Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach

Area of Science:

• Computational fluid dynamics
• Soft matter physics
• Surface science

Background:

• Standard lattice Boltzmann methods are limited to Cartesian grids, hindering studies on curved surfaces.
• Investigating fluid interfaces and their dynamics on complex geometries is crucial for understanding various physical phenomena.

Purpose of the Study:

• To develop and implement a versatile finite difference lattice Boltzmann scheme for multicomponent flows on arbitrary curved surfaces.
• To analyze the behavior of fluid droplets and stripes on a torus, including their migration patterns and equilibrium configurations.
• To simulate and compare the phase separation dynamics of binary fluids on curved surfaces versus flat surfaces.

Main Methods:

• Coupling continuity, Navier-Stokes, and Cahn-Hilliard equations.
• Utilizing a vielbein formalism to adapt the Boltzmann equation for arbitrary geometries.
• Employing a finite difference method to solve the evolution of fluid distribution functions.

Main Results:

• Demonstrated opposite migration of fluid droplets (outward) and stripes (inward) on a torus.
• Identified unique and bistable global minimum configurations for fluid stripes based on width.
• Validated simulation results against analytical predictions for Laplace pressure and oscillatory motion.
• Observed differences in phase separation dynamics between curved (torus) and flat surfaces.

Conclusions:

• The developed finite difference lattice Boltzmann scheme effectively handles multicomponent flows on curved surfaces.
• The study provides new insights into the behavior of fluid interfaces on toroidal geometries.
• The scheme's adaptability allows for extension to other surfaces and coupling with additional dynamical equations for broader applications.