Implementation of a ternary lattice Boltzmann model in LAMMPS

The properties of multicomponent fluids are governed by the interplay of phase behavior, fluid dynamics, and interfacial thermodynamics. A mixture formulation that leverages this interplay is an important aspect in many fabrication processes based on emulsion templating. The lattice Boltzmann method (LBM) has become a popular approach for simulating hydrodynamic effects in complex fluids and soft matter. Here we present an implementation of a ternary lattice Boltzmann model that allows to simulate a mixture of three immiscible fluids. We build on the LATBOLTZ extension of the open-source package LAMMPS and implement a ternary free energy model recently introduced by Semprebon et al. [Phys. Rev. E 93, 033305 (2016)]. We validate the static and dynamic properties by simulating liquid lenses, double emulsions, and ternary mixtures. From the simulations, we obtain the complete morphology diagram of the ternary mixture in composition space. We further discuss an application of the method to phase segregation of ternary films. The implementation of the ternary LBM in LAMMPS opens vast opportunities for mesoscale simulations of interfacial phenomena and non-equilibrium transport processes in multicomponent fluid mixtures. Program summary: Program Title: fix lb/multicomponent CPC Library link to program files: https://doi.org/10.17632/gn8znmyxrh.1 Developer's repository link: https://github.com/uschille/lammps/tree/ternary-lbm Licensing provisions: GPLv2 Programming language: C++ Journal reference of previous version: C. Denniston, N. Afrasiabian, M.G. Cole-André, F.E. Mackay, S.T.T Ollila, T. Whitehead. LAMMPS lb/fluid fix version 2: Improved hydrodynamics forces implemented into LAMMPS through a lattice-Boltzmann fluid. Comput. Phys. Commun. 275, 108318 (2022). Does the new version supersede the previous version?: No Reasons for the new version: The lb/multicomponent fix provides new capabilities for simulating ternary fluid mixtures. Summary of revisions: An implementation of the ternary free-energy lattice Boltzmann model [1] has been added to the LATBOLTZ extension of LAMMPS. The new functionality is available through the script command fix lb/multicomponent. Nature of problem: Multicomponent fluids involve non-local interactions that give rise to fluid-fluid surface tension and a non-ideal pressure tensor. This requires a modification of the standard lattice Boltzmann method. Solution method: The implementation extends the existing lattice Boltzmann code in LAMMPS [2] and introduces data structures and methods for the ternary algorithm introduced in [1]. The code carries out the streaming and collision steps for three fluid components using the appropriate equilibrium distributions. The equilibrium distribution is calculated based on thermodynamic quantities derived from the free energy. Additional comments including restrictions and unusual features: The current version of the lb/multicomponent fix is restricted to the D3Q19 lattice. References: [1] C. Semprebon, T. Krüger, H. Kusumaatmaja. Ternary free-energy lattice Boltzmann model with tunable surface tensions and contact angles. Phys. Rev. E 93, 033305 (2016). [2] C. Denniston, N. Afrasiabian, M. G. Cole-André, F. E. Mackay, S. T. T. Ollila, T. Whitehead. LAMMPS lb/fluid fix version 2: Improved hydrodynamic forces implemented into LAMMPS through a lattice-Boltzmann fluid. Comput. Phys. Commun. 275, 108318 (2022).