Session AM - Chaos and Fractals.
ORAL session, Sunday morning, November 23
Saratoga, SMH
The chaotic mixing of fluids in the partitioned-pipe mixer (PPM) is studied by using a numerically obtained velocity field. The PPM is composed of alternately placed horizontal and vertical plates in a cylindrical duct rotating with a constant angular velocity. This rotation and an axial pressure gradient generate the flow in the PPM. We examine the dependence of the mixing performance for many axial periods on the parameters of this system. We also calculate the maximum cross-sectional stretching rate, \lambda, of the infinitesimal line segments of the fluid. Under the assumption of the Stokes flow, we obtain two types of the evolution of \lambda, and find that they are distinguished by the distance between their cross-sectional initial positions and the lines of separation, defined as the set of cross-sectional initial locations of fluid particles which move to one of the leading edges of the plates within a specified periods. It is also found that the stretching of the fluid just inside the cylindrical wall after its separation by the leading edges mainly contributes the mixing in the PPM. Furthermore, we also examine the dependence of the mixing behavior on the Reynolds number.