Low temperature phase diagram and critical behaviour of the four-state chiral clock model

The low temperature behaviour of the four-state chiral clock ($CC_4$) model is reexamined using a systematic low temperature series expansion of the free energy. Previously obtained results for the low temperature phases are corrected and the low temperature phase diagram is derived. In addition, the phase transition from the modulated region to the high temperature paraphase is shown to belong to the universality class of the 3d-XY model.Comment: 17 pages in ioplppt style, 3 figure

Effect of shear on droplets in a binary mixture

In this article we use a lattice-Boltzmann simulation to examine the effects of shear flow on a equilibrium droplet in a phase separated binary mixture. We find that large drops break up as the shear is increased but small drops dissolve. We also show how the tip-streaming, observed for deformed drops, leads to a state of dynamic equilibrium.Comment: 10 pages, LaTex, to appear in International Journal of Physics

Superhydrophobicity on hairy surfaces

We investigate the wetting properties of surfaces patterned with fine elastic hairs, with an emphasis on identifying superhydrophobic states on hydrophilic hairs. We formulate a two dimensional model of a large drop in contact with a row of equispaced elastic hairs and, by minimising the free energy of the model, identify the stable and metastable states. In particular we concentrate on "partially suspended" states, where the hairs bend to support the drop -- singlet states where all hairs bend in the same direction, and doublet states where neighbouring hairs bend in opposite directions -- and find the limits of stability of these configurations in terms of material contact angle, hair flexibility, and system geometry. The drop can remain suspended in a singlet state at hydrophilic contact angles, but doublets exist only when the hairs are hydrophobic. The system is more likely to evolve into a singlet state if the hairs are inclined at the root. We discuss how, under limited circumstances, the results can be modified to describe an array of hairs in three dimensions. We find that now both singlets and doublets can exhibit superhydrophobic behaviour on hydrophilic hairs. We discuss the limitations of our approach and the directions for future work

Capillary filling in microchannels patterned by posts

We investigate the capillary filling of three dimensional micro-channels with surfaces patterned by posts of square cross section. We show that pinning on the edges of the posts suppresses, and can halt, capillary filling. We stress the importance of the channel walls in controlling whether filling can occur. In particular for channels higher than the distance between adjacent posts, filling occurs for contact angles less than a threshold angle \sim 55 deg., independent of the height of the channel.Comment: To appear in Phys. Rev.

Modelling receding contact lines on superhydrophobic surfaces

We use mesoscale simulations to study the depinning of a receding contact line on a superhydrophobic surface patterned by a regular array of posts. In order that the simulations are feasible, we introduce a novel geometry where a column of liquid dewets a capillary bounded by a superhydrophobic plane which faces a smooth hydrophilic wall of variable contact angle. We present results for the dependence of the depinning angle on the shape and spacing of the posts, and discuss the form of the meniscus at depinning. We find, in agreement with [17], that the local post concentration is a primary factor in controlling the depinning angle, and show that the numerical results agree well with recent experiments. We also present two examples of metastable pinned configurations where the posts are partially wet.Comment: Revised version accepted for publication in Langmui

The Role of Spin Anisotropy in the Unbinding of Interfaces

We study the ground state of a classical X-Y model with $p \ge 3$-fold spin anisotropy $D$ in a uniform external field, $H$. An interface is introduced into the system by a suitable choice of boundary conditions. For large $D$, as $H \to 0$, we prove using an expansion in $D^{-1}$ that the interface unbinds from the surface through an infinite series of layering transitions. Numerical work shows that the transitions end in a sequence of critical end points.Comment: 7 pages RevTeX, plus 1 postscript figure available from the authors OUTP-94-41

Dissipative particle dynamics: the equilibrium for finite time steps

Dissipative particle dynamics (DPD) is a relatively new technique which has proved successful in the simulation of complex fluids. We caution that for the equilibrium achieved by the DPD simulation of a simple fluid the temperature depends strongly on the time step. An analytic expression for the dependence is obtained and shown to agree well with simulation results.Comment: 5 pages, LaTeX, 1 Postscript figure, submitted to Europhys.Letts., Algebraic corrections made to final resul

Wetting on Lines and Lattices of Cylinders

This paper discusses wetting and capillary condensation transitions on a line and a rectangular array of cylinders using an interface potential formalism. For a line of cylinders, there is a capillary condensation transition followed by complete wetting if the cylinders are sufficiently close together. Both transitions disappear as the cylinder separation is increased. The dependence of the wetting phase diagram of a rectangular array of cylinders is discussed as a function of the chemical potential, substrate--fluid interaction strength and surface tension.Comment: 17 pages in total: 11 pages of Latex document and 6 pages of figures, Latex Version 2.09, OUTP-93-40