Surface Instabilities and Patterning in Liquids: Exemplifications of the "Hairy Ball Theorem"

2015/03/24 by Edward Bormashenko, Bormashenko, Edward
Chemistry · Engineering · Materials Science · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Thin Films #Soft Condensed Matter (cond-mat.soft) #Surface Modification and Superhydrophobicity #Surfactants and Colloidal Systems

paper · pdf · doi:10.48550/arxiv.1503.06996

openalex publication_date 2015/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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