A 3D Lattice Boltzmann method for accurate wetting of ternary fluids with broad rheological variability

A numerical framework is presented to predict the dynamics of droplets in contact with both hydrophilic and hydrophobic surfaces. We propose a three-dimensional Lattice Boltzmann solver based on the conservative phase-field method for ternary fluid systems. The interface evolution is retrieved by solving the conservative Allen–Cahn equation for two of the three phase-field variables involved in the ternary fluid system whose dynamics is governed by the mass and momentum equations. Such equations are discretized on the lattice nodes: the mass and momentum equations are described using a set of hydrodynamic distribution functions, while the Allen–Cahn equations using two sets of phase-field distribution functions. The boundary conditions for wettability are integrated using a novel non-equilibrium bounce back method for surfaces lying on the lattice nodes. The effectiveness of the solver is validated by means of several test cases of increasing complexity involving: droplets in a quiescent fluid for both low- and high- density ratios, spinodal decomposition of a ternary fluid system, the spreading of a liquid lens, and both static and dynamic configurations of droplets on wettable substrates. The results obtained throughout the validation show very good agreement with the related analytical solutions. A better conservation of physical variables at the boundaries is ensured, thus improving accuracy and mass conserving properties of the overall solver, especially in dynamic cases with high density- and/or viscosity- ratios. Finally, the deformation of a three-layer leukocyte under shear is investigated by means of three-dimensional simulations to demonstrate the effectiveness of the proposed framework.