Comparison of Lattice Boltzmann, Finite Element and Volume of Fluid Multicomponent Methods for Microfluidic Flow Problems and the Jetting of Microdroplets

We show that the lattice Boltzmann method (LBM) based color-gradient model with a central moments formulation (CG-CM) is capable of accurately simu-lating the droplet-on-demand inkjetting process on a micrometer length scale by com-paring it to the Arbitrary Lagrangian Eulerian Finite Element Method (ALE-FEM). A full jetting cycle is simulated using both CG-CM and ALE-FEM and results are quanti-tatively compared by measuring the ejected ink velocity, volume and contraction rate. We also show that the individual relevant physical phenomena are accurately captured by considering three test-cases; droplet oscillation, ligament contraction and capillary rise. The first two cases test accuracy for a dynamic system where surface tension is the driving force and the third case is designed to test wetting boundary conditions. For the first two cases we also compare the CG-CM and ALE-FEM results to Volume of Fluid (VOF) simulations. Comparison of the three methods shows close agreement when compared to each other and analytical solutions, where available. Finally we demonstrate that asymmetric jetting is achievable using 3D CG-CM simulations uti-lizing asymmetric wetting conditions inside the jet-nozzle. This allows for systematic investigation into the physics of asymmetric jetting, e.g. due to jet-nozzle manufactur-ing imperfections or due to other disturbances.