N-Component Free Energy Lattice Boltzmann Method with Reduction Consistency and Global Momentum Conservation

TL;DR

This paper introduces a reduction consistent free energy lattice Boltzmann model for simulating multi-component fluid systems with exact momentum conservation, validated through various benchmark problems.

Contribution

It presents a novel discretization ensuring reduction consistency and global momentum conservation in multi-component fluid simulations.

Findings

Accurate simulation of liquid lenses and Janus droplets.

Excellent agreement with theoretical predictions in phase separation.

Successful demonstration on microfluidic emulsion generation.

Abstract

We present a free energy lattice Boltzmann model capable of simulating fluid systems with an arbitrary number of immiscible components in principle. Our method is strictly reduction consistent, ensuring that absent fluid components do not spontaneously nucleate. We introduce a novel discretization of the surface tension force that globally conserves momentum to machine precision, and we enforce reduction consistency through a flux correction that is independent of the mobility. The method is benchmarked with a range of static and dynamic problems, including: liquid lenses, Janus droplets, quaternary phase separation, and six-component layered Poiseuille flow, and we obtain excellent agreement with theoretical predictions throughout. Finally, we demonstrate the applicability of the proposed method through patterned liquid surfaces and microfluidic emulsion droplet generation.