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Rennick, M., Zhang, X., Kusumaatmaja, H. Coarsening Dynamics of N-Component Phase Separation: Implications of the Four-Color Theorem (manuscript in preparation)

Rennick, M., Zhang, X., Kusumaatmaja, H.  N-Component Lattice Boltzmann Model With Low Spurious Velocity (manuscript in preparation)

We developed a diffuse solid method that is versatile and accurate for modeling wetting and multiphase flows in highly complex geometries. In this scheme, we harnessed N+1-component phase field models to investigate interface shapes and flow dynamics of N fluid components, and we optimized how to constrain the evolution of the component employed as the solid phase to conform to any pre-defined geometry. Implementations for phase field energy minimization and lattice Boltzmann method are presented. Our approach does not need special treatment for the fluid–solid wetting boundary condition, which makes it simple to implement. To demonstrate its broad applicability, we employed the diffuse solid method to explore wide-ranging examples, including droplet contact angle on a flat surface, particle adsorption on a fluid–fluid interface, critical pressure on micropillars and on Salvinia leaf structures, capillary rise against gravity, Lucas-Washburn's law for capillary filling, and droplet motion on a sinusoidally undulated surface. Our proposed approach can be beneficial to computationally study multiphase fluid interactions with textured solid surfaces that are ubiquitous in nature and engineering applications.

Oktasendra, F., Rennick, M., Avis, S., Panter, J., Kusumaatmaja, H. The Diffuse Solid Method for Multiphase Fluid Simulations in Complex Geometries, Physics of Fluids 34, 112113 (2025)