Motion of the liquid on the surface of Leidenfrost droplets and the hairy ball theorem

Leidenfrost droplets are non-stick droplets, rapidly self-propelling above the hot surface. Leidenfrost effect is a phenomenon in which a liquid, in close contact with a mass significantly hotter than the liquid's boiling point, produces an insulating vapor layer which keeps that liquid from boiling rapidly. The field of the liquid velocities arising on the surface of Leidenfrost droplets is considered. The pattern of surface velocities demonstrates the zero points predicted by the Poincaré-Brouwer theorem for surfaces possessing the Euler characteristic χ = 2. Evaporation of droplets does not change their topology. Zero-velocity points appear when the Leidenfrost droplets are at rest and when they are self-propelled. Topological transformations of bouncing Leidenfrost-like non-stick droplets (called liquid marbles) converted under high values of Weber numbers into tori (χ = 0) results in disappearing of zero-velocity points in their surfaces. Zero-velocity points should also necessarily appear at the surfaces of rolling droplets, placed on superhydrophobic surfaces or liquid marbles.