Selective withdrawal of polymer solutions: Computations |
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Authors: | Diwen Zhou James J Feng |
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Institution: | 1. Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, BC V6T 1Z3, Canada;2. Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada;1. Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, The University of Oxford, OX1 3LB, United Kingdom;2. Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, United States;3. Mechanical Science and Engineering, University of Illinois, Urbana-Champaign, IL, United States;1. College of Science, Nanjing Agricultural University, Nanjing 210095, PR China;2. Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Po Ling Road, Tai Po, New Territories, Hong Kong |
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Abstract: | This paper reports numerical simulations of selective withdrawal of Newtonian and polymeric liquids, and complements the experimental study reported in the accompanying paper (Zhou and Feng 2]). We use finite elements to solve the Navier–Stokes and constitutive equations in the liquid on an adaptively refined unstructured grid, with an arbitrary Lagrangian–Eulerian scheme to track its free surface. The rheology of the viscoelastic liquids are modeled by the Oldroyd-B and Giesekus equations, and the physical and geometric parameters are matched with those in the experiments. The computed interfacial deformation is in general agreement with the experimental observations. In particular, the critical condition for interfacial rupture is predicted to quantitative accuracy. Furthermore, we combine the numerical and experimental data to explore the potential of selective withdrawal as an extensional rheometer. For Newtonian fluids, the measured steady elongational viscosity is within 47% of the actual value, apparently with better accuracy than other methods applicable to low-viscosity liquids. For polymer solutions, an estimated maximum error of 300% compares favorably with prior measurements. |
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