A 3D lattice Boltzmann – phase-field model of three-phase contact line dynamics on curved boundaries

In this paper, we present a three-dimensional multiphase fluid lattice Boltzmann model based on the phase-field theory. The conservative Allen-Cahn equation was used to describe the interface dynamics between two different fluids. The proposed model extends the model proposed in [Fakhari et al., Physical Review E 96 (2017) No. 053301] to three space dimensions and we show how to improve the accuracy of the model at high density ratios by computing gradients more accurately. We also propose an accurate method for implementing the three-phase contact angle on curved boundaries. Several benchmark test cases have been performed with realistic parameters for a water-air system to demonstrate the improvement in accuracy of our model, compared to existing methods. Specifically, flow in a cylindrical capillary has been simulated and the results have been compared to previous methods and analytical solutions.