Lattice Boltzmann method for thin-liquid-film hydrodynamics

Area of Science:

• Fluid dynamics
• Computational physics
• Materials science

Background:

• Numerical simulations are crucial for understanding complex fluid behaviors.
• Thin-film flows present unique challenges due to their small scales and surface tension effects.
• Existing methods may struggle with complex geometries and boundary conditions.

Purpose of the Study:

• To develop and validate a novel numerical approach for thin-film flow simulations.
• To apply the method to key fluid dynamics problems including instability and droplet dynamics.
• To demonstrate the method's capability in handling heterogeneous and complex substrates.

Main Methods:

• Lattice Boltzmann Method (LBM) adapted for thin-film flow dynamics.
• Validation against established thin-film equations and physical laws (e.g., Cox-Voinov law).
• Application to benchmark problems: Rayleigh-Taylor instability, sessile drop spreading, droplet sliding, and dewetting on structured surfaces.

Main Results:

• The LBM approach successfully recovers expected thin-film equations in relevant limits.
• Accurate prediction of sessile drop spreading, Cox-Voinov law adherence, and slip length effects.
• Linear scaling of Capillary number with Bond number for sliding droplets, matching experimental findings.
• Demonstrated control over dewetting on chemically patterned substrates.

Conclusions:

• The proposed lattice Boltzmann method is a robust and versatile tool for simulating diverse thin-film flows.
• The method accurately captures complex interfacial phenomena and substrate interactions.
• It offers a promising avenue for investigating microfluidic devices and advanced material applications.