  Application of the "hairy ball theorem" to the analysis of the surface
instabilities inherent for liquid/vapor interfaces is reported. When a
continuous tangential velocity field exists on the surface of the liquid sample
which is homeomorphic to a ball, zero velocity points will be necessarily
present at the surface. The theorem is exemplified with the analysis of the
instability occurring under the rapid evaporation of polymer solutions. Zero
velocity points, accumulating pores, enable direct visualization of the
instability. The patterning may be essentially different on the surface of a
torus.
