Floating droplets shed new light on the flow of fluid at interfaces
When an experiment doesn’t behave the way we expect, either our understanding of the relevant physics is flawed, or the phenomenon is more complicated than it appears. When a theoretical prediction is off by two orders of magnitude – like what was observed in this recent paper by Hua Yung Lo, Yuan Liu, and Lei Xu of the Chinese University of Hong Kong – something is seriously wrong.
If Lo and colleagues drop a liquid droplet onto a smooth, flat surface, it will take on an equilibrium shape which depends on the properties of the liquid and solid materials at the interface (eg. water on Teflon will form a nearly perfect spherical drop while water on stainless steel will spread out, forming a spherical cap). For low viscosity fluids, the equilibration process happens almost instantly… unless the surface is very flat and very smooth.
If the surface below a droplet is atomically smooth (not a single atom is out of place to roughen the surface), a thin layer of air will form between the droplet and the surface, keeping the droplet from making contact with the surface. Eventually the trapped air will escape, draining out like how a liquid would, allowing the droplet to collapse onto the surface. Traditional fluid dynamics simulations predict that the collapse would take between 10 – 100 seconds. In experiments, however, contact generally happens in less than one second. Lo and coworkers set about investigating this seeming contradiction by observing the flow that happens within the air and liquid at the boundary between a droplet and a smooth surface.
To study this problem, the researchers dropped small spherical oil droplets (1.7 mm diameter) onto a glass surface with a very thin coating of oil which could be tilted. They observed that droplets would compress and bounce as they floated on a pocket of air, before collapsing onto the surface. The contact area was imaged from the bottom and side simultaneously using two high-speed cameras. Side-on sequences are shown in Figure 1 with a slightly tilted surface (a) and a perfectly leveled surface (b). While both droplets collapsed onto the surface far quicker than predicted by simulations, the droplet on the leveled surface was observed to float just above the surface approximately 10 times longer than on the tilted surface before collapsing.
The effect the tilted surface has on this phenomenon became more apparent when viewed from below. On the tilted surface, the droplet would “skid”, observed as a sliding of the droplet’s center from the red point to the blue point in the direction of the green arrow as shown in Figure 2 a) while the size and shape of the air pocket was measured using two-wavelength interferometry . Tilting the surface caused an asymmetric air pocket to develop, with a thinner gap at the front of the droplet and a thicker gap at the back. When a droplet did not skid, it formed a symmetric air pocket like in Figure 2 b). A thinner gap (with difference of just half micrometer) lets the air drain out (and allows contact to be made) much faster than it would for a symmetric air pocket on a flat surface. However, even a flat surface drained 10-times faster than expected.
To understand the flow of air from under the droplet, the researchers modeled it as a low-viscosity fluid. When a low-viscosity fluid flows past a wall (like water through a tube), the friction at the walls may reduce the flow near the walls to something-close-to-zero. This is called a “no-slip boundary condition”. On the other hand, a “plug flow boundary condition” means there is significant slip and therefore flow along the walls. Each of these boundary conditions lead to characteristic velocity profiles like those presented in Figure 3 a). Typically, one would assume that air flowing through the air pocket near the oil interface would have a no-slip boundary condition while something like a sludge or gel would demonstrate plug flow. Yet, it is this assumption that ends up being incorrect.
The researchers measured the velocity of oil within the oil droplet and the surface coating using particle image velocimetry, a technique where small light-reflecting particles are mixed into a material and tracked down as they move along with the surrounding fluid. An image of the oil droplet seeded with the tracer particles is shown in Figure 3. In this way, the researchers were able to directly visualize flow of oil at the air-oil boundaries, finding a sort of “slip layer” along the walls corresponding to the layer of oil being dragged along by the air. This lets larger volumes of air drain from under the droplet, explaining the surprisingly short time it takes for droplets to collapse onto the surface.
Despite its apparent simplicity, Lo et al. revealed a fundamental misunderstanding in the way scientists thought about how fluids flow near an interface. Accounting for the effect of slip, the researchers unified both theory and observation and explain why liquid droplets will make contact with a perfectly smooth surface so much faster than originally expected.
 a technique that uses light interference to quantify changes in thickness as light and dark bands; narrow bands correspond to rapidly changing thicknesses, much like the lines on a topographic map show changes in elevation. ^