CHAOTIC MOTION OF FLUID PARTICLES DUE TO THE ALTERNATE ROTATIONS OF 2 ECCENTRIC CYLINDERS

Chaotic or regular motions of the fluid particles by the Stokes flow between two eccentric cylinders counter rotating alternately and of radius ratio 0.3 are investigated numerically and analytically. We examine the dependence of the motions on eccentricity epsilon, focusing on an equilibrium point of the Poincare map of the particle position after every rotations. If both of the winding numbers of the cylinders are small, the area of the chaotic region is small and increases monotonically with epsilon, whereas when at least one of them is not small, this area is relatively large and takes a maximum at a certain epsilon. In the latter case, within a certain region of the winding numbers, the bifurcation of the equilibrium point from elliptic to hyperbolic type occurs at another value of epsilon = epsilon(b), resulting in the increase in the area for epsilon around epsilon(b). A perturbation analysis can roughly predict this region and the value of epsilon(b).