Breakup and wrapping of free surface within a laterally oscillating container: Effect of multimodal evolution of surface energy

This paper tries to analyze the behavior of liquid-air free-surface within a partially liquid filled rectangular container excited by lateral harmonic oscillation. The analysis is based on the results from full-scale numerical simulations, under various frequencies and amplitude of container oscillation, focusing on the evolution of the surface energy of the liquid-air interface. For the computational model, we consider liquid-air system initially at rest and filled up to a height (h) from the base inside a closed container, represented by a two-dimensional rectangular domain with dimensions W×H (W = 7 cm, H = 9 cm, h = 4 cm as the initial condition). The container is subjected to a lateral sinusoidal displacement-time pattern. The free-surface shape is captured using Compressive Interface Capturing Scheme for Arbitrary Meshes, with cell-based Courant number maintained below 0.25 for constancy. Also, we take the time-step sizes based on the frequency of oscillation such that at least 50 time-step points are available per cycle of oscillation. We observe time periodic evolution of surface energy where two modes of evolution can be identified. A primary mode with frequency twice the frequency of oscillating container, and secondary mode with frequency smaller than the primary mode. Existence of primary mode is found to be fundamental in all situations. For situations, where free-surface breakup and/or wrapping takes place, we observe the dominance of secondary mode(s) over the primary mode. This is a unique signature of demarcation between breakup and no-breakup regimes of free-surface behavior for the present situation.