Splashing of liquid droplets upon impact on a solid surface has been investigated for over a century. A long-lasting pursuit of finding the parameters governing the splashing transition identified factors ranging from the droplet impact speed to the roughness of the impacted surface to the pressure of the surrounding gas (see, e.g., the work by our colleagues Sid Nagel and Wendy Zhang).

More recently, there has also been a growing interest in what happens to the spreading and splashing if particles are added to the liquid or when a non-Newtonian fluid is used. On micron scales, ZrO2 suspensions have been used in studies aiming to optimize ink-jet printing applications, and on truly macroscopic scales there has been the development of 3D printers that dispense cement slurry. In all of these situations, an important concern is to prevent splashing, and particles from escaping, when droplets hit a surface. However, the question of when and why particles are ejected has remained unsettled.

We investigate the impact of droplets of dense suspensions onto a solid substrate. We show that

a global hydrodynamic balance is unable to predict the splash onset and propose to replace it by an energy balance at the level of the particles in the suspension. We experimentally verify that the resulting, particle-based Weber number gives a reliable, particle size and density dependent splash onset criterion. We further show that the same argument also explains why in bidisperse systems smaller particles are more likely to escape than larger ones.

1. •Ivo R. Peters, Qin Xu, and Heinrich M. Jaeger, “Splashing Onset in Dense Suspension Droplets”, Phys. Rev. Lett. 111, 028301 (2013), pdf file
   

The images above are stills from high-speed videos. They show the splats right after impact and are produced by dense suspensions of ZrO2 particles in water that are dropped onto a smooth glass plate. Outcomes are shown for different droplet radii r_d (see text above the images) and particle radii: (a-i) r_p = 362 µm, (j-l) rp = 138 µm, (m-s) rp = 78 µm. Images (a-o) are organized in vertical columns, with drop impact speed and impact parameter K increasing from top to bottom in order to bracket the onset of splashing, defined here as the ejection of individual particles. For the K values listed in the top/middle/bottom rows we never/sometimes/always observed particle ejection. The blurred background in (a) and (b) is the out-of-focus image of the syringe. We note that (o) has been thresholded and dilated in order visualize the ejected particles that would otherwise be invisible due to their small size. (p,q) side and bottom view of a droplet that does not splash (We_p = 12). (r,s) side and bottom view of a splashing droplet (We_p = 26). The scale bar in the images is 5 mm, images (a-o) all have the same scale.