Trivedi Rohit, Liu Shan, Williams Scott
Metals and Ceramics Sciences, Ames Laboratory (US-DOE) and Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011, USA.
Nat Mater. 2002 Nov;1(3):157-9. doi: 10.1038/nmat749.
The problem of interface pattern selection in nonlinear dissipative systems is critical in many fields of science, occurring in physical, chemical and biological systems. One of the simplest pattern formations is the Saffman-Taylor finger pattern that forms when a viscous fluid is displaced by a less viscous fluid. Such finger-shaped patterns have been observed in distinctly different fields of science (hydrodynamics, combustion and crystal growth) and this has led to a search for a unified concept of pattern formation, as first proposed by the classic work of D'arcy Thomson. Two-dimensional finger-shaped patterns, observed in flame fronts and the ensembled average shape of the diffusion-limited aggregation pattern, have been shown to be similar to Saffman-Taylor finger shapes. Here we present experimental studies that establish that the cell shapes formed during directional solidification of alloys can be described by the form of the Saffman-Taylor finger shape equation when a second phase is present in the intercellular region.
非线性耗散系统中的界面模式选择问题在许多科学领域都至关重要，出现在物理、化学和生物系统中。最简单的模式形成之一是萨夫曼-泰勒指状模式，当一种粘性较小的流体驱替粘性较大的流体时就会形成这种模式。这种指状模式已在截然不同的科学领域（流体动力学、燃烧和晶体生长）中被观察到，这促使人们寻找一种统一的模式形成概念，正如达西·汤姆森的经典著作首次提出的那样。在火焰前沿以及扩散限制聚集模式的集合平均形状中观察到的二维指状模式，已被证明与萨夫曼-泰勒指状形状相似。在此，我们展示了实验研究结果，这些研究表明，当细胞间区域存在第二相时，合金定向凝固过程中形成的细胞形状可以用萨夫曼-泰勒指状形状方程的形式来描述。
