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We investigate the applicability of a mesoscale modeling approach, lattice Boltzmann simulations, to the problem of contact line motion in one and two component, two phase fluids. In this, the first of two papers, we consider liquid-gas systems. Careful implementation of the thermodynamic boundary condition allows us to fix the static contact angle in the simulations. We then consider the behavior of a sheared interface. We show that the contact line singularity is overcome by evaporation or condensation near the contact line which is driven by the curvature of the diffuse interface. An analytic approximation is derived for the angular position of a sheared interface.

The lattice Boltzmann algorithm efficiently simulates the Navier Stokes equation of isothermal fluid flow, but ignores thermal fluctuations of the fluid, important in mesoscopic flows. We show how to adapt the algorithm to include noise, satisfying a fluctuation-dissipation theorem (FDT) directly at lattice level: this gives correct fluctuations for mass and momentum densities, and for stresses, at all wavevectors k. Unlike previous work, which recovers FDT only as k → 0, our algorithm offers full statistical mechanical consistency in mesoscale simulations of, e.g., fluctuating colloidal hydrodynamics.c EDP Sciences

We present evidence, based on lattice Boltzmann simulations, to show that the coarsening of the domains in phase-separating binary fluids is not a scale-invariant process. Moreover we emphasize that the pathway by which phase separation occurs depends strongly on the relation between diffusive and hydrodynamic time scales. [S0031-9007(98)

We suggest a minimal model for the coupling of the lateral phase behavior in an asymmetric lipid membrane across its two monolayers. Our model employs one single order parameter for each monolayer leaflet, namely its composition. Regular solution theory on the mean-field level is used to describe the free energy in each individual leaflet. Coupling between monolayers entails an energy penalty for any local compositional differences across the membrane. We calculate and analyze the phase behavior of this model. It predicts a range of possible scenarios. A monolayer with a propensity for phase separation is able to induce phase separation in the apposed monolayer. Conversely, a monolayer without this propensity is able to prevent phase separation in the apposed monolayer. If there is phase separation in the membrane, it may lead to either complete or partial registration of the monolayer domains across the membrane. The latter case which corresponds to a three-phase coexistence is only found below a critical coupling strength. We calculate that critical coupling strength. Above the critical coupling strength, the membrane adopts a uniform compositional difference between its two monolayers everywhere in the membrane, implying phase coexistence between only two phases and thus perfect spatial registration of all domains on the apposed membrane leafs. We use the lattice Boltzmann simulation method to also study the morphologies that form during phase separation within the three-phase coexistence region. Generally, domains in one monolayer diffuse but remain fully enclosed within domains in the other monolayer.

Lattice Boltzmann simulations have been very successful in simulating liquid-gas and other multiphase fluid systems. However, the underlying second-order analysis of the equation of motion has long been known to be insufficient to consistently derive the fourth-order terms that are necessary to represent an extended interface. These same terms are also responsible for thermodynamic consistency--i.e., to obtain a true equilibrium solution with both a constant chemical potential and a constant pressure. In this article we present an equilibrium analysis of nonideal lattice Boltzmann methods of sufficient order to identify those higher-order terms that lead to a lack of thermodynamic consistency. We then introduce a thermodynamically consistent forcing method.

We use lattice Boltzmann simulations to study the effect of shear on the phase ordering of a two-dimensional binary fluid. The shear is imposed by generalising the lattice Boltzmann algorithm to include Lees-Edwards boundary conditions. We show how the interplay between the ordering effects of the spinodal decomposition and the disordering tendencies of the shear, which depends on the shear rate and the fluid viscosity, can lead to a state of dynamic equilibrium where domains are continually broken up and re-formed.

Abstract. We present a progress report on our work on lattice Boltzmann methods for colloidal suspensions. We focus on the treatment of colloidal particles in binary solvents and on the inclusion of thermal noise. For a benchmark problem of colloids sedimenting and becoming trapped by capillary forces at a horizontal interface between two fluids, we discuss the criteria for parameter selection, and address the inevitable compromise between computational resources and simulation accuracy.