A versatile lattice Boltzmann model for immiscible ternary fluid flows

We propose a lattice Boltzmann color-gradient model for immiscible ternary fluid flows, which is applicable to the fluids with a full range of interfacial tensions, especially in near-critical and critical states. An interfacial force for N-phase systems is derived and then introduced into the model using a body force scheme, which helps reduce spurious velocities. A generalized recoloring algorithm is applied to produce phase segregation and ensure immiscibility of three different fluids, where an enhanced form of segregation parameters is derived by considering the existence of Neumann's triangle and the effect of the equilibrium contact angle in a three-phase junction. The proposed model is first validated by two typical examples, namely, the Young-Laplace test for a compound droplet and the spreading of a droplet between two stratified fluids. It is then used to study the structure and stability of double droplets in a static matrix. Consistent with the theoretical stability diagram, seven possible equilibrium morphologies are successfully reproduced by adjusting the interfacial tension ratio. By simulating near-critical and critical states of double droplets where the outcomes are very sensitive to the model accuracy, we show that the present model is advantageous to three-phase flow simulations and allows for accurate simulation of near-critical and critical states. Finally, we investigate the influence of interfacial tension ratio on the behavior of a compound droplet in a three-dimensional shear flow, and four different deformation and breakup modes are observed.