The flow of fluids is one of the most complex, beautiful, and amazing things in physics. Slow motion pictures of drops landing on water or of two fluids mixing can be simply gorgeous. Even more amazing, the basic physics of fluid flow was worked out way back in the 19th century. Those equations, though, hold riches that are still being uncovered today.

Some of the most spectacular work in recent years has involved uncovering what happens as a drop of fluid hits a surface. And one particularly stubborn aspect—why do you get lift-off (a precursor to a splash) near the end of the impact?—has revealed itself after a barrage of high-speed camera images.

To splash or not to splash?

At first, the impact of a slow-speed droplet on a surface seemed very difficult to understand. Eventually, it was decided that the momentum of the droplet competes with its surface tension. Essentially, the momentum tries to force the drop to spread out at a speed governed by the mass of fluid and the speed at which the drop impacts. But surface tension tries to pull the droplet back together, resisting the spreading motion. Hence, a droplet rapidly expands to some radius where the forces balance. Note that viscosity—how resistant a fluid is to flow—is seemingly unimportant.

Then something weird happens: the edges of the drop become unstable and lift off the surface. If the fluid is moving fast enough, that lift-off turns into a splash. Why would lift-off occur? If you do the calculation, it seems that the instability causing the lift-off could be driven by the adhesion between the fluid and the surface. But that adhesion begins at the moment of impact, right? So lift-off, and any ensuing splash, should occur almost instantly.

Why doesn't this happen? As the drop falls, it traps a small amount of air between it and the surface. That air compresses to a thickness of a just a few nanometers and races outward with the spreading drop, preventing direct contact between the surface and the droplet. This should prevent lift-off for slow droplets—except those lift off too.

To explain this, scientists proposed that the droplet eventually outruns the air and comes in direct contact with the surface. But observing that proved to be very difficult—until now, that is.

Imaging with TIRM

To watch a droplet hit a surface and detect if there is any air between the drop and surface, the researchers used a technique called total internal reflection microscopy (TIRM). In an amusing demonstration of how science communication works, TIRM was invented in the labs of physicists, disappeared into the labs of biologists, and has been brought back from there by the fluid physics people. Apparently, optics people don't talk directly to fluid people.

Imagine that you have a bit of glass that is cut into a half-disk shape. If you shine light into the half disk at the flat side, it will be transmitted but in a slightly different direction. This change in direction is due to the refractive index difference between air and glass. The light ray is bent so that it travels slightly closer to parallel with the glass surface. If we rotate the disk so that the light is hitting the flat surface at a more glancing angle, then eventually we will find an angle where the light is simply reflected. At this angle, the light exiting the glass would (if it could) travel exactly parallel to the glass surface. Since it can't do that, all the light is reflected.

That parallel beam of light is important though, because it does exist. It takes the form of an evanescent wave. Essentially, just at the surface of the glass, there is a field that penetrates into the air on the other side. The evanescent wave contains an electric and magnetic field, just like an ordinary light wave. However, in an ordinary light wave, the electric field generates a magnetic field as it collapses and the magnetic field generates an electric field as it collapses. This happens in such a way that the both advance through space.

In an evanescent wave, none of this happens. This is because the mutual phase relationship (the way the peaks and troughs line up with each other) between the two fields doesn't allow it. As a result, this field decays with distance very fast. By the time you are a couple of hundred nanometers from the surface, the evanescent is pretty much gone.

Now I have my glass disk positioned so that the light is hitting at just the angle of total internal reflection. If I place a drop of water on the glass disk, that increases the refractive index, and the light is no longer reflected. Instead, some of it is transmitted.

If I were to place a camera on the air side of the disk, I would be able to see the droplet of water, illuminated by the light from below. But once the droplet is gone, the image goes dark. In other words, if I were to rain droplets on the glass surface, I would only image those droplets that are in contact with the surface while not seeing any of the others. By using an imaging system like this, the researchers can selectively image droplets when they are in contact with the surface.

It gets even better than that. Remember the evanescent wave I mentioned above? That acts as a distance sensor for the microscope. Recall that the evanescent wave doesn't travel far is that the electric and magnetic fields are phased such that they cannot regenerate each other. However, when they penetrate a water droplet, the phase between the two fields is shifted, and they start to regenerate each other again. The amplitude of the field has decayed proportional to the distance between the droplet and the surface, so emerging light field has a brightness that depends on the distance between the droplet and the surface. The weaker the light, the further away from the surface the droplet is.

That means that our microscope doesn't just image droplets that are on the surface of the glass, the brightness of the light tells us how much distance there is between the droplet and the surface. By a bit of careful calibration, air layers as thin as a few nanometers can be detected.

The secret life of a spreading droplet

So we can use this to track the expansion of a droplet and measure the thickness of the air layer between the surface and the droplet. Researchers combined traditional high speed photography with total internal reflection microscopy. In this setup, the researchers are looking at the droplet from the point of view of the surface. When the droplet hits, they can, from the brightness of the image, figure out how much air is between the droplet and the surface. And by filming at 180,000 frames per second, they could observe the expansion of the droplet and the development of the instability that leads to splashing.

By examining droplets with a range of impact velocities and viscosities, the researchers discovered that viscosity does play a role. The initial impact and spreading is independent of viscosity—as was found by earlier research. But later in the spreading process, viscosity starts to become more and more important. It seems that viscosity is one of the drivers for the lift-off instability.

This dependence can be seen in two things. First, the fluid never outruns the air, and the lift-off instability is not due to contact with the impact surface. Second, despite the speed of spreading being independent of viscosity, the time between impact and lift-off is dependent on viscosity.

So, what happens? It seems that as the droplet spreads out, the leading edge is shaped a bit like a wedge (or cusp), the sharp end of which is pointing towards the surface. The cusp of the wedge is moving faster than the top, so fluid runs out along the surface, eventually rounding itself out into a smooth curve. This curve then lifts off the surface as if it were the end of a whip. (Sadly, I couldn't tell from the paper exactly how that happens.)

The finding, however, is very important. From ink jet printers to internal combustion engines, we rely on fluid mechanics. Future improvements to these technologies (especially printer technologies) rely on this sort of research.

Physical Review Letters, 2014, DOI: 10.1103/PhysRevLett.112.134501