Phase-field lattice Boltzmann simulation of minute droplet onto isotropic porous media

Abstract

Imbibition of single droplet onto porous surface can be observed in engineering devices such as the oil mist filter, inkjet printings, etc. This two-phase flow is governed by physical properties of liquid and porous media. When the droplet size is comparable to the pore scale, the droplet behavior additionally depends on the structural characteristics of the porous media, which has not been clarified yet. It requires to consider not only the physical properties of two-phase flow but also the solid structure. We employed the phase-field lattice Boltzmann method (PFLBM) to compute the two-phase flow on the complicated structures. Since the conventional PFLBM has less precision in the solid representation, wettability and the phase volume consideration on curved boundaries, we improved this method by employing hybrid interpolated bounce-back scheme in the three dimensional system with considering wall normal direction geometrically. It shows the reasonable droplet behavior on a flat plate inclined from the grid line. A static droplet on a sphere is represented by the reasonable position and shape of the contact line. The phase-volume error derived from the conventional interpolated bounce-back is successfully suppressed. Next, the characteristic of the droplet entrapment and/or infiltration by isotropic open cell (Kelvin cell) porous media is numerically studied. It is found that the threshold wettability exists between entrapment and infiltration regardless of the surface topology of the porous media. As the droplet size becomes smaller, the effect of the porous surface becomes remarkable in the threshold contact angle and infiltration ratio at higher contact angle. In case of the droplet entrapment above the porous surface, the lyophobicity of the porous surface becomes remarkable, which merges to the given contact angle at the super-lyophobicity due to the less wetted ligaments.

Keywords

• two phase flow
• droplet
• lattice boltzmann method
• phase-field model
• allen-cahn equation
• porous media
• droplet imbibition