Incompressible Poiseuille flows of Newtonian liquids with a pressure-dependent viscosity |
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Authors: | Anna Kalogirou Stella Poyiadji Georgios C Georgiou |
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Institution: | 1. School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK;2. School of Mathematics & Statistics, The University of Western Australia, Crawley 6009, Australia;3. Department of Mathematics & Department of Engineering, University of Leicester, University Road, Leicester LE1 7RH, UK;1. Department of Mechanical Engineering University of Victoria, Victoria, BC, Canada;2. Department of Mathematics, RWTH Aachen University, Aachen, Germany;1. Oceanography Centre, University of Cyprus, PO Box 20537, 1678 Nicosia, Cyprus;2. Department of Mathematics and Statistics, University of Cyprus, PO Box 20537, 1678 Nicosia, Cyprus |
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Abstract: | The pressure-dependence of the viscosity becomes important in flows where high pressures are encountered. Applications include many polymer processing applications, microfluidics, fluid film lubrication, as well as simulations of geophysical flows. Under the assumption of unidirectional flow, we derive analytical solutions for plane, round, and annular Poiseuille flow of a Newtonian liquid, the viscosity of which increases linearly with pressure. These flows may serve as prototypes in applications involving tubes with small radius-to-length ratios. It is demonstrated that, the velocity tends from a parabolic to a triangular profile as the viscosity coefficient is increased. The pressure gradient near the exit is the same as that of the classical fully developed flow. This increases exponentially upstream and thus the pressure required to drive the flow increases dramatically. |
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