(193f) Menagerie of Topology in 3d Steady Flow

3D chaotic steady laminar flows have been shown to have at least one local neutral direction and one local stretching direction. The relative orientations of these directions have been measured (u-n angle) and used to describe the topology of sub-volumes of a chaotic flow domain as they deform, forming shapes from tendrils to sheets. Each flow with a specific set of boundary conditions has a separate distribution of angles that describes the topology that it induces. This local measure is only a function of the Eulerian velocity field, yet it affects Lagrangian dynamics creating different topologies (tendrils and sheets), which can cause the creation of very different amounts of intermaterial surface area in mixing applications. Because the exposed surface area of material injected into a stirred tank can impact such characteristics as diffusion and reaction, this topology may of critical importance to unit operations involved in mixing. Within the wide class of ?steady three dimensional flows,? systems generating substantially different topologies can be identified. Three different mixing apparatuses are examined here: the Kenics mixer, an eccentric stirred tank with a disk impeller, and a stirred tank with a Rushton impeller. It is shown that their distributions of angles (and the resulting mixture topologies) vary remarkably both for different apparatuses and for the same apparatus but for different parameter values.