A lattice mesoscopic model of dynamically heterogeneous fluids

We introduce a mesoscopic three-dimensional Lattice Boltzmann Model which attempts to mimick the physical features associated with cage effects in dynamically heterogeneous fluids. To this purpose, we extend the standard Lattice Boltzmann dynamics with self-consistent constraints based on the non-local density of the surrounding fluid. The resulting dynamics exhibits typical features of dynamic heterogeneous fluids, such as non-Gaussian density distributions and long-time relaxation. Due to its intrinsically parallel dynamics, and absence of statistical noise, the method is expected to compute significantly faster than molecular dynamics, Monte Carlo and lattice glass models.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let

Generalized Lattice Boltzmann Method with multi-range pseudo-potential

The physical behaviour of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces. In particular, an extended pseudo-potential method is developed, which permits to tune the equation of state and surface tension independently of each other. The spurious velocity contributions of this extended model are shown to vanish in the limit of high grid refinement and/or high order isotropy. Higher order schemes to implement self-consistent forcings are rigorously computed for 2d and 3d models. The extended scenario developed in this work clarifies the theoretical foundations of the Shan-Chen methodology for the lattice Boltzmann method and enhances its applicability and flexibility to the simulation of multiphase flows to density ratios up to O(100)

Impalement transitions in droplets impacting microstructured superhydrophobic surfaces

Liquid droplets impacting a superhydrophobic surface decorated with micro-scale posts often bounce off the surface. However, by decreasing the impact velocity droplets may land on the surface in a fakir state, and by increasing it posts may impale droplets that are then stuck on the surface. We use a two-phase lattice-Boltzmann model to simulate droplet impact on superhydrophobic surfaces, and show that it may result in a fakir state also for reasonable high impact velocities. This happens more easily if the surface is made more hydrophobic or the post height is increased, thereby making the impaled state energetically less favourable.Comment: 8 pages, 4 figures, to appear in Europhysics Letter

Investigation of a lattice Boltzmann model with a variable speed of sound

A lattice Boltzmann model is considered in which the speed of sound can be varied independently of the other parameters. The range over which the speed of sound can be varied is investigated and good agreement is found between simulations and theory. The onset of nonlinear effects due to variations in the speed of sound is also investigated and good agreement is again found with theory. It is also shown that the fluid viscosity is not altered by changing the speed of sound

Numerical simulations of compressible Rayleigh-Taylor turbulence in stratified fluids

We present results from numerical simulations of Rayleigh-Taylor turbulence, performed using a recently proposed lattice Boltzmann method able to describe consistently a thermal compressible flow subject to an external forcing. The method allowed us to study the system both in the nearly-Boussinesq and strongly compressible regimes. Moreover, we show that when the stratification is important, the presence of the adiabatic gradient causes the arrest of the mixing process.Comment: 15 pages, 11 figures. Proceedings of II Conference on Turbulent Mixing and Beyond (TMB-2009

A note on the lattice Boltzmann method beyond the Chapman Enskog limits

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the Lattice Boltzmann method, can provide semi-quantitative results also in the non-hydrodynamic, finite-Knudsen regime, up to $Kn\sim {\cal O}(1)$. This may help the interpretation of recent Lattice Boltzmann simulations of microflows, which show satisfactory agreement with continuum kinetic theory in the moderate-Knudsen regime.Comment: 7 PAGES, 1 FIGUR

Dynamics of the spontaneous breakdown of superhydrophobicity

Drops deposited on rough and hydrophobic surfaces can stay suspended with gas pockets underneath the liquid, then showing very low hydrodynamic resistance. When this superhydrophobic state breaks down, the subsequent wetting process can show different dynamical properties. A suitable choice of the geometry can make the wetting front propagate in a stepwise manner leading to {\it square-shaped} wetted area: the front propagation is slow and the patterned surface fills by rows through a {\it zipping} mechanism. The multiple time scale scenario of this wetting process is experimentally characterized and compared to numerical simulations.Comment: 7 pages, 5 figure

Modelling thermal flow in a transition regime using a lattice Boltzmann approach

Lattice Boltzmann models are already able to capture important rarefied flow phenomena, such as velocity-slip and temperature jump, provided the effects of the Knudsen layer are minimal. However, both conventional hydrodynamics, as exemplified by the Navier-Stokes-Fourier equations, and the lattice Boltzmann method fail to predict the nonlinear velocity and temperature variations in the Knudsen layer that have been observed in kinetic theory. In the present paper, we propose an extension to the lattice Boltzmann method that will enable the simulation of thermal flows in the transition regime where Knudsen layer effects are significant. A correction function is introduced that accounts for the reduction in the mean free path near a wall. This new approach is compared with direct simulation Monte Carlo data for Fourier flow and good qualitative agreement is obtained for Knudsen numbers up to 1.58