Mean-field Free-energy Lattice Boltzmann Research Articles

A mean-field free energy lattice Boltzmann model for multicomponent fluids

We propose a mean-field free energy approach to simulate multi- component fluids. The model has been validated in terms of the Laplace equation of capillarity and dispersion relation of interfacial waves. Simulations of a ternary system shows that the total free energy decreases and reaches a minimum after phase separation has occurred. Different drop shapes can be obtained by adjusting the interaction strengths between individual components. These results demonstrate that both macroscopic free energy and microscopic fluid-fluid interactions have been well described in our multicomponent model.

Metastable contact angles and self-propelled drop movement on chemically heterogeneous surfaces by a mean-field lattice Boltzmann model

Contact angle behaviors on heterogeneous surfaces were studied by the mean-field free-energy lattice Boltzmann method. Our results suggest that the relation for contact angles on heterogeneous surfaces proposed by Israelachvili and Gee [Langmuir, 5, 288 (1989)] is in general not valid for the case examined. Droplet self-propelled movement on chemically patterned surfaces was also modeled by means of a local surface tension gradient.

Contact Line and Contact Angle Dynamics in Superhydrophobic Channels

The dynamics of the wetting and movement of a three-phase contact line confined between two superhydrophobic surfaces were studied using a mean-field free-energy lattice Boltzmann model. Principle features of superhydrophobic surfaces, such as trapped vapor/air between rough microstructures, high contact angles, reduced contact angle hysteresis, and low resistance to fluid flow, were all observed. Movement of the three-phase contact line over a well-patterned superhydrophobic surface displays a periodic stick-jump-slip behavior, while the dynamic contact angle changes accordingly from maximum to minimum. Two regimes were found for the flow velocity as a function of surface roughness and can be related directly to the balance between driving force and flow resistance. This work provides a better understanding of dynamic wetting and fluid flow behaviors over superhydrophobic surfaces and hence could be useful in related applications.

On the validity of the Cassie equation via a mean-field free-energy lattice Boltzmann approach

We studied wetting phenomena on heterogeneous surfaces by a mean-field free-energy lattice Boltzmann method recently proposed [Phys. Rev. E 69 (2004) 32,602]. Our results suggest that the Cassie equation in macroscopic contact angle measurements is in general not valid. It was found that the Cassie equation is valid only when the patch size is on the same order of the liquid–vapor interfacial thickness. We also demonstrated that contact angle manifests itself from local surface properties near the contact point and does not result from the specific solid–liquid interactions across the contact area.

Apparent slip over a solid-liquid interface with a no-slip boundary condition

We studied solid-liquid slip by a mean-field free-energy lattice Boltzmann approach recently proposed [Phys. Rev. E 69, 032602 (2004)]. With a general bounce-back no-slip boundary condition applied to the interface, liquid slip was observed because of the specific solid-fluid interactions. Our work relates interfacial slip to a more realistic solid-fluid interaction and hence contact angle. The kinetic nature of LBM is manifested in this interfacial study. A small negative slip length can also be produced with a stronger solid-fluid attraction.

Lattice boltzmann study on the contact angle and contact line dynamics of liquid-vapor interfaces.

The moving contact line problem of liquid-vapor interfaces was studied using a mean-field free-energy lattice Boltzmann method recently proposed [Phys. Rev. E 2004, 69, 032602]. We have examined the static and dynamic interfacial behaviors by means of the bubble and capillary wave tests and found that both the Laplace equation of capillarity and the dispersion relation were satisfied. Dynamic contact angles followed the general trend of contact line velocity observed experimentally and can be described by Blake's theory. The velocity fields near the interface were also obtained and are in good agreement with fluid mechanics and molecular dynamics studies. Our simulations demonstrated that incorporating interfacial effects into the lattice Boltzmann model can be a valuable and powerful alternative in interfacial studies.