# Drop Splashing on a Dry Smooth Surface

Original entry: Scott Tsai, APPHY 226, Spring 2009

"Drop Splashing on a Dry Smooth Surface"

Lei Xu, Wendy W. Zhang, and Sidney R. Nagel

PRL **94**, 184505 (2005)

## Soft Matter Keywords

Droplet, splashing, surface tension, viscosity

## Overview

(From paper)

The corona splash due to the impact of a liquid drop on a smooth dry substrate is investigated with highspeed photography. A striking phenomenon is observed: splashing can be completely suppressed by decreasing the pressure of the surrounding gas. The threshold pressure where a splash first occurs is measured as a function of the impact velocity and found to scale with the molecular weight of the gas and the viscosity of the liquid. Both experimental scaling relations support a model in which compressible effects in the gas are responsible for splashing in liquid solid impacts.

## Soft Matter Examples

Upon impact of a drop onto a solid surface, the drop either wets or splashes. Whether a drop wets or splashes on a surface is often said to depend on impact velocity, drop diameter, drop viscosity, and fluid surface tension. The authors here describe experiments which show that there is also a surrounding-pressure threshold to drop splashing on a smooth surface. In fact, they show that they can suppress splashes by lowering the pressure in the air surrounding the drop.

In their experiments, they use 3.4mm diameter drops, and drop them from heights ranging from 0.2 to 3.0m. They were able to vary the surrounding pressure from 1 to 100kPa. And they used drops of methanol, ethanol, and 2-propanol to vary the surface tension and viscosity of the fluid. As Fig. 1 shows, at 100kPa(standard atmospheric pressure), a 3.4mm diameter alcohol drop hitting the substrate at 3.74m/s will splash. However, the amount of splash decreases as the pressure of the surrounding air decreases. At a pressures of 30.00 and 17.2kPa, the splash is entirely suppressed. Figure 2 also shows the effect of surrounding pressure on threshold droplet impact velocity (threshold between wetting and splashing).

In their analysis, they focused on the restraining pressure of the surrounding gas on the spreading liquid upon impact (<math> \Epsilon_{G} </math>), which destabilizes the advancing front and pushes it up to initiate splash, and the surface tension of the liquid (<math> \Epsilon_{L} </math>) , which acts to pull the liquid together against splashing. By taking into account the compressibility of air, they show that <math> /Epsilon_{G} </math> is proportional to the gas density, speed of sound in the gas, and the expanding velocity of the liquid front. They also show that <math> /Epsilon_{L} </math> is essentially just the surface tension of the fluid, divided by the boundary layer thickness over the substrate.

Finally, they arrive at the following model:

<math> \Epsilon_{G} / \Epsilon_{L} = \sqrt{\gamma M_{G} P} \sqrt{\frac{RV_{o}}{2k_{B}T}} \frac{\sqrt{\nu_{L}}}{\sigma} </math>

Where <math> \gamma </math> is the adibatic constant of the gas, T is the temperature, <math> k_{B} </math> is Boltzmann's constant, R is the initial radius of the drop, <math> M_{G} </math> is the molar mass of the gas, P is the pressure in the gas, <math> V_{o} </math> is the impact velocity, <math> \nu_{L} </math> is the fluid viscosity, and <math> \sigma </math> is the surface tension of the fluid.

They plotted the model against the threshold impact velocity in Fig. 4.