Chevalier C, Lindner A, Clément E
Laboratoire de Physique et Mécanique des Milieux Hétégogènes (PMMH), UMR 7636 CNRS - ESPCI - Universités Paris 6 et 7, 10, rue Vauquelin, 75231 Paris Cedex 05, France.
Phys Rev Lett. 2007 Oct 26;99(17):174501. doi: 10.1103/PhysRevLett.99.174501. Epub 2007 Oct 24.
We study the Saffman-Taylor instability in a granular suspension formed by micrometric beads immersed in a viscous liquid. When using an effective viscosity for the flow of the suspension in the Hele-Shaw cell to define the control parameter of the system, the results for the finger width of stable fingers are found to be close to the classical results of Saffman-Taylor. One observes, however, an early destabilization of the fingers that can be attributed to the discrete nature of the individual grains. Classically, the threshold of destabilization is linked to the noise in the cell and is thus difficult to quantify. We show that the grains represent a "controlled noise" and produce an initial perturbation of the interface with an amplitude proportional to the grain size. The finite amplitude instability mechanism proposed by Bensimon et al. allows us to link this perturbation to the value of the threshold observed.
我们研究了由浸没在粘性液体中的微米级珠子形成的颗粒悬浮液中的萨夫曼-泰勒不稳定性。当使用悬浮液在赫勒-肖槽中流动的有效粘度来定义系统的控制参数时，发现稳定指状物的指宽结果与萨夫曼-泰勒的经典结果相近。然而，可以观察到指状物的早期失稳，这可归因于单个颗粒的离散性质。传统上，失稳阈值与槽中的噪声有关，因此难以量化。我们表明，颗粒代表一种“可控噪声”，并产生与颗粒尺寸成比例的界面初始扰动。本西蒙等人提出的有限振幅不稳定性机制使我们能够将这种扰动与观察到的阈值联系起来。
