Smoothed boundary method modified phase-field lattice Boltzmann study of solidification dynamics of wetting droplet on a cold substrate

Droplet solidification on cold substrates plays a vital role in applications from anti-icing to material processing. In this paper, we propose a comprehensive multiphase model that integrates the phase-field method, the enthalpy-based method, and the lattice Boltzmann method. The governing equations for droplet solidification are reformulated using the smoothed boundary method to efficiently handle complex boundary conditions. The model is rigorously validated against analytical solutions and benchmark cases, demonstrating accurate capture of interface evolution, volume change, and heat–mass coupling. Numerical investigations reveal that the final droplet morphology is governed by the solid–liquid density ratio, forming a sharp tip due to expansion or a flattened plateau due to contraction. Increased gas-phase thermal diffusivity promotes early top-shell formation, altering solidification kinetics, while larger contact angles delay solidification and enhance apical curvature. This work provides a robust computational framework for strongly coupled solidification phenomena in complex geometric and physical environments.