Investigation of deformation and breakup of a falling droplet using a multiple-relaxation-time lattice Boltzmann method

In this paper, a multi-relaxation-time lattice Boltzmann method for multiphase flows is employed to simulate different modes of deformation and fragmentation of an axisymmetric falling droplet under buoyancy force. To show the accuracy of the model, the Laplace law for stationary drops is conducted first. Then, drop deformation and breakup in a free fall is studied in an axially symmetric pipe. Surface tension effects as well as impacts of gas and drop viscosities are investigated for a wide range of Eötvös, Morton, and Archimedes numbers. The drag coefficient of the drop, as it falls, is measured and compared to the empirical correlations, and reasonable agreement is shown. The findings are further verified by comparing a typical bag breakup mechanism with experimental observations. It is seen that at low Eötvös numbers the drop deforms slightly and reaches a steady state. Increase of Eötvös number enhances the rate of deformation, and at a high enough Eötvös value breakup of the drop happens. While the gas viscosity is shown to have a trivial effect on the breakup of the droplet, drop viscosity is the overriding factor in the mechanism of disintegration. Consequently, various breakup modes of the falling droplet are observed just by varying the drop-based Archimedes number. By capturing different breakup mechanisms of a falling droplet such as bag breakup, shear breakup, and, particularly, multimode breakup, the present lattice Boltzmann method exhibits an excellent superiority over the sharp interface tracking schemes that fail to capture dissociation of the interface.