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Experiments on continuous chaotic mixing of viscous liquids
Abstract
The objective of this work is to study chaotic mixing in three-dimensional and continuous viscous flows. We are interested in this because of the possibility of exploiting chaos to generate good mixing, and to understand the fundamental mixing mechanisms so that future mixer designs will have a more rational basis. The two mixers studied in this work, the Eccentric Helical Annular Mixer (EHAM) and the Partitioned Pipe Mixer (PPM), are examples of two large classes of continuous chaotic flows. The EHAM is a time-periodic flow while the PPM is a spatially-periodic flow. The design of a novel experimental apparatus, built to perform continuous chaotic mixing experiments, experimental procedures and an uncertainty analysis are presented. The EHAM is the axial flow between eccentric rotating cylinders. An advantage of the EHAM configuration is the existence of an analytic solution for the velocity field. Steady flows in the EHAM are not chaotic; experiments and computations match to within the experimental uncertainty. Time-periodic cross-sectional flows generate chaos in the EHAM. As expected, the mixing is much better in chaotic flows; however, there are barriers to complete mixing. These barriers are KAM surfaces of the chaotic cross-sectional flow which form tubes that move about the cross-section of the mixer in time. Associated computations illustrate (i) shortcomings in trying to match the experimental behavior and (ii) the stretching of material vectors is exponential in the chaotic regions and linear in the non-chaotic regions. The PPM is a sequence of rectangular plates held orthogonally inside a rotating tube. Experimentally it is shown that steady flows are chaotic. Barriers to complete mixing exist as deformed tubes that move about the cross-section of the mixer as the tubes move down the mixer. The tubes are more structurally robust than predicted by a preexisting model. Developing flows, which are neglected by the model, seem to dominate the experimental flowfield. The PPM with no axial flow generates a three-dimensional spatially periodic structure which is believed to be an example of a bounded steady chaotic flow.
Subject Area
Chemical engineering
Recommended Citation
Kusch, Henry Albert, "Experiments on continuous chaotic mixing of viscous liquids" (1991). Doctoral Dissertations Available from Proquest. AAI9207420.
https://scholarworks.umass.edu/dissertations/AAI9207420