Chaotic Mixing in Time-Periodic 3-D Flows

Mixing in a special class of three-dimensional, non-inertial time-periodic flows is studied quantitatively. In the type of flow considered here, the cross-sectional velocity components are independent of the axial flow which is assumed to be fully developed. Using the eccentric helical annular mixer as a prototype, the time-periodic flow field is induced by adding a sinusoidal component to the rotation speed of the inner cylinder. For a given 3-D mixer geometry, the degree of mixing achieved is a function of two parameters that measure the strength of the cross-sectional stirring protocol relative to the mean residence time of the fluid in the mixer: the average number of turns of the outer cylinder, and the average number of modulation periods. We find that for a given mixer geometry and mean residence time, there is an optimum modulation frequency for which the standard deviation of the temperature field at the exit is a minimum.