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

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