Splashing. How does a drop of liquid splash when it hits a smooth dry solid surface? Our intuition tells us it must splash and eject thousands of tiny droplets.  We would expect the same behavior anywhere - here on Earth, on Mars and on the Moon. We would be wrong! In collaboration with Wendy Zhang, we have found that we can suppress splashing completely by removing the surrounding atmosphere.  A drop which splashes in Chicago would not necessarily splash on the top of Mt. Everest where the pressure is less and would definitely not splash on the Moon which has no atmosphere.

Recently, we discovered the splashing of a liquid drop on impact with a dry, smooth substrate is a strongly air-dependent phenomena. We find at sufficiently low pressures, splashing can be completely suppressed, even for highest impact velocities we can achieve (about 8 m/s).

1 atm

0.2 atm

Singularities in Free-surface Flows.  A drop falling from a faucet is a common example of a liquid fissioning into two or more pieces.  The cascade of structure that is produced in this process is of uncommon beauty.  As the drop falls, a long neck, connecting two masses of fluid, stretches out and then breaks.  What is the shape of the drop at the instant of breaking apart? Something dire must happen to the mathematical description of the liquid at that point since the drop undergoes a topological transition where it starts out as a single, connected fluid and ends up in two or more separate pieces.  This is an example of a finite-time singularity since the drop breakup occurs a short time after the drop becomes unstable and starts to fall. At the transition, a singularity occurs since the radius of the neck holding the drop to the nozzle becomes vanishingly thin.  As its radius goes to zero, the curvature diverges and the surface tension forces become infinite.  How can such dramatic dynamics occur in something which had such smooth and innocuous initial conditions and forcing terms?  Using photographic techniques, we have been studying transitions such as these to understand how the non-linearities in the governing equations (in this case the Navier-Stokes equations) can be tamed and understood.  Singularities of this kind occur in many areas of physics from stellar structure to turbulence to bacterial colony growth.  This drop breakup problem is one of the simplest places to start an experiment that directly probes the singularity itself. In collaboration with Wendy Zhang, we have uncovered a variety of different singularities - some of which surprisingly retain a memory of their initial conditions throughout the entire breakup process.

The break-up of an air bubble in water.  Recent experiments have shown that air bubble break up exhibits memory of its initial condition until the moment of pinch off.  This is in stark contrast with the break up of water in air (a dripping faucet) and many other generic pinch off phenomena, which completely forgot their initial conditions near the break up.

  1. •“Memory-encoding vibrations in a disconnecting air bubble”, L. Schmidt, N.C. Keim, W.W. Zhang, and S.R. Nagel, Nature Physics, DOI: 10.1038/NPHYS1233, (2009).


  1. •“Breakup of Air Bubbles in Water: Breakdown of Cylindrical Symmetry,”  N. C. Keim,  P. Møller, W. W. Zhang, and S. R. Nagel, Phys. Rev. Lett. 97, 144503 (2006).

  1. • “Splashing of liquids: Interplay of surface roughness with surrounding gas,” L. Xu, L.  Barcos, and S. R. Nagel Phys. Rev. E  76, 066311 1-5 (2007).

  2. •“Drop Splashing on a Dry Smooth Surface,” L. Xu, W. W. Zhang, and S. R. Nagel, Phys.  Rev. Lett. 94, 184505 1-4 (2005).

  3. •“Liquid drop splashing on smooth, rough, and textured surfaces,” L. Xu, Phys. Rev. E 75, 056316 1-8 (2007).

jamming/glass transition granular materials fluid dynamicsJamming.htmlGranular.htmlshapeimage_7_link_0shapeimage_7_link_1shapeimage_7_link_2

Active Research Areas:

Coalescence.  When fluid drops merge, a dramatic transformation occurs: the topology changes as the fluid masses, originally separated, merge into a single entity.  At first, the drops are separated by only a small distance.  Then a thin fluid bridge is formed between them which rapidly widens due to surface tension forces as shown in the figure.  The expected universal dynamics associated with the initial stage of droplet coalescence are difficult to study visually due to the rapid motion of the liquid and the awkward viewing geometry. We have employed an electrical method to study the coalescence of two low-viscosity droplets at early times. We measured the growth dynamics of the bridge connecting the two droplets and observed a new asymptotic regime inconsistent with previous theoretical predictions.  The measurements indicate that this regime is dominated by the overall deformability of the drops, consistent with a model in which the two liquids coalesce with a slightly deformed interface.

Sequence of images showing the formation of a fluid bridge as two drops coalesce.  The liquid is a low-viscosity mixture of glycerin, NaCl and water.  The drop radius is 2 mm.  The frames are separated by 150 µs. 

  1. •“Coalescence of low-viscosity fluids in air”, S.C. Case, Phy. Rev. E, 79, 026307, 1-10 (2009).

  2. •“Coalescence in low-viscosity liquids,” S. C. Case and S. R. Nagel, Phys. Rev. Lett. 100, 084503 1-4 (2008).