Energy-Based Wetting for Color-Gradient Lattice Boltzmann Fluid Simulations

Abstract

Drop-on-Demand Inkjet Printing requires jetting ink particles at 100kHz at velocities of 10m/s from sub-millimeter-scale printhead assemblies, and represents a physics-rich engineering problem. CFD simulations have been used to study the jetting process. From meniscus deformation at the nozzle, to the presence of entrained particles in the jet, modelling contact line dynamics is very important.
Color-Gradient Lattice Boltzmann (CG-LBM) simulations can capture surface tension between fluids. Contact angles with solids are often imposed on geometrical grounds as boundary conditions. Alternative energy-based wetting, based on solid-liquid surface tension/energy arguments, is investigated for its applicability in the inkjet printing regime.
CG-LBM fluid-fluid interfaces are diffuse, despite modelling macroscopically sharp interfaces. This requires interpolation of viscosity in the interface region: new arguments are given to support the idea that this interpolation is free, and can be chosen, for example, on the basis of validation results.
New theory on CG-LBM for any number N of fluids is developed, and broadens the applicability of known N-fluid algorithms, allowing the use of in-simulation phase definitions that are more suitable for large density ratios among fluids.
The use of superviscous particles is investigated, where an N-fluid CG-LBM implementation is leveraged by using very viscous fluids to model solids. Wetting would then be mediated by the CG-LBM fluid-fluid interaction framework. The way CG-LBM maintains fluid-fluid interfaces is now also extended to the solid-fluid interfaces, and can lead to catastrophic spurious smearing of physical features.
Separately, recognizing the fundamental physical similarity of surface-tension across fluid-fluid and fluid-solid interfaces, wetting phenomena were simulated with additional fluid-fluid-like interactions near walls. This solid-phase perturbation approach was consistently formulated thanks to the new N-fluid CG-LBM theory developed earlier. Inaccuracies arise when these interactions are not paired with a diffuse fluid-solid interface, similar to those maintained between fluids in CG-LBM.
Sufficient results are obtained to motivate future development of solid-phase perturbation, which indeed describes solid-fluid and fluid-fluid surface-tensile interaction in a unified framework.