A Quantitative Comparison of Physical Accuracy and Numerical Stability of Lattice Boltzmann Color Gradient and Pseudopotential Multicomponent Models for Microfluidic Applications

The performances of the Color-Gradient(CG)and the Shan-Chen(SC)multicomponent Lattice Boltzmann models are quantitatively compared side-by-side on multiple physical flow problems where breakup,coalescence and contraction of fluid ligaments are important.The flow problems are relevant to microfluidic applications,jetting of microdroplets as seen in inkjet printing,as well as emulsion dynamics.A significantly wider range of parameters is shown to be accessible for CG in terms of density-ratio,viscosity-ratio and surface tension values.Numerical stability for a high density ratio O(1000)is required for simulating the drop formation process during inkjet printing which we show here to be achievable using the CG model but not using the SC model.Our results show that the CG model is a suitable choice for challenging simulations of droplet formation,due to a combination of both numerical stability and physical accuracy.We also present a novel approach to incorporate repulsion forces between interfaces for CG,with possible applications to the study of stabilized emulsions.Specifically,we show that the CG model can produce similar results to a known multirange potentials extension of the SC model for modelling a disjoining pressure,opening up its use for the study of dense stabilized emulsions.

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 simulating the droplet-on-demand inkjetting process on a micrometer length scale by comparing it to the Arbitrary Lagrangian Eulerian Finite Element Method(ALE-FEM).A full jetting cycle is simulated using both CG-CM and ALE-FEMand results are quantitatively 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 utilizing asymmetric wetting conditions inside the jet-nozzle.This allows for systematic investigation into the physics of asymmetric jetting,e.g.due to jet-nozzle manufacturing imperfections or due to other disturbances.

Effective Force Stabilising Technique for the Immersed Boundary Method

The immersed boundary method has emerged as an efficient approach for the simulation of finite-sized solid particles in complex fluid flows.However,one of the well known shortcomings of the method is the limited support for the simulation of light particles,i.e.particles with a density lower than that of the surrounding fluid,both in terms of accuracy and numerical stability.Although a broad literature exists,with several authors reporting different approaches for improving the stability of the method,most of these attempts introduce extra complexities and are very costly from a computational point of view.In this work,we introduce an effective force stabilizing technique,allowing to extend the stability range of the method by filtering spurious oscillations arising when dealing with light-particles,pushing down the particle-to-fluid density ratio as low as 0.04.We thoroughly validate the method comparing with both experimental and numerical data available in literature.