Schmidt Laura E, Zhang Wendy W
The Department of Physics & The James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA.
Phys Rev Lett. 2008 Feb 1;100(4):044502. doi: 10.1103/PhysRevLett.100.044502. Epub 2008 Jan 28.
In viscous withdrawal, a converging flow imposed in an upper layer of viscous liquid entrains liquid from a lower, stably stratified layer. Using the idea that a thin tendril is entrained by a local straining flow, we propose a scaling law for the volume flux of liquid entrained from miscible liquid layers. A long-wavelength model including only local information about the withdrawal flow is degenerate, with multiple tendril solutions for one withdrawal condition. Including information about the global geometry of the withdrawal flow removes the degeneracy while introducing only a logarithmic dependence on the global flow parameters into the scaling law.
在粘性抽取过程中，施加在上层粘性液体中的汇聚流会夹带来自下层稳定分层液体层的液体。利用细卷须被局部应变流夹带的观点，我们提出了一个从互溶液体层夹带的液体体积通量的标度律。一个仅包含抽取流局部信息的长波长模型是退化的，对于一种抽取条件有多个卷须解。包含抽取流全局几何结构的信息消除了退化性，同时仅对标度律引入了对全局流动参数的对数依赖。
