Deformation and regimes of liquid column during water exit of a partially submerged sphere using the front-tracking lattice Boltzmann method

Abstract

When a solid sphere exits water at a given velocity, the liquid column is pulled out of a liquid reservoir. The present study focuses on the dynamic deformation of the liquid column and on the identification of the liquid column regime on the Weber number and dimensionless time (We-t*) map. The three-dimensional model of water exit has been established on the basis of the lattice Boltzmann method. A mass tracking algorithm was incorporated to capture the free surface, where the liquid–gas​ two-phase flow is simplified to a single-phase free surface flow. The surface tension is included by adding a perturbation term and the gravity as a body force is introduced in form of calculating the equilibrium distribution with an altered velocity. The contact angle condition in numerical simulation is not considered. The accuracy of the numerical results is demonstrated through the comparisons with the prior numerical and the experimental results in the literature. A parametric study has been conducted numerically on the radius and volume and of liquid column. Besides, the relationship between the pinch-off time of a liquid column and the Froude number has been obtained. Moreover, the evolution of the liquid column shape with a wide range of the Weber number and time scales are discussed based on the number of ligaments and droplets. The liquid column exhibits different characteristics and has been divided into three regimes. The transition between different regimes has been analyzed and the critical Weber number is given.