Droplet impact onto a spring-supported plate: analysis and simulations

TL;DR

This study investigates droplet impact on a spring-supported plate using analytical and numerical methods, revealing how system parameters influence oscillations and fluid dynamics during impact.

Contribution

It introduces a combined analytical and numerical framework to model droplet impact on flexible supports, enhancing understanding of fluid-structure interaction effects.

Findings

Plate mass and spring stiffness significantly affect oscillation behavior.

Hydrodynamic pressure distribution is altered by plate motion.

Hybrid modeling improves analysis across multiple scales.

Abstract

The high-speed impact of a droplet onto a flexible substrate is a highly nonlinear process of practical importance which poses formidable modelling challenges in the context of fluid-structure interaction. We present two approaches aimed at investigating the canonical system of a droplet impacting onto a rigid plate supported by a spring and a dashpot: matched asymptotic expansions and direct numerical simulation (DNS). In the former, we derive a generalisation of inviscid Wagner theory to approximate the flow behaviour during the early stages of the impact. In the latter, we perform detailed DNS designed to validate the analytical framework, as well as provide insight into later times beyond the reach of the proposed mathematical model. Drawing from both methods, we observe the strong influence that the mass of the plate, resistance of the dashpot and stiffness of the spring have on the motion of the solid, which undergoes forced damped oscillations. Furthermore, we examine how the plate motion affects the dynamics of the droplet, predominantly through altering its internal hydrodynamic pressure distribution. We build on the interplay between these techniques, demonstrating that a hybrid approach leads to improved model and computational development, as well as result interpretation, across multiple length- and time-scales.