Unsteady shear flow of a viscoplastic material |
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| Institution: | 1. Southern University of Science and Technology (SUSTech), and the Engineering Research Center of Integrated Circuits for Next-Generation Communications, Ministry of Education, Southern University of Science and Technology, Shenzhen 518055, China;2. Department of Materials Science and Engineering & Shenzhen Engineering Research Center for Novel Electronic Information Materials and Devices, Southern University of Science and Technology, Shenzhen, China;3. State Key Laboratory of Millimeter Waves and Institute of Electromagnetic Space, Southeast University, Nanjing 210096, China;1. Department of Mathematics, CHRIST (Deemed to be University), Bengaluru 560029, India;2. College of Science, Harbin Institute of Technology Shenzhen, PR China;1. IFP Energies nouvelles, Solaize, France;2. Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh |
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| Abstract: | A viscoplastic, or yield-stress, liquid occupies the space between two infinite parallel plates. Initially the whole system is at rest. The lower plate is suddenly jerked into motion with given speed or shear stress, while the upper plate is kept fixed. The flow consists of two regions; (1) a lower sheared region bounded above by the yield surface, (2) an upper unyielded region bounded below by the yield surface. The yield surface propagates to the upper plate as time proceeds. We first consider the equivalent one plate problem of flow over a jerked plate, and find similarity solutions and small time asymptotic solutions for prescribed shear and speed cases respectively. These solutions are used as initial solutions for the two plate case. The motion of the yield surface and the time taken for the entire material to yield are investigated. The problems considered here are two dimensional representations of some control devices, for example the light duty clutch, which consists of two corotating, coaxial discs separated by a layer of electrorheological material. In this application it is useful to know the time taken for all the material to yield. |
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