Molecular dynamics of flows in the Knudsen regime

Novel technological applications often involve fluid flows in the Knudsen regime in which the mean free path is comparable to the system size. We use molecular dynamics simulations to study the transition between the dilute gas and the dense fluid regimes as the fluid density is increased.Comment: REVTeX, 15 pages, 4 EPS figures, to appear in Physica

Extensional rupture of model non-Newtonian fluid filaments

We present molecular dynamics computer simulations of filaments of model non-Newtonian liquid stretched in a uniaxial deformation to the point of breaking. The liquid consists of Lennard-Jones monomers bound into chains of 100 monomers by nonlinear springs, and several different constant velocity and constant strain rate deformations are considered. Generally we observe nonuniform extensions originating in an interplay between the stretching forces and elastic and capillary restoring mechanisms, leading to highly uneven shapes and alternating stretched and unstretched regions of liquid. Except at the fastest pulling speeds, the filaments continue to thin indefinitely and break only when depleted of molecules, rather than common viscoelastic rupture mechanisms.Comment: 7 pages text, 14 pages (eps) figure

Lattice-Boltzmann Method for Non-Newtonian Fluid Flows

We study an ad hoc extension of the Lattice-Boltzmann method that allows the simulation of non-Newtonian fluids described by generalized Newtonian models. We extensively test the accuracy of the method for the case of shear-thinning and shear-thickening truncated power-law fluids in the parallel plate geometry, and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution. Finally, we also tested the method in the reentrant-flow geometry, in which the shear-rate is no-longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points. In this geometry, we also found excellent agreement with the solutions obtained by standard finite-element methods, and the agreement improves with higher lattice resolution

Hybrid method for simulating front propagation in reaction-diffusion systems

We study the propagation of pulled fronts in the $A \leftrightarrow A+A$ microscopic reaction-diffusion process using Monte Carlo (MC) simulations. In the mean field approximation the process is described by the deterministic Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation. In particular we concentrate on the corrections to the deterministic behavior due to the number of particles per site $\Omega$. By means of a new hybrid simulation scheme, we manage to reach large macroscopic values of $\Omega$ which allows us to show the importance in the dynamics of microscopic pulled fronts of the interplay of microscopic fluctuations and their macroscopic relaxation.Comment: 5 pages, 4 figure

Wetting Hysteresis at the Molecular Scale

The motion of a fluid-fluid-solid contact line on a rough surface is well known to display hysteresis in the contact angle vs. velocity relationship. In order to understand the phenomenon at a fundamental microscopic level, we have conducted molecular dynamics computer simulations of a Wilhelmy plate experiment in which a solid surface is dipped into a liquid bath, and the force-velocity characteristics are measured. We directly observe a systematic variation of force and contact angle with velocity, which is single-valued for the case of an atomically smooth solid surface. In the microscopically rough case, however, we find (as intuitively expected) an open hysteresis loop. Further characterization of the interface dynamics is in progress

Resistance of Random Walks

Unrestricted lattice random walks in which a unit conductor is placed along each bond traversed are considered. The mean end-to-end resistance is studied as a function of the number of steps in the walk and the spatial dimension. A critical scaling law is found whose exponent is consistently given by four different calculational schemes