We propose a scheme for studying thin liquid films on a solid substrate using a phase field model. For a van der Waals fluid-far from criticality-the most natural phase field function is the fluid density. The theoretical description is based on the Navier-Stokes equation with extra phase field terms and the continuity equation. In this model free of interface conditions, the contact angle can be controlled through the boundary conditions for the density field at the solid walls [L. M. Pismen and Y. Pomeav, Phys. Rev. E 62, 2480 (2000)]. We investigate the stability of a thin liquid film on a flat homogeneous solid support with variable wettability. For almost hydrophobic surfaces, the liquid film breaks up and transitions from a flat film to drops occur. Finally, we report on two-dimensional numerical simulations for static liquid drops resting on a flat horizontal solid support and for drops sliding down on inclined substrates under gravity effects.
Mixing of droplets with a body of different liquids shows an interesting behavior for small contact angles at solid substrate. The droplets interact with each other, a liquid exchange appears between the approaching drops owing to surface tension gradients at the droplets interface. But the drops remain separated for some seconds (up to minutes), until the merging into a single drop occurs (Langmuir 24, 6395 (2008)). We investigate this phenomenon using lubrication approximation and phase field approach. For both methods, 2D quantitative computer simulations for delayed fusion of perfectly miscible thin liquid films/droplets with low contact angles are reported.
We developed a phase-field model for Marangoni convection in a liquid-gas system with a deformable interface, heated from below. In order to describe both Marangoni instabilities (with short and long wavelengths), an additional force component must be considered in the Navier-Stokes equation. This term describes the coupling of the temperature to the velocity field via the phase-field function. It results by minimizing the free-energy functional of the system. For a bidimensional problem in linear approximation we performed a numerical code that successfully computes both Marangoni instabilities. In the limit of sharp and rigid interfaces, our results are compared with the literature.
Recently we proposed a phase field model to describe Marangoni convection in a compressible fluid of van der Waals type far from criticality [Eur. Phys. J. B 44, 101 (2005)]. The model previously developed for a two-layer geometry is now extended to drops and bubbles. A randomly distributed initial density evolves towards phase separation and single droplet formation. For a two-component liquid-liquid system we report on numerical simulations for drop Marangoni migration in a vertical thermal gradient.
Using computer simulations in three spatial dimensions, we examine the interaction between two deformable drops consisting of two perfectly miscible liquids sitting on a solid substrate under a given contact angle. Driven by capillarity and assisted by Marangoni effects at the droplet interfaces, several distinct coalescence regimes are achieved after the droplets' collision.
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