journal article·2015-03-01Open access

Surface instabilities and patterning at liquid/vapor interfaces: Exemplifications of the “hairy ball theorem”

Edward Bormashenko

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.
Source: openalex_inverted_index · Quality: baseline

Research context

OpenAlex topics: Fluid Dynamics and Thin Films · Fluid Dynamics and Heat Transfer · Surface Modification and Superhydrophobicity

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (25)

Show source-provided references
1. Nepomnyashchy · 2002
2. Colinet · 2001
3. Surface instabilities10.1134/S1061933X0806001X ↗
4. Plateau · 1873
5. On the instability of jets10.1112/plms/s1-10.1.4 ↗
6. de Gennes · 2003
7. The Instability of liquid surfaces when accelerated in a direction perpendicular to their planes10.1098/rspa.1950.0052 ↗
8. C. Pérez‐García, G. Carneiro, Linear stability analysis of Bénard–Marangoni convection in fluids with a deformable free surface, Phys. Fluids A 3 (1991) 292–298.10.1063/1.858137 ↗
9. Nonlinear evolution and secondary instabilities of Marangoni convection in a liquid–gas system with deformable interface10.1017/S0022112097005582 ↗
10. Long-wavelength surface-tension-driven Benard convection: experiment and theory10.1017/S0022112097006101 ↗
11. A. A. Nepomnyashchii, I. B.Simanovskii, I. B. Long-wave thermocapillary convection in layers with deformable interfaces, Appl. Math. Mech. 54 (1990) 490–496.10.1016/0021-8928(90)90061-E ↗
12. D. A. Nield, Surface tension and buoyancy effects in cellular convection, J. Fluid Mech. 19 (1964)41–352.10.1017/S0022112064000763 ↗
13. Mesoscopic patterning in thin polymer films formed under the fast dip‐coating process10.1002/mame.200400217 ↗
14. Mesoscopic patterning in evaporated polymer solutions: new experimental data and physical mechanisms10.1021/la0518492 ↗
15. Self-assembly in evaporated polymer solutions: influence of the solution concentration10.1016/j.jcis.2005.11.025 ↗
16. Strawhecker · Macromolecules · 2001 · 34 · 466910.1021/ma001440d ↗
17. Self-organized structures at the surface of thin polymer films10.1016/S0928-4931(99)00070-3 ↗
18. Zd. Mitov, E. Kumacheva, Convection-Induced patterns in phase-separating polymeric fluids, Phys. Rev. Lett. 81 (1998) 3427.10.1103/PhysRevLett.81.3427 ↗
19. Ed. Bormashenko, S. Balter, R. Pogreb, Y. Bormashenko, O. Gendelman, D. Aurbach, On the mechanism of patterning in rapidly evaporated polymer solutions: Is temperature-gradient-driven Marangoni instability responsible for the large-scale patterning? J. of Colloid Interface Sci. 343 (2010) 602–607.10.1016/j.jcis.2009.12.005 ↗
20. Instabilities during the evaporation of a film: non-glassy polymer+volatile solvent10.1007/s10189-001-8055-3 ↗
21. A proof of the hairy ball theorem10.2307/2320587 ↗
22. Pickover · 2009
23. Responsive nematic solid shells: topology, compatibility and shape10.1209/0295-5075/97/36007 ↗
24. Divalent metal nanoparticles10.1126/science.1133162 ↗
25. Magnetic flux lines in type-II superconductors and “the hairy ball theorem”10.1038/ncomms1047 ↗