Outflow boundary condition of multiphase microfluidic flow based on phase ratio equation in lattice Boltzmann method

This article proposes a new outflow boundary condition for the color gradient model in the multiphase lattice Boltzmann method. The boundary condition is based on the phase ratio equation and made use of the Zou–He boundary condition in single-phase flow. The boundary condition is provided in two-dimension-nine-velocity (D2Q9) and three-dimension-twenty-seven-velocity (D3Q27) schemes, for which an extension of the Zou–He boundary condition to D3Q27 is also derived and its correctness verified. Application cases, including two-phase parallel flows, droplet flows, T-junction flows, three-phase Janus droplet flows in two-dimensional (2D), and three-dimensional (3D) spaces, demonstrate the effectiveness of this new boundary condition, and the performance of a test case shows its improved pressure stability and mass conservation characteristics.