Lattice Boltzmann simulation of interfacial dynamics induced by vertical vibrational force

Two-phase flows with deformable interfaces under vibrational forcing arise in many engineering and geophysical applications, yet their simulation within the lattice Boltzmann framework remains largely unexplored. In particular, harmonic vertical vibrational forcing has not previously been incorporated explicitly into the lattice Boltzmann method. In the present work, lightweight modification of the phase-field lattice Boltzmann method is introduced to account for harmonic vertical vibrations acting on an extended deformable interface between immiscible fluids. Simulations are performed for a wide range of density and kinematic viscosity ratios. Simulations of the Rayleigh–Taylor instability demonstrate that vertical vibrations modify the characteristic wavelength of the most unstable perturbations. Without vibrations, the instability develops at the largest available scale, whereas vibrational forcing shifts the dominant wavelength toward shorter scales, indicating partial stabilization of long-wave modes. It is also shown that vertical vibrations can generate gravity–capillary waves at an initially flat interface. The predicted wavelengths agree well with the analytical dispersion relation. As vibrational acceleration increases, the wave amplitude grows until the wave-based description breaks down. Furthermore, sufficiently strong vibrational forcing can produce macroscopic phase redistribution, including upward transport of the heavier fluid against gravity. Both single-droplet dynamics and collective motion of a fluid layer are investigated, revealing a threshold vibrational parameter corresponding to the transition from interfacial oscillations to global fluid motion. For conditions close to experiments, the results indicate the possibility of vibrational stabilization of liquid layers and multilayer structures.