An alternate approach to simulate the dynamics of perturbed liquid drops

TL;DR

This paper introduces a spring-mass network model using neo-Hookean springs to simulate and analyze the complex polygonal oscillations of perturbed liquid drops, capturing their key features and revealing new dynamic behaviors.

Contribution

The study presents a novel simplified model that effectively reproduces polygonal oscillations and uncovers previously unobserved dynamics in perturbed liquid drops.

Findings

Model reproduces experimental polygonal oscillations

Network exhibits rotation and frequency relations

Unobserved dynamics are demonstrated

Abstract

Liquid drops when subjected to external periodic perturbations can execute polygonal oscillations. In this work, a simple model is presented that demonstrates these oscillations and their characteristic properties. The model consists of a spring-mass network such that the masses are analogous to liquid molecules and the springs are to intermolecular forces. Neo-Hookean springs are considered to represent these intermolecular forces. The restoring force of a neo-Hookean spring depends nonlinearly on its length such that the force of a compressed spring is much higher than the force of a spring elongated by the same amount. This is equivalent to the incompressibility of liquids, making these springs suitable to simulate the polygonal oscillations. It is shown that this spring-mass network can imitate most of the characteristic features of experimentally reported polygonal oscillations. Additionally, it is shown that the network can execute certain dynamics which so far have not been observed in a perturbed liquid drop. The features of dynamics which are observed in the perturbed network are: polygonal oscillations, rotation of network, numerical relations (rational and irrational) between the frequencies of polygonal oscillations and the forcing signal, and the dependency of the shape of the polygons on the parameters of perturbation.