ICAMS / Interdisciplinary Centre for Advanced Materials Simulation

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)].


Capillary fluctuations of a planar interface in the modified-equilibrium model using spatially uncorrelated noise. The equal-time spectrum of interfacial height fluctuations obtained from simulation (dots) is compared to the theoretical capillary structure factor (solid line). k denotes the wave number along the interface.

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)].

Project Files:

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Capillary fluctuations of a planar interface in the modified-equilibrium model using spatially uncorrelated noise.
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Animation: Thermal-noise dominated regime for droplet spreading on a substrate.
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Thermal-noise dominated regime for droplet spreading on a substrate.
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final report (pdf)

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