Chaotic mixing of a viscous fluid in a screw impeller mixer

Abstract

Several studies on model systems have established the potential utility of the theory of chaotic systems for the analysis of mixing in laminar flow fields. Here we present an application of the theory to the mixing, under creeping flow conditions, in a screw impeller mixer, which is used in a number of industrial mixing operations. The flow in the system was found to comprise five main components: (i) unidirectional flow in the annulus; (ii) turning slow flow in the lower compartment; (iii) double helical motion in the screw element; (iv) helical motion in the upper part of the draft tube; and (v) turning flow in the upper compartment. Under creeping flow conditions, the flow is independent of the rotational speed of the impeller, thus mixing can be altered only by changing the system geometry. The flow is time independent with respect to a frame of reference fixed on the impeller, and can be considered to be a more complicated version of that in the partitioned pipe mixer. Streak lines of the flow are invariant to 2π rotations of the impeller, and illustrate the stretching and folding of material lines by the flow. The development of a streak line starting in the annulus was studied experimentally using a fluorescent tracer dye. Each streak line was found to be segmented into an infinite number of loops each starting at a point on the impeller blade. Each loop in turn was found to be wrapped toroidally around the draft tube. Poincare sections were obtained by noting the points of intersection of a tracer particle trajectory with a horizontal plane. The coordinate system was fixed either on the tank or on the impeller. Experimentally obtained Poincare sections were chaotic but showed no structure in either case indicating a well mixed-system to the resolution of the measurements. Studies are currently underway with impellers of varying pitch and length to study their effect on the quality of mixing in terms of Poincare sections and the extent of stretching of a streak line loop in each rotation of the impeller.