We present a lattice Boltzmann solution of the equations of motion describing the spreading of droplets on topologically patterned substrates. We apply it to model superhydrophobic behavior on surfaces covered by an array of micrometer-scale posts. We find that the patterning results in a substantial increase in contact angle, from 110 degrees to 156 degrees. The dynamics of the transition from drops suspended on top of the posts to drops collapsed in the grooves is described.

Abstract. -We investigate the transition between the Cassie-Baxter and Wenzel states of a slowly evaporating, micron-scale drop on a superhydrophobic surface. In two dimensions analytical results show that there are two collapse mechanisms. For long posts the drop collapses when it is able to overcome the free energy barrier presented by the hydrophobic posts. For short posts, as the drop loses volume, its curvature increases allowing it to touch the surface below the posts. We emphasise the importance of the contact line retreating across the surface as the drop becomes smaller: this often preempts the collapse. In a quasi-three dimensional simulation we find similar behaviour, with the additional feature that the drop can de-pin from all but the peripheral posts, so that its base resembles an inverted bowl.

We have discovered 12 independent new empirical scaling laws in foreign exchange data-series that hold for close to three orders of magnitude and across 13 currency exchange rates. Our statistical analysis crucially depends on an event-based approach that measures the relationship between different types of events. The scaling laws give an accurate estimation of the length of the price-curve coastline, which turns out to be surprisingly long. The new laws substantially extend the catalogue of stylised facts and sharply constrain the space of possible theoretical explanations of the market mechanisms.

We discuss the cellular automata approach and its extensions, the lattice Boltzmann and multiparticle methods. The potential of these techniques is demonstrated in the case of modeling complex systems. In particular, we consider applications taken from various fields of physics, such as reaction-diffusion systems, pattern formation phenomena, fluid flows, fracture processes and road traffic models.

We propose two designs of effectively single mode porous polymer fibers for low-loss guiding of terahertz radiation. First, we present a fiber of several wavelengths in diameter containing an array of sub-wavelength holes separated by sub-wavelength material veins. Second, we detail a large diameter hollow core photonic bandgap Bragg fiber made of solid film layers suspended in air by a network of circular bridges. Numerical simulations of radiation, absorption and bending losses are presented; strategies for the experimental realization of both fibers are suggested. Emphasis is put on the optimization of the fiber geometries to increase the fraction of power guided in the air inside of the fiber, thereby alleviating the effects of material absorption and interaction with the environment. Total fiber loss of less than 10 dB/m, bending radii as tight as 3 cm, and fiber bandwidth of approximately 1 THz is predicted for the porous fibers with sub-wavelength holes. Performance of this fiber type is also compared to that of the equivalent sub-wavelength rod-in-the-air fiber with a conclusion that suggested porous fibers outperform considerably the rod-in-the-air fiber designs. For the porous Bragg fibers total loss of less than 5 dB/m, bending radii as tight as 12 cm, and fiber bandwidth of approximately 0.1 THz are predicted. oupling to the surface states of a multilayer reflector facilitated by the material bridges is determined as primary mechanism responsible for the reduction of the bandwidth of a porous Bragg fiber. In all the simulations, polymer fiber material is assumed to be Teflon with bulk absorption loss of 130 dB/m.

We report experiments investigating the behaviour of micron-scale fluid droplets jetted onto surfaces patterned with lyophobic and lyophilic stripes. The final droplet shape is shown to depend on the droplet size relative to that of the stripes. In particular when the droplet radius is of the same order as the stripe width, the final shape is determined by the dynamic evolution of the drop and shows a sensitive dependence on the initial droplet position and velocity. Lattice Boltzmann numerical solutions of the dynamical equations of motion of the drop provide a close quantitative match to the experimental results. This proves helpful in interpreting the data and allows for accurate prediction of fluid droplet behaviour for a wide range of surfaces.

This contribution proposes an alternative lattice Boltzmann grid refinement algorithm that overcomes the drawbacks that plague existing approaches. We demonstrate that this algorithm is accurate and applicable for all values of the relaxation time. We also show that this algorithm can significantly speed up the flow settlement process. By using a hierarchy of grid levels, the stationary regime can be approached up to a thousand times faster than with a single grid resolution.

Abstract. -We compare numerical and experimental results exploring the behaviour of liquid drops moving across a surface patterned with hydrophobic and hydrophilic stripes. A lattice Boltzmann algorithm is used to solve the hydrodynamic equations of motion of the drops allowing us to investigate their behaviour as the stripe widths and the wettability contrast are altered. We explain how the motion of the drop is determined by the interplay between the driving force and the variation in surface force as the drop moves between regions of different contact angle and we find that the shape of the drops can undergo large periodic deviations from spherical. When compared, the numerical results agree well with experiments on micron-scale drops moving across substrates patterned by microcontact printing.Introduction. -The question of how liquid drops wet and move across a solid surface has long caught the interests of academic and industrial communities alike, with applications ranging from microfluidic devices to ink-jet printing and surface coating. Though much progress has been made since the first pioneering work by Young and Laplace, many interesting, unanswered questions remain. One which has recently come to the fore because of experimental advances allowing the fabrication of surfaces with mesoscopic hydrophobic and hydrophilic regions is the behaviour of drops on chemically patterned substrates. Several authors [1][2][3][4][5][6] have shown that the wetting behaviour on these substrates can be very rich, with the drop shapes depending sensitively on parameters such as the dimensions and contact angles of the patterning. In this letter we build on this work to address the dynamics of drops moving across an array of alternating hydrophobic and hydrophilic stripes, focussing on the centre of mass motion as well as the morphological transitions induced by the imposed external flow. The drop is pushed by a constant gravity-like acceleration as opposed to [7] where a thermal gradient is applied to generate the drop motion.