Mass correction approach to reduce the droplet spontaneous shrinkage in free-energy-based lattice Boltzmann method

The free-energy-based lattice Boltzmann method has emerged as a reliable tool for simulating multiphase flows, but its application to small droplet interactions with surrounding flows is hindered by the issue of spontaneous droplet shrinkage. In contrast to previous analyses based on phase-field theory, we investigate spontaneous droplet shrinkage within the framework of the lattice Boltzmann equation for a free-energy-based model and identify that local density continues to evolve even after the system reaches equilibrium. To address this undesired density evolution, we introduce a mass correction formulated as a Laplacian term, ensuring that local mass conservation is improved without sabotaging global mass conservation. Numerical tests in several three-dimensional scenarios demonstrate that the proposed mass correction effectively mitigates droplet shrinkage and maintains droplet volume, without adversely affecting other aspects of the simulation, such as numerical stability, mass conservation, and flow velocity evolution.