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Chaos is a relatively new subject in mathematical science. It has rapidly, however, found applications in a diverse range of areas in pure science and engineering. This work considers the application of chaos in viscous fluid mixing, fluids that are, for example, found in the food or polymer industry. It has been shown by many authors that under steady state conditions laminar fluids flow in a streamline motion. It has also been shown that it is possible to increase the degree of disorder in such a system by introducing time dependant moving boundaries. It is well established however, that chaotic motion is not dependent on the variation in streamlines alone. The system is required to be operated within a specific range of boundary conditions for chaos to occur. This work presents further investigations of chaotic flow domains concentrating on a property that relates to the divergence and separation of particles originating from small generation zones within the flow domain. The property of divergence of particles is noted to yield conclusions consistent with previously published work in two dimensions. It is then applied to investigate the degree of disorder in three three-dimensional continuous chaotic systems, operating with a range of time and spatially periodic boundary conditions. In order to highlight the benefits of increased levels of mixing when operating the systems under specific conditions characteristic plots, for incremental variations of operating conditions, are presented. It is hoped that by the development of the characteristic plots and concepts presented here that engineers will be able to predict and characterise the degree of disorder in future industrial chaotic mixing equipment.

Laminar Fluid Chaotic Mixing in Three-Dimensional Continuous Flow Domains