Phase behavior of droplets and solid particles in a fluid environment
Understanding phase behavior of droplets and solid particles in a fluid environment is of great interest for a large number of industrial applications ranging from cosmetic and food (e.g., stability and flow properties) industry to automotive branch (e.g., anti-corrosive coatings and painting).
In most of these applications, solid particles are (1) embeded in a droplet and (2) subject to Brownian motion. Therefore, one must first address the fundamental problem as how to introduce thermal fluctuations in two phase liquid models. Recently, we have successfully tackled this issue and have extended the Lattice Boltzmann method for non-ideal fluids -- which is a well-established tool for the simulation of hydrodynamics -- to include thermal fluctuations [Phys. Rev. E 82, 056714 (2010)].
With our method, we could, for example, accurately reproduce the capillary wave spectrum on a liquid-vapor interface (top figure) or the recently predicted thermal-noise dominated regime for droplet spreading on a substrate [Davidovitch et al, PRL (2005)], which reveals itself in a deviation from Tanner's classic law (middle and bottom figure).
We have also shown how the fluctuating Lattice Boltzmann equation can be obtained from the fluctuating discrete Boltzmann equation and how it is related to well-known continuum Langevin methods [J. Stat. Mech, P03030 (2011)].