A simple phase-field model for interface tracking in three dimensions

Abstract

Based on a conservative phase-field lattice Boltzmann (LB) method, we present a 3D model for tracking an interface in multiphase flows. In addition to being mass-conserving, the main advantage of this LB method is that the collision process is made entirely local by invoking central moments in the calculation of vectors normal to the interface. We construct the model on different 3D lattices (D3Q7 and D3Q15) with inherently distinct isotropy properties. To test the model we conduct a variety of benchmark studies, such as the evolution of an interface in the form of a slotted sphere in a rotational flow field, and the evolution of a spherical interface in a vortex flow, a deformation flow, and a shear flow. The results of these benchmarks are compared against the finite-difference-based version of the LB model, in which a non-local finite-difference scheme is used to calculate the interface normal. In terms of error, the moment-based model, while competitive, is generally outperformed by the finite-difference model. Despite this, the moment-based interface tracking model is inherently more efficient, and deserves consideration, particularly for memory-distributed parallel computing. We also consider the interaction between a binary fluid and a solid wall, and introduce a method to implement the three-phase contact angle within this framework. The proposed model for dealing with the contact line is simple, clean, and straightforward to implement, and shown to recover desired contact angles very well.