Multicomponent Flow on Curved Surfaces: A Vielbein Lattice Boltzmann Approach
arXiv:1904.10070 · doi:10.1103/PhysRevE.100.063306
Abstract
We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. Standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write down the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focussing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of a torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.
References in corpus (22)
- Topology and Dynamics of Active Nematic Vesicles
- Symmetry-breaking in drop bouncing on curved surfaces
- Inertial effects in three dimensional spinodal decomposition of a symmetric binary fluid mixture: A lattice Boltzmann study
- Lattice Boltzmann Simulations of Liquid Crystal Hydrodynamics
- Stick-Slip Sliding of Water Drops on Chemically Heterogeneous Surfaces
- Breakdown of scale-invariance in the coarsening of phase-separating binary fluids
- Ternary Free Energy Lattice Boltzmann Model with Tunable Surface Tensions and Contact Angles
- Ternary free-energy entropic lattice Boltzmann model with high density ratio
- Lattice Boltzmann study on Kelvin-Helmholtz instability: the roles of velocity and density gradients
- Dynamical patterns in active nematics on a sphere
- Aging and rejuvenation of active matter under topological constraints
- A Symmetric Free Energy Based Multi-Component Lattice Boltzmann Method
- Hybrid Lattice Boltzmann/Finite Difference simulations of viscoelastic multicomponent flows in confined geometries
- Conservative 3+1 General Relativistic Boltzmann Equation
- Phase ordering of two-dimensional symmetric binary fluids: a droplet scaling state
- Lattice Boltzmann simulation of mixtures with multicomponent van der Waals equation of state
- Corner transport upwind lattice Boltzmann model for bubble cavitation
- Lattice Boltzmann models based on the vielbein formalism for the simulation of flows in curvilinear geometries
- Interface geometry of binary mixtures on curved substrates
- Multiphase lattice Boltzmann simulations for porous media applications -- a review
- Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature
- Phase Separation on Bicontinuous Cubic Membranes: Symmetry Breaking, Re-entrant and Domain Facetting