[Paper Review] Supressed splashing on elastic membranes

Marise V. Gielen, Riëlle de Ruiter+2 more|arXiv (Cornell University)|Nov 15, 2017

Fluid Dynamics and Heat Transfer22 references3 citations

TL;DR

This study experimentally investigates how elastic membranes suppress drop splashing by measuring membrane deformation via laser profilometry and correlating it with splashing thresholds. The authors propose a modified splashing criterion that incorporates membrane deformation dynamics, showing quantitatively that delayed sheet ejection due to elastic energy absorption increases the splashing threshold, with good agreement between model and data using a single fitting parameter.

ABSTRACT

The dynamics of drop impact on solid surfaces can be changed significantly by tuning the elasticity of the solid. Most prominently, the substrate deformation causes an increase in the splashing threshold as compared to impact onto perfectly rigid surfaces, and can thus lead to splash suppression. Here, we experimentally determine the splashing threshold for impact on thin membranes as a function of the tension in the membrane and its elastic properties. The drop dynamics is correlated to the membrane deformation, which is simultaneously measured using a laser profilometry technique. The experimental results enable us to adapt current models for splashing, showing quantitatively how substrate deformation alters the splashing threshold.

Motivation & Objective

• To determine how membrane elasticity and tension influence the splashing threshold of impacting drops.
• To measure membrane deformation dynamics in real time using laser profilometry during drop impact.
• To interpret the observed suppression of splashing in terms of delayed ejecta sheet formation due to substrate deformation.
• To adapt the recent gas-drag-based splashing criterion (Riboux & Gordillo, 2014) by incorporating membrane deformation timescales.
• To validate the modified model against experimental data across varying membrane tensions.

Proposed method

• A thin elastic membrane (13 ± 0.5 µm thick) was mounted on a Teflon frame and subjected to drop impacts at controlled velocities.
• Side-view high-speed imaging captured drop impact dynamics and splashing behavior.
• Laser profilometry measured the temporal evolution of membrane deformation with sub-micron resolution.
• Two key deformation metrics were extracted: membrane deformation velocity (scaling with impact velocity) and maximum deformation (scaling with momentum conservation).
• The splashing threshold was determined as a function of membrane tension and impact velocity.
• A modified splashing criterion was derived by replacing the sheet ejection timescale in the Riboux & Gordillo (2014) model with the sum of sheet ejection time and membrane deformation time, introducing a fitting parameter $ c_t $.

Experimental results

Research questions

• RQ1 How does membrane tension affect the splashing threshold of impacting drops?
• RQ2 What is the role of membrane deformation dynamics in suppressing splashing?
• RQ3 Can the recent gas-drag-based splashing criterion (Riboux & Gordillo, 2014) be adapted to account for elastic substrate deformation?
• RQ4 How do the membrane’s deformation velocity and maximum displacement scale with impact velocity and tension?
• RQ5 What is the quantitative relationship between membrane deformation and the delay in ejecta sheet formation?

Key findings

• The splashing threshold increases with decreasing membrane tension, indicating effective splash suppression on softer membranes.
• Membrane deformation velocity scales quadratically with impact velocity up to the splashing threshold, suggesting a critical deformation rate beyond which splashing occurs.
• Maximum membrane deformation is well described by a momentum-conservation-based scaling law, validating the model’s physical consistency.
• The modified splashing criterion, incorporating both sheet ejection and membrane deformation timescales, shows good quantitative agreement with experimental data using $ c_t = 0.07 $.
• The critical splashing number $ C hickapprox 0.0093 $, derived from rigid substrate measurements, remains valid when applied to elastic membranes, indicating robustness of the gas-drag-based framework.
• The model successfully captures the trend of increasing splashing threshold with reduced membrane elasticity, even without direct measurement of sheet ejection time due to occlusion by deformation.