Geometrical analysis of chaotic mixing in a low Reynolds number magnetohydrodynamic quadripolar flow - art. no. 056309

A mixing device for highly viscous fluids with finite electrical conductivi ty is investigated theoretically. Stirring is performed by means of electro magnetic forces provided by inductor wires located outside the flow domain. The flow shows hyperbolic and elliptic singular points. Inductors are disp laced in a periodic manner, leading to an efficient stretching and folding mechanism. The goodness of mixing is quantified by means of a geometrical a nalysis based on box-counting techniques. This analysis gives valuable info rmation about advection of a spot of dye injected in the flow, in the limit of infinite Peclet numbers. A spatiotemporal criterion for mixing efficien cy is derived, and characteristic scales are analyzed. The influence of var ious parameters on mixing efficiency is discussed by making use of both the geometrical analysis and Poincare sections.