Chaotic advections for Stokes flows in circular cavity

Steady Stokes flows in a circular cavity is analytically solved by using Green's function. The familiar phenomenon of Lagrangian chaos for Stokes flows in a long, circular cylinder filled with a viscous fluid subject to various boundary conditions is studied numerically, To achieve chaotic mixing for the fluid particles, two mobile outer walls in close contact with a fixed inner wall that have two corresponding openings are made to (independently) oscillate periodically in time, The expansion rate for a thin fluid filament Is also determined when the oscillatory modulation is turned on. Our study shows that counterrotating boundaries have a greater tendency to create mixing than corotating ones.