Extracting the equation of state of lattice gases from Random Sequential Adsorption simulations by means of the Gibbs adsorption isotherm

A novel approach for deriving the equation of state for a 2D lattice gas is proposed, based on arguments similar to those used in the derivation of the Langmuir-Szyszkowski equation of state for localized adsorption. The relationship between surface coverage and excluded area is first extracted from Random Sequential Adsorption simulations incorporating surface diffusion (RSAD). The adsorption isotherm is then obtained using kinetic arguments and the Gibbs equation gives the relation between surface pressure and coverage. Provided surface diffusion is fast enough to ensure internal equilibrium within the monolayer during the RSAD simulations, the resulting equations of state are very close to the most accurate equivalents obtained by cumbersome thermodynamic methods. An internal test of the accuracy of the method is obtained by noting that adsorption RSAD simulations starting from an empty lattice and desorption simulations starting from a full lattice provide convergent upper and lower bounds on the surface pressure

The no-slip condition for a mixture of two liquids

When a mixture of two viscous liquids flows past a solid wall there is an ambiguity in the use of the no-slip boundary condition. It is not obvious whether the mass-averaged velocity, the volume-averaged velocity, the individual species velocities, all or none of the above, or none of the above should exhibit no-slip. Extensive molecular dynamics simulations of the Poiseuille flow of mixtures of coexisting liquid species past an atomistic wall indicate that the velocity of each individual liquid species satisfies the no-slip condition and, therefore, so do mass and volume averages.Comment: 4 pages, including 4 figure

Hysteresis, force oscillations and non-equilibrium effects in the adhesion of spherical nanoparticles to atomically smooth surfaces

Molecular dynamics simulations are used to examine hysteretic effects and distinctions between equilibrium and non-equilibrium aspects of particle adsorption on the walls of nano-sized fluidfilled channels. The force on the particle and the system's Helmholtz free energy are found to depend on the particle's history as well as on its radial position and the wetting properties of the fluid, even when the particle's motion occurs on time scales much longer than the spontaneous adsorption time. The hysteresis is associated with changes in the fluid density in the gap between the particle and the wall, and these structural rearrangements persist over surprisingly long times. The force and free energy exhibit large oscillations with distance when the lattice of the structured nanoparticle is held in register with that of the tube wall, but not if the particle is allowed to rotate freely. Adsorbed particles are trapped in free energy minima in equilibrium, but if the particle is forced along the channel the resulting stick-slip motion alters the fluid structure and allows the particle to desorb

Microscopic Motion of Particles Flowing through a Porous Medium

We use Stokesian Dynamics simulations to study the microscopic motion of particles suspended in fluids passing through porous media. We construct model porous media with fixed spherical particles, and allow mobile ones to move through this fixed bed under the action of an ambient velocity field. We first consider the pore scale motion of individual suspended particles at pore junctions. The relative particle flux into different possible directions exiting from a single pore, for two and three dimensional model porous media is found to approximately equal the corresponding fractional channel width or area. Next we consider the waiting time distribution for particles which are delayed in a junction, due to a stagnation point caused by a flow bifurcation. The waiting times are found to be controlled by two-particle interactions, and the distributions take the same form in model porous media as in two-particle systems. A simple theoretical estimate of the waiting time is consistent with the simulations. We also find that perturbing such a slow-moving particle by another nearby one leads to rather complicated behavior. We study the stability of geometrically trapped particles. For simple model traps, we find that particles passing nearby can ``relaunch'' the trapped particle through its hydrodynamic interaction, although the conditions for relaunching depend sensitively on the details of the trap and its surroundings.Comment: 16 pages, 19 figure

Crossover from fast relaxation to physical aging in colloidal adsorption at fluid interfaces

The adsorption dynamics of a colloidal particle at a fluid interface is studied theoretically and numerically, documenting distinctly different relaxation regimes. The adsorption of a perfectly smooth particle is characterized by a fast exponential relaxation to thermodynamic equilibrium where the interfacial free energy has a minimum. The short relaxation time is given by the ratio of viscous damping to capillary forces. Physical and/or chemical heterogeneities in a colloidal system, however, can result in multiple minima of the free energy giving rise to metastability. In the presence of metastable states we observe a crossover to a slow logarithmic relaxation reminiscent of physical aging in glassy systems. The long relaxation time is determined by the thermally-activated escape rate from metastable states. Analytical expressions derived in this work yield quantitative agreement with molecular dynamics simulations and recent experimental observations. This work provides new insights on the adsorption dynamics of colloidal particles at fluid interfaces