Strongly corrugated liquid interfaces.

We study numerically the shapes of a liquid meniscus in contact with ultrahydrophobic pillar surfaces in Cassie's wetting regime, when the surface is covered with identical and periodically distributed micropillars. Using the full capillary model we obtain the advancing and the receding equilibrium meniscus shapes when the cross-sections of the pillars are both of square and circular shapes, for a broad interval of pillar concentrations. The bending of the liquid interface in the area between the pillars is studied in the framework of the full capillary model and compared to the results of the heterogeneous approximation model.

Contact angle hysteresis and pinning at periodic defects in statics.

This article deals with the theoretical prediction of the wetting hysteresis on nonideal solid surfaces in terms of the surface heterogeneity parameters. The spatially periodical chemical heterogeneity is considered. We propose precise definitions for both the advancing and the receding contact angles for the Wilhelmy plate geometry.

Asymmetric simple exclusion process on chains with a shortcut.

We consider the asymmetric simple exclusion process (TASEP) on an open network consisting of three consecutively coupled macroscopic chain segments with a shortcut between the tail of the first segment and the head of the third one. The model was introduced by Y.-M.

Contact angle hysteresis and meniscus corrugation on randomly heterogeneous surfaces with mesa-type defects.

The results of a numerical study of the various characteristics of the static contact of a liquid meniscus with a flat but heterogeneous surface, consisting of two types of homogeneous materials, forming regularly and randomly distributed microscopic defects are presented. The solutions for the meniscus shape are obtained numerically using the full expression of the system free energy functional. The goal is to establish how the magnitude and the limits of the hysteresis interval of the equilibrium contact angle, the Cassie's angle, and the contact line (CL) roughness exponent are related to the parameters, characterizing the heterogeneous surface-the equilibrium contact angles on the two materials and their fractions.

Asymptotic solutions for the relaxation of the contact line in the Wilhelmy-plate geometry: The contact line dissipation approach.

The relaxation of straight contact lines is considered in the context of the Wilhelmy-plate experiment: a homogeneous solid plate is moving vertically at constant velocity in a tank of liquid in the partial wetting regime. We apply the contact line dissipation approach to describe the quasistatic relaxation of the contact line toward the stationary state (below the entrainment transition). Asymptotic solutions are derived from the differential equations describing the capillary rise height and the contact angle relaxation for small initial deviations of the height from the final stationary value in the model considering the friction dissipation at the moving contact line, in the model considering the viscous flow dissipation in the wedge, and in the combined model taking into account both channels of dissipation.

Dynamic modeling of contact-line deformation: comparison with experiment.

The quasistatic contact-line dissipation model is applied to the dynamics of relaxation of periodically perturbed contact lines in the Wilhelmy plate geometry where a solid plate is withdrawn vertically at constant velocity from a bath of liquid. The resulting motion of the three-dimensional liquid meniscus is solved rigorously by numerical simulation. A detailed comparison is performed with the recent experimental results of Delon et al.

Nonaxisymmetric drop shape analysis and its application for determination of the local contact angles.

We describe here a numerical method for finding the local contact angles of a drop in the case of partial wetting for given values of the drop volume and capillary length when there are data available for the whole contact line of the drop. There are no special restrictions imposed on the type of the contact line: the solid substrate on which the drop rests can be heterogeneous or rough or both, it can be horizontal or tilted. The method is intended to be used in conjunction with experimental results similarly to the axisymmetric drop shape analysis-diameter (ADSA-D) and analysis-profile (ADSA-P) methods.

On the quasi-static relaxation of a drop in a combined model of dissipation.

The spontaneous quasi-static relaxation of liquid drops on solid surfaces in the partial wetting regime is studied. We base our study on the combined approach suggested in de Ruijter et al. (Langmuir 1999, 15, 2209), which uses the standard mechanical description of dissipative system dynamics.

Quasistatic relaxation of arbitrarily shaped sessile drops.

We study a spontaneous relaxation dynamics of arbitrarily shaped liquid drops on solid surfaces in the partial wetting regime. It is assumed that the energy dissipated near the contact line is much larger than that in the bulk of the fluid. We have shown rigorously in the case of quasi-static relaxation using the standard mechanical description of dissipative system dynamics that the introduction of a dissipation term proportional to the contact line length leads to the well-known local relation between the contact line velocity and the dynamic contact angle at every point of an arbitrary contact line shape.

Drop spreading on heterogeneous substrates via Monte Carlo simulations.

We study the dynamics of liquid drops in the partial wetting regime first on pure surfaces and then on heterogeneous substrates. We model the spreading of a drop by a 3-dimensional Ising model (3D IM). The initial nonequilibrium configuration is a parallelepiped of occupied sites with appropriately chosen boundary conditions from which we let the system evolve towards its equilibrium state via a particle-conserving dynamics.

Totally asymmetric exclusion process on chains with a double-chain section in the middle: computer simulations and a simple theory.

Computer simulations of the totally asymmetric simple-exclusion process on chains with a double-chain section in the middle are performed in the case of random-sequential update. The outer ends of the chain segments connected to the middle double-chain section are open, so that particles are injected at the left end with rate alpha and removed at the right end with rate beta. At the branching point of the graph (the left end of the middle section) the particles choose with equal probability 1/2 which branch to take and then simultaneous motion of the particles along the two branches is simulated.