Universal scale governing the dynamics of a single particle suspemded in shear
Abstract
It has been shown computationally [Aidun, Lu, and Ding, JFM, 1998; Ding and Aidun, JFM,2000] and confirmed experimentally [Zettner and Yoda, JFM, 2001] that elliptical cylinders and ellipsoids suspended in shear flow can follow a transition from time periodic rotation to steady state as the particle Reynolds number increases beyond a critical value. In general, this transition is always through a saddle node bifurcation, and therefore, the period of oscillation near transition scales as \vert R_c-R\vert -1/2 where Rc is the critical value of any parameter R, such as the Reynolds number, density ratio, or channel confinement leading to this transition. Further analyses show that as long as the transition occurs, this scale is independent of the particle shape, channel confinement, and solid to fluid density ratio. Furthermore, we show that there exists a region adjacent to the stability boundary where the steady state and the periodic state co-exist. That is each equilibrium state is locally stable while unstable to large amplitude disturbances.
- Publication:
-
APS Division of Fluid Dynamics Meeting Abstracts
- Pub Date:
- November 2001
- Bibcode:
- 2001APS..DFD.AF003A