# Splashing on elastic membranes: The importance of early-time dynamics

"Splashing on elastic membranes: The importance of early-time dynamics"

Rachel E. Pepper, Laurent Courbin, and Howard A. Stone

Physics of Fluids 20, 082103 (2008)

## Soft Matter Keywords

Splashing, membrane, droplet, lamella, surface tension, interface, wettability, soft substrates.

## Overview

(From paper)

We study systematically the effect of substrate compliance on the threshold for splashing of a liquid drop using an elastic membrane under variable tension. We find that the splashing behavior is strongly affected by the tension in the membrane and splashing can be suppressed by reducing this tension. The deflection of the membrane upon droplet impact is measured using a laser sheet, and the results allow us to estimate the energy absorbed by the film upon drop impact. Measurements of the velocity and acceleration of the spreading drop after impact indicate that the splashing behavior is set at very early times after, or possibly just before, impact, far before the actual splash occurs. We also provide a model for the tension dependence of the splashing threshold based on the pressure in the drop upon impact that takes into account the interplay between membrane tension and drop parameters.

## Soft Matter Examples

The authors of this paper describe their study of liquid droplet impacting on a soft substrate. They emphasize that it is important to understand splashing on soft substrates because there are many common industrial applications such as spray cooling of flexible surfaces, and examples in nature, such as raindrops falling on leaves, that can be modeled as liquid drops falling on a soft substrate.

Splashing is often defined as when satellite droplets are formed and ejected out of the rim that formed after a primary droplet impacts a solid surface. In the splashing literature an empirical relationship between the Weber and Reynolds numbers is often cited for the transition from spreading to splashing upon droplet impact.

$We^{1/2}Re^{1/4}=K$

Where the Weber number, We is defined as $2 \rho R_{o} V_{o}^2 / \gamma$. And the Reynolds number, Re is defined as $2 \rho R_{o} V_{o} / \mu$.

The authors did a series of experiments where they showed that as the tension in the substrate (substrate tension) decreases, the threshold velocity for splashing increases.