Lattice Boltzmann simulations for flow and heat/mass transfer problems in a three-dimensional porous structure

“This is a preprint of an article published in INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2003; 43(2): 183–198.”ArticleINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS. 43(2): 183-198 (2003)journal articl

Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids

We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. We find the average domain size growing with time as $t^\gamma$, where $\gamma$ increases in the range $0.545 < \gamma < 0.717$, consistent with a crossover between diffusive $t^{1/3}$ and hydrodynamic viscous, $t^{1.0}$, behaviour. We find good collapse onto a single scaling function, yet the domain growth exponents differ from others' works' for similar values of the unique characteristic length and time that can be constructed out of the fluid's parameters. This rebuts claims of universality for the dynamical scaling hypothesis. At early times, we also find a crossover from $q^2$ to $q^4$ in the scaled structure function, which disappears when the dynamical scaling reasonably improves at later times. This excludes noise as the cause for a $q^2$ behaviour, as proposed by others. We also observe exponential temporal growth of the structure function during the initial stages of the dynamics and for wavenumbers less than a threshold value.Comment: 45 pages, 18 figures. Accepted for publication in Physical Review

Numerical study of wetting transitions on biomimetic surfaces using a lattice Boltzmann approach with large density ratio

The hydrophobicity of natural surfaces have drawn much attention of scientific communities in recent years. By mimicking natural surfaces, the manufactured biomimetic hydrophobic surfaces have been widely applied to green technologies such as self-cleaning surfaces. Although the theories for wetting and hydrophobicity have been developed, the mechanism of wetting transitions between heterogeneous wetting state and homogeneous wetting state is still not fully clarified. As understanding of wetting transitions is crucial for manufacturing a biomimetic superhydrophobic surface, more fundamental discussions in this area should be carried out. In the present work the wetting transitions are numerically studied using a phase field lattice Boltzmann approach with large density ratio, which should be helpful in understanding the mechanism of wetting transitions. The dynamic wetting transition processes between Cassie-Baxter state and Wenzel state are presented, and the energy barrier and the gravity effect on transition are discussed. It is found that the two wetting transition processes are irreversible for specific inherent contact angles and have different transition routes, the energy barrier exists on an ideally patterned surface and the gravity can be crucial to overcome the energy barrier and trigger the transition

Modelling opinion formation by means of kinetic equations

In this chapter, we review some mechanisms of opinion dynamics that can be modelled by kinetic equations. Beside the sociological phenomenon of compromise, naturally linked to collisional operators of Boltzmann kind, many other aspects, already mentioned in the sociophysical literature or no, can enter in this framework. While describing some contributions appeared in the literature, we enlighten some mathematical tools of kinetic theory that can be useful in the context of sociophysics