You spilled your coffee, a terrible accident or an opportunity to start noticing?
Why do some droplets splash while others stay, well, drop like? It turns out that there is some surprising physics at play here. When a drop of water, or coffee, falls from a height and onto a flat surface (such as glass), we are accustomed to seeing the droplet fracture into a type of crown of smaller droplets that form a mess over the surface. Visually spectacular, these splashing droplets have even been made into an art form (here).
Fast frame-rate photography reveals how each micro-droplet breaks away from the splashing drop:
Video taken from Vimeo – “Drop impact on a solid surface”, a review by Josserand and Thoroddsen.
So it perhaps surprising to discover that there are many things about this process that we do not yet understand. Firstly, if you reduce the gas pressure that surrounds the drop as it falls, it does not make a splash. In the extreme, this means that if you were to spill your coffee in a vacuum, you would not see the crown-like splashing behaviour that we have come to expect of falling liquids. Rather than splash, a droplet falling in low pressure spreads out on impact as a flattening droplet. This counterintuitive result was first described in a 2005 study (here) that compared the effect on splashing of droplets with different viscosities (methanol, ethanol, 2-propanol) falling through different gasses.
But would a latte splash more or less than a long black?
The authors of the study ruled out the effect of air entrapment surrounding the droplet as it falls as high speed photography had not indicated any air bubbles in the droplet just before impact. Instead they considered that whether a drop splashes on impact – or not – depended on the balance between the surface tension of the falling liquid and the stress on the drop created by the restraining pressure of the surrounding gas. Calculating these stresses led to a second surprising result. Whether a drop splashes on impact or not depends on its viscosity (as well as the gas pressure and the speed of impact). But the surprising bit is that the more viscous the liquid, the greater the splash.
From a common-sense perspective (that may or may not have any bearing on the reality of the situation), an extremely viscous liquid like honey should not splash as much as a less viscous liquid like coffee. This suggests that there is an upper-limit in viscosity to the relation predicted in the 2005 study. After all, although the authors did change the viscosity of the liquids, the range of viscosity they studied was not as great as the difference between coffee and honey. This sounds like a perfect experiment for some kitchen-top science and so if any reader can share the results of their experiments on the relative splashes formed by coffee and honey, I would love to hear of them.