Three-dimensional lattice Boltzmann simulations of droplet formation in a cross-junction microchannel

An immiscible liquid–liquid multiphase flow in a cross-junction microchannel was numerically studied by the lattice Boltzmann method. An improved, immiscible lattice BGK model was proposed by introducing interfacial tension force based on the continuum surface force (CSF) method. The recoloring step was replaced by the anti-diffusion scheme in the mixed region to reduce the side-effect and control the thickness of the interface. The present method was tested by the simulations on a static bubble and the simulations of Taylor deformation. Laplace’s law, spurious velocities, the thickness of interface, the pressure distribution and the small deformation theory were examined. It proves that our model is more advantageous for the simulation of immiscible fluids over the original immiscible lattice BGK model. The simulations of droplet formation in a cross-junction microchannel were performed and compared with the experiments. The numerical results show good agreements with the experimental ones for the evolution of droplet and the droplet size at various inlet velocities. Besides, a dimensionless analysis was carried out. The resulting droplet sizes depend on the Capillary number to a great extent under current conditions.