Phase field-lattice Boltzmann model for two-phase flows with near-contact interactions

This study presents a phase field-lattice Boltzmann method for modeling two-phase flows with near-contact interactions. The second-order conservative phase-field equation is coupled with the velocity-based Navier–Stokes equations for phase interface tracking and flow field prediction, respectively. To account for the near-contact interactions between droplets or bubbles in two-phase flows, a continuum repulsive force model is introduced, which is inversely proportional to the cubic power of the interfacial distance. A double-population multiple-relaxation-time lattice Boltzmann scheme is proposed to solve the governing equations. The model is validated through several numerical examples involving near-contact interactions. First, a static concentric droplet problem is quantitatively analyzed, in which the pressure jumps across the phase interfaces due to surface tension and repulsive forces are captured accurately. It can be seen clearly that the maximum relative errors in most cases are below 5% and still meet the requirements under high density ratio. Next, simulations of droplet motion in shear flow and bubble rise under gravity are conducted to investigate the non-coalescence mechanisms of droplets and bubbles in two-phase flows. Finally, as an application example of the present model, the generation of micro-droplets in a microchannel with a T-junction is simulated. The numerical results demonstrate that the coalescence of droplets and bubbles can be effectively prevented under the influence of the repulsive force, and thus, the validity of proposed model is verified.