Controlled Deposition of Droplets

Splashing of droplets containing small suspended particles

The study of the impact and splashing of liquid droplets has a long history. Suspending small, solid particles inside the liquid can fundamentally change the impact dynamics.  Simpler and easier to control than that of pure liquids, the impact dynamics of concentrated suspensions opens up new possibilities for material deposition applications, including coating and additive manufacturing.

Before impact, the suspension droplet is confined purely by surface tension, and the strength of this confinement is tested when the droplet hits a solid surface. Upon impact, this droplet can spread out, or splash through the ejection of particles, or at the limit of high-impact speeds spread out into a monolayer. Because the impact causes strong deformation on a short time scale, the non-Newtonian behavior of the suspension is expected to play a large role.  

The combined experiments (Jaeger) & simulations (Zhang) show that particles at surface are key.   The splash, no-splash & bounce regimes can be delineated as function of 2 parameters:  Wep and St, and the resulting model offers a surprise: bouncing due to strong viscous drag limits (plastic) droplet deformation.

"From splashing to bouncing:  The influence of viscosity on the impact of suspension droplets on a solid surface," Martin H. Kelin Schaarsberg, Ivo R. Peters, Menachem Stern, Kevin Dodge, Wendy W. Zhang, and Heinrich M. Jaeger, Phys. Rev. E 93, 062609 (2016).




Snapshots of suspension droplets impacting on a glass substrate. (a)–(c) Side views.


Splashing state diagram with the particle-based Weber number and the Stokes number. Data delineate the transition. Error bars give the width of the transition region.  The experiments where we have observed bouncing motion are indicated with black triangles. The figure shows a limiting case represented by the horizontal dashed line, for St∞, where the splashing onset becomes independent of the Stokes number.  


Snapshots from the numerical simulation of two-dimensional suspension droplets at different Stokes numbers (all at infinite Weber number; only the suspended particles are rendered, and the liquid is not shown). Time after impact increases from top to bottom with t0 the moment of impact. Colors indicate the vertical velocity component of individual particles. St0.25 shows a bounce, along with a significant amount of rotation.