Laser-optical observation of chaotic mixing structure in a stirred vessel

The purpose of the present work was to observe the chaotic mixing structure in a stirred vessel via flow-visualization using laser-induced fluorescence. Under laminar flow conditions in the stirred vessel, two types of mixing region were observed, i.e. the active mixing region (AMR) and the isolated mixing region (IMR). The IMRs clearly took the form of two toroidal vortices respectively above and below the turbine impeller in a range of less than Reynolds number (Re) = 100. These regions did not exchange much fluid material with the AMR. From a cross sectional view, it was found that the good mixing in the AMR resulted from the stretching and folding motion of the turnstile-lobe-like regions generated by each stroke of the turbine blades. Under the nearly same rotational conditions, a set of three stable filaments surrounding the core torus of the IMRs was found in the case of the six-bladed turbine, while a set of four filaments was found in the case of the four-bladed turbine. Hence it can be considered that these structures depend on the periodical perturbations caused by the rotating turbine blades. In order to observe the internal structure of the ring-doughnut-shaped core regions, an unsteady rotation procedure was applied. Another set of filaments was observed to exist inside the core. It was found that the IMRs had complex multi-structures consisting of various Kolmogorov, Anold, and Moser (KAM) tori. The rotating period of an island P-i and the passing period of turbine blade P-t had a rational relationship. Furthermore, the rational number of the ratio, P-i/P-t, corresponded to the number of islands. These results clearly show the structure complicated with stable/unstable manifolds obtained from the Poincare-Birkhoff theorem.