Dynamics of Spreading of Chainlike Molecules with Asymmetric Surface Interactions

In this work we study the spreading dynamics of tiny liquid droplets on solid surfaces in the case where the ends of the molecules feel different interactions with respect to the surface. We consider a simple model of dimers and short chainlike molecules that cannot form chemical bonds with the surface. We use constant temperature Molecular Dynamics techniques to examine in detail the microscopic structure of the time dependent precursor film. We find that in some cases it can exhibit a high degree of local order that can persist even for flexible chains. Our model also reproduces the experimentally observed early and late-time spreading regimes where the radius of the film grows proportional to the square root of time. The ratios of the associated transport coefficients are in good overall agreement with experiments. Our density profiles are also in good agreement with measurements on the spreading of molecules on hydrophobic surfaces.Comment: 12 pages, LaTeX with APS macros, 21 figures available by contacting [email protected], to appear in Phys. Rev.

Dewetting, partial wetting and spreading of a two-dimensional monolayer on solid surface

We study the behavior of a semi-infinite monolayer, which is placed initially on a half of an infinite in both directions, ideal crystalline surface, and then evolves in time due to random motion of the monolayer particles. Particles dynamics is modeled as the Kawasaki particle-vacancy exchange process in the presence of long-range attractive particle-particle interactions. In terms of an analytically solvable mean-field-type approximation we calculate the mean displacement X(t) of the monolayer edge and discuss the conditions under which such a monolayer spreads (X(t) > 0), partially wets (X(t) = 0) or dewets from the solid surface (X(t) < 0).Comment: 4 pages, 2 figures, to appear in PRE (RC

Spreading of a Macroscopic Lattice Gas

We present a simple mechanical model for dynamic wetting phenomena. Metallic balls spread along a periodically corrugated surface simulating molecules of liquid advancing along a solid substrate. A vertical stack of balls mimics a liquid droplet. Stochastic motion of the balls, driven by mechanical vibration of the corrugated surface, induces diffusional motion. Simple theoretical estimates are introduced and agree with the results of the analog experiments, with numerical simulation, and with experimental data for microscopic spreading dynamics.Comment: 19 pages, LaTeX, 9 Postscript figures, to be published in Phy. Rev. E (September,1966

Dynamics of Elastic Excitable Media

The Burridge-Knopoff model of earthquake faults with viscous friction is equivalent to a van der Pol-FitzHugh-Nagumo model for excitable media with elastic coupling. The lubricated creep-slip friction law we use in the Burridge-Knopoff model describes the frictional sliding dynamics of a range of real materials. Low-dimensional structures including synchronized oscillations and propagating fronts are dominant, in agreement with the results of laboratory friction experiments. Here we explore the dynamics of fronts in elastic excitable media.Comment: Int. J. Bifurcation and Chaos, to appear (1999

Motion of a driven tracer particle in a one-dimensional symmetric lattice gas

We study the dynamics of a tracer particle subject to a constant driving force $E$ in a one-dimensional lattice gas of hard-core particles whose transition rates are symmetric. We show that the mean displacement of the driven tracer grows in time, $t$, as $\sqrt{\alpha t}$, rather than the linear time dependence found for driven diffusion in the bath of non-interacting (ghost) particles. The prefactor $\alpha$ is determined implicitly, as the solution of a transcendental equation, for an arbitrary magnitude of the driving force and an arbitrary concentration of the lattice gas particles. In limiting cases the prefactor is obtained explicitly. Analytical predictions are seen to be in a good agreement with the results of numerical simulations.Comment: 21 pages, LaTeX, 4 Postscript fugures, to be published in Phys. Rev. E, (01Sep, 1996

Molecular ordering of precursor films during spreading of tiny liquid droplets

In this work we address a novel feature of spreading dynamics of tiny liquid droplets on solid surfaces, namely the case where the ends of the molecules feel different interactions to the surface. We consider a simple model of dimers and short chain--like molecules which cannot form chemical bonds with the surface. We study the spreading dynamics by Molecular Dynamics techniques. In particular, we examine the microscopic structure of the time--dependent precursor film and find that in some cases it can exhibit a high degree of local order. This order persists even for flexible chains. Our results suggest the possibility of extracting information about molecular interactions from the structure of the precursor film.Comment: 4 pages, revtex, no figures, complete file available from ftp://rock.helsinki.fi/pub/preprints/tft/ or at http://www.physics.helsinki.fi/tft/tft_preprints.html (to appear in Phys. Rev. E Rapid Comm.

Spreading in narrow channels

We study a lattice model for the spreading of fluid films, which are a few molecular layers thick, in narrow channels with inert lateral walls. We focus on systems connected to two particle reservoirs at different chemical potentials, considering an attractive substrate potential at the bottom, confining side walls, and hard-core repulsive fluid-fluid interactions. Using kinetic Monte Carlo simulations we find a diffusive behavior. The corresponding diffusion coefficient depends on the density and is bounded from below by the free one-dimensional diffusion coefficient, valid for an inert bottom wall. These numerical results are rationalized within the corresponding continuum limit.Comment: 16 pages, 10 figure

A microscopic model for thin film spreading

A microscopic, driven lattice gas model is proposed for the dynamics and spatio-temporal fluctuations of the precursor film observed in spreading experiments. Matter is transported both by holes and particles, and the distribution of each can be described by driven diffusion with a moving boundary. This picture leads to a stochastic partial differential equation for the shape of the boundary, which agrees with the simulations of the lattice gas. Preliminary results for flow in a thermal gradient are discussed.Comment: 4 pages, 3 figures. Submitte

Molecular Weight Dependence of Spreading Rates of Ultrathin Polymeric Films

We study experimentally the molecular weight $M$ dependence of spreading rates of molecularly thin precursor films, growing at the bottom of droplets of polymer liquids. In accord with previous observations, we find that the radial extension R(t) of the film grows with time as R(t) = (D_{exp} t)^{1/2}. Our data substantiate the M-dependence of D_{exp}; we show that it follows D_{exp} \sim M^{-\gamma}, where the exponent \gamma is dependent on the chemical composition of the solid surface, determining its frictional properties with respect to the molecular transport. In the specific case of hydrophilic substrates, the frictional properties can be modified by the change of the relative humidity (RH). We find that \gamma \approx 1 at low RH and tends to zero when RH gets progressively increased. We propose simple theoretical arguments which explain the observed behavior in the limits of low and high RH.Comment: 4 pages, 2 figures, to appear in PR

The energy budget in Rayleigh-Benard convection

It is shown using three series of Rayleigh number simulations of varying aspect ratio AR and Prandtl number Pr that the normalized dissipation at the wall, while significantly greater than 1, approaches a constant dependent upon AR and Pr. It is also found that the peak velocity, not the mean square velocity, obeys the experimental scaling of Ra^{0.5}. The scaling of the mean square velocity is closer to Ra^{0.46}, which is shown to be consistent with experimental measurements and the numerical results for the scaling of Nu and the temperature if there are strong correlations between the velocity and temperature.Comment: 5 pages, 3 figures, new version 13 Mar, 200