J. Merikoski

Lattice-Boltzmann Simulation of Capillary Rise Dynamics

We report results of extensive two-phase lattice-Boltzmann simulations of capillary rise dynamics. We demonstrate that the method can be used to model the hydrodynamic behaviour inside a capillary tube provided that the diameter of the tube is large enough, typically at least 30 lattice units. We also present results for the dependence of the cosine of the dynamic contact angle on the capillary number Ca. Its deviation from the static advancing contact angle has a power-law form, with the value of the exponent very close to 3/2 for capillary rise at zero gravity, while behaviour is more complex in the presence of gravity.

Spreading dynamics of three-dimensional droplets by the lattice-Boltzmann method ☆

Abstract We have simulated spreading of small droplets on smooth and rough solid surfaces using the three-dimensional lattice-Boltzmann method. We present results for the influence of the initial distance and shape of the drop from the surface on scaling of droplet radius R as a function of time. For relatively flat initial drop shapes our observations are consistent with Tanners law R ∼ t q , where q =1/10. For increasingly spherical initial shapes, the exponent q increases rapidly being above one half for spherical droplets initially just above the surface. As expected, surface roughness slows down spreading, decreases the final drop radius, and results in irregular droplet shape due to pinning of the droplet edge. Our results show that lattice-Boltzmann method can be a powerful tool in realistic simulations of droplet spreading.

Kinetic roughening in slow combustion of paper.

Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal development of the interface fluctuations. The asymptotic scaling properties, on long length and time scales, are well described by the Kardar-Parisi-Zhang (KPZ) equation with short-range, uncorrelated noise. To obtain a more detailed picture of the strong-coupling fixed point, characteristic of the KPZ universality class, universal amplitude ratios, and the universal coupling constant are computed from the data and found to be in good agreement with theory. Below the spatial and temporal scales at which a crossover takes place to the standard KPZ behavior, the fronts display higher apparent exponents and apparent multiscaling. In this regime the interface velocities are spatially and temporally correlated, and the distribution of the magnitudes of the effective noise has a power-law tail. The relation of the observed short-range behavior and the noise as determined from the local velocity fluctuations is discussed.

Island Diffusion on Metal fcc (100) Surfaces

We present Monte Carlo simulations for the size and temperature dependence of the diffusion coefficient of adatom islands on the Cu(100) surface. We show that the scaling exponent for the size dependence is not a constant but a decreasing function of the island size and approaches unity for very large islands. This is due to a crossover from periphery dominated mass transport to a regime where vacancies diffuse inside the island. The effective scaling exponents are in good agreement with theory and experiments.

Temporal and spatial persistence of combustion fronts in paper.

The spatial and temporal persistence, or first-return distributions are measured for slow-combustion fronts in paper. The stationary temporal and (perhaps less convincingly) spatial persistence exponents agree with the predictions based on the front dynamics, which asymptotically belongs to the Kardar-Parisi-Zhang universality class. The stationary short-range and the transient behavior of the fronts are non-Markovian, and the observed persistence properties thus do not agree with the predictions based on Markovian theory. This deviation is a consequence of additional time and length scales, related to the crossovers to the asymptotic coarse-grained behavior.

NON-ARRHENIUS BEHAVIOR OF SURFACE DIFFUSION NEAR A PHASE TRANSITION BOUNDARY

We study the non-Arrhenius behavior of surface diffusion near the second-order phase transition boundary of an adsorbate layer. In contrast to expectations based on macroscopic thermodynamic effects, we show that this behavior can be related to the average microscopic jump rate which in turn is determined by the waiting-time distribution W(t) of single-particle jumps at short times. At long times, W(t) yields a barrier that corresponds to the rate-limiting step in diffusion. The microscopic information in W(t) should be accessible by STM measurements.

SURFACE RECONSTRUCTION AND MANY-ATOM MODELS

The (110)(1*2) missing-row reconstruction of the seven FCC metals Ni, Pd, Pt, Cu, Ag, Au and Al has been studied using the effective medium theory (EMT). A clear trend in the tendency to reconstruct has been observed when going from the 3d metals Ni and Cu to 5d metals Pt and Au. The results are discussed together with some previous calculations using other many-atom models for total energy calculation in metals. The tendency to undergo reconstruction is found to be related to the anisotropy of surface energies on (111) and (110) surfaces. By investigating the effective two-body and three-body interactions on the surface it is shown that the missing-row reconstruction is related to the effective repulsion between adjacent nearest neighbour rows on the unreconstructed (110) surface. Restriction of the atomic interactions to the nearest neighbours only makes all the recent many-atom models favour the missing-row structure.

Effect of a columnar defect on the shape of slow-combustion fronts.

We report experimental results for the behavior of slow-combustion fronts in the presence of a columnar defect with enhanced or reduced driving, and compare them with those of mean-field theory. We also compare them with simulation results for an analogous problem of driven flow of particles with hard-core repulsion (ASEP) and a single defect bond with a different hopping probability. The difference in the shape of the front profiles for enhanced vs reduced driving in the defect clearly demonstrates the existence of a Kardar-Parisi-Zhang-type nonlinear term in the effective evolution equation for the slow-combustion fronts. We also find that slow-combustion fronts display a faceted form for large enough enhanced driving, and that there is a corresponding increase then in the average front speed. This increase in the average front speed disappears at a nonzero enhanced driving in agreement with the simulated behavior of the ASEP model.

Cluster size distributions in particle systems with asymmetric dynamics.

We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with an increasing system size for ordinary TASEP dynamics and as a logarithm divided by a double logarithm for generalized dynamics, where the hopping probability of a particle depends on the size of the cluster it belongs to. The connection with the asymptotic theory of extreme order statistics is discussed in detail. We also consider a related model of interface growth, where the deposited particles are allowed to relax to the local gravitational minimum.

Comment on “Surface diffusion near the points corresponding to continuous phase transitions” [J. Chem. Phys. 109, 3197 (1998)]

It is well known that unlike static equilibrium properties, kinetic quantities in Monte Carlo simulations are very sensitive to the details of the algorithm used for the microscopic transition rates. This is particularly true near the critical region where fluctuations are pronounced. We demonstrate that when diffusion of oxygen adatoms near the order–disorder transition of a lattice-gas model of the O/W(110) model system is studied, the transition rates must be chosen carefully. In particular, we show that the choice by Uebing and Zhdanov [J. Chem. Phys. 109, 3197 (1998)] is inappropriate for the study of critical effects in diffusion.