Viscous dissipation with fluid inertia in oscillatory shear flow |
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| Institution: | 1. Department of Mechanical Engineering and Rheology Research Center, University of Wisconsin, Madison, WI 53706, USA;2. Department of Chemical Engineering and Rheology Research Center, University of Wisconsin, Madison, WI 53706, USA;1. Oxford University Hospitals, Oxford, UK;2. St Mary''s Hospital, Imperial College Healthcare NHS Trust, London, UK;3. Wellington Hospital, London, UK;4. Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences (NDORMS), University of Oxford, Oxford, UK;5. Formerly The Windsor Hand Clinic, Berkshire, UK;1. Yildiz Technical University, Faculty of Mechanical Engineering, Department of Mechanical Engineering, Yildiz Campus, 34349 Besiktas, Istanbul, Turkey;2. Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, 37041 Baku, Azerbaijan;1. Research Center of System Health Maintenance, Chongqing Technology and Business University, Chongqing 400067, China;2. Chongqing Engineering Laboratory for Detection Control and Integrated System, Chongqing 400067, China;1. Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano, Italy;2. Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721, USA |
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| Abstract: | For liquids with high viscosity and low thermal conductivity, viscous dissipation can cause appreciable errors in rheological property measurements. Here, the influences of both viscous dissipation and fluid inertia on the property measurements in oscillatory sliding plate rheometry are investigated. For Newtonian fluids, Bird (1965) solved the combined problem analytically, but only for high frequencies. Here his solution is extended to any frequencies. Also, the equations of motion and energy are solved for linear viscoelastic fluids, and new analytical solutions for the velocity and temperature profiles are given. In both Newtonian and linear viscoelastic fluids, the temperature rise in the gap increases with frequency. The location of the maximum temperature shifts from the mid-plane at low frequency towards the moving wall at high frequency. The fluid inertia increases the viscous dissipation in both fluids. By solving the combined problem, this paper simplifies rheometer design by providing one unified criterion for avoiding measurement errors. Operating limits are presented graphically for minimizing the effects of both fluid inertia and viscous dissipation in oscillatory sliding plate rheometry. |
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