Simulating drop formation at an aperture by means of a Multi-Component Pseudo-Potential Lattice Boltzmann model

The growth and release of a pendent liquid droplet with the complex motion of the phase interface as a result of a liquid flow from an aperture has been studied by means of a Multi-Component Pseudo-Potential Lattice Boltzmann method. In this method, automatic component separation is attained by means of the Shan and Chen (1993) interaction strength G. We demonstrate that droplet formation can satisfactorily be described by combining three elements: using two components alpha and beta (of the same density and viscosity), the G-driven separation of alpha and beta, and gravity working on just alpha such that it becomes heavy and behaves as a liquid, while the gravity-free beta mimics a gas. We present several time sequences of the growth and release of a pendent liquid droplet. Although the simulations were just 2-D, the dynamics of the necking, the tear shape of the droplet, and the motion of the apex after pinch-off all qualitatively agree with literature. The results are interpreted in terms of non-dimensional Bond, Ohnesorge and Archimedes numbers. We find convincing agreement between the relationships derived by dimensional analysis and the numerical simulations.