液体中的表面不稳定性和图案化："毛球定理"的例证
Surface Instabilities and Patterning in Liquids: Exemplifications of the "Hairy Ball Theorem"
摘要：
应用“毛球定理”分析了液/汽界面的表面不稳定性。当液体样品的表面上存在连续切向速度场时（该速度场同胚为球），则在该表面上必然存在零速度点。该定理的例子与聚合物溶液的快速蒸发下发生的不稳定性的分析。零速度点，积累孔隙，使不稳定性的直接可视化。在环面的表面上，图案化可以基本上不同。
英文摘要：
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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