Wetting boundary conditions for multiphase LBMs
As part of his doctoral work, Andreas Hantsch and I used the moment-based boundary condition philosophy to implement wetting conditions for a Lee-Fischer model. The method allows for density ratios of approximately 200000 for small departures from neutral wetting and the achievable density ratio remains of the order 100 for all but the most extreme contact angles.
Colour gradient LBMs
There are many classes of multiphase lattice Boltzmann methods, as discussed in this review article. I have been most interested in extensions to the Rothman-Keller lattice gas models, the so-called “colour gradient” models. This is because they aim to preserve narrow (but finite) phase boundaries and claim to be able to set the surface tension a priori. They are motivated by applications of multiphase flow in porous media and microfluidic applications, where a numerical tool that can maintain sharp transition regions in surface tension dominated flows is highly desirable .
As part of my doctoral work, Prof. Tim Phillips and I reconstructed the colour gradient model to ensure it furnishes the multiphase Navier-Stokes equations with the interfacial capillary tensor. This model has been published here. This model has since reported favourable predications in comparison with other models, as discussed here, and here, for example, and has been successfully applied to a variety of industrially-relevant flows. I am currently working on improving similar models – more about this soon!