Three-Dimensional Lbm Simulation of Oscillations of a Pendent ‎Growing Drop‎

In this work, the force-displacement equation and non-linear threedimensional oscillations of a pendant drop are investigated numerically. The presented novel force-displacement function allows following the dynamics of a pendant drop and realizing its elastic behavior. The growth and detachment of drop, which is pending due to gravity from a capillary tip, is considered (assuming high density and high viscosity ratios and immiscible two-phase flows). The three-dimensional multirelaxation time lattice Boltzmann method (MRT-LBM) was used to simulate the growth, detachment, and oscillations of the drop. It was realized that the growing drop shows three different elastic behaviors simultaneously (hardening, linear, and softening). It was shown that the growing drop has oscillatory acceleration (in the direction of flow). The acceleration had a maximum dimensionless amplitude of about 35 and a dimensionless frequency of about 40. It was concluded that drop generates acoustic waves upstream while growing. Although the flow was in the gravity direction, low amplitude transverse oscillations with the dimensionless frequency of 500 to 800 were detected during the drop growth.