Ordered drop arrays levitating over heated surfaces

In the famous Leidenfrost effect, liquid drops levitate over a heated solid surface without touching it. For this effect to occur, the surface should be heated well above the boiling temperature of the liquid. On the other hand, levitation over a liquid surface can occur for much lower surface temperatures. We have all seen this when drinking hot tea or coffee. There is often what looks like a misty film over the surface. It is formed when the evaporating water condenses and some of the resulting microdrops levitate over the surface. These drops are remarkably uniform in size and form arrays with a high degree of order. Leidenfrost drops do not form such ordered arrays. In a recent article in Physical Review Letters, a group of Russian physicists was able to show that ordered drop arrays can occur over solid surfaces as well, well below the Leidenfrost temperature, and give an explanation for this phenomenon. To create such arrays, they started with a layer of water on top of a copper substrate.  With a short pulse of an air jet they created a millimetre-sized dry spot on the surface. The spot stayed dry after the air flow ceased, because the surface was rough enough that the contact line was pinned. Then they heated the substrate to 85 C. As expected, they observed an array of microdrops above the liquid, but some of the hovering drops moved over the dry spot and formed an ordered array there as well, though with less order.

In order to explain the phenomenon, the authors considered the dynamics of evaporation of the drops and associated air flows. When a drop is evaporating in air, the vapour concentration is, obviously, higher near the drop. However, the total concentration of molecules (air plus vapour) is roughly the same everywhere, and therefore the air molecule concentration is lower near the drop surface and there should be diffusion of air molecules towards the surface. But since the air molecules cannot penetrate the drop, there should be a counterbalancing convective flow away from the drop surface, which is called Stefan flow, after the Austrian-Slovene scientist of the Stefan-Boltzmann law fame. The authors claim that it is this flow that repels the drops from the liquid or solid surface and from each other, making them levitate and form ordered arrays.

While the authors do some calculations to justify their explanation, there are approximations involved, so simulations avoiding these approximations may be useful. Moreover, the sizes of the drops they observe, the distances between them and the heights above the substrate are about 5-10 microns, just large enough for continuum hydrodynamics to apply. It is plausible that smaller drops may be observed (this depends, in particular, on the temperature to which the substrate is heated), in which case taking gas-kinetic effects into account may be warranted.

This work has also been covered in Physics World.