Stress communication and filtering of viscoelastic layers in oscillatory shear |
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| Authors: | Brandon Lindley Eddie Lee Howell Breannan D Smith Gregory J Rubinstein M Gregory Forest Sorin M Mitran David B Hill Richard Superfine |
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| Institution: | 1. Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill 27599-3250, United States;2. The Virtual Lung Project and Department of Mathematics, University of North Carolina, Chapel Hill 27599-3250, United States;3. Cystic Fibrosis Center, University of North Carolina, Chapel Hill 27599-7248, United States;4. Department of Physics and Astronomy, University of North Carolina, Chapel Hill 27599-3250, United States;1. INSA de Rouen, Laboratoire de Mathématiques de l’INSA, Avenue de l’Universite, 76801 St Etienne du Rouvray Cedex, France;2. Université de Pau, LMA-CNRS, UFR Sciences et Technologies de la Côte Basque, All. Parc Montaury, 64600 Anglet, France;2. Immune Disease Institute, Children’s Hospital Boston, Massachusetts;3. Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, Massachusetts;4. Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina;5. Department of Pathology and Laboratory Medicine, University of North Carolina, Chapel Hill, North Carolina;11. Department of Physics and Astronomy, Clemson University, Clemson, South Carolina;1. The University of Texas Rio Grande Valley, Edinburg, TX, USA;2. University of Coruña, Department of Industrial Engineering II, Spain;3. The Hong Kong Polytechnic University, Department of Mechanical Engineering, Hong Kong;4. The University of New Orleans, New Orleans, LA, USA;5. Faculty of Science, Engineering and Technology, Swinburne University of Technology, John Street, Hawthorn, VIC 3122, Australia;1. GeoRessources (UMR 7359, Université de Lorraine / CNRS / CREGU), Vand?uvre-lès-Nancy F-54518 France;2. Centre d′Hydrogéologie et de Géothermie, Université de Neuchâtel, 11 rue Emile-Argand, Neuchâtel 2000, Switzerland |
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| Abstract: | We revisit a classical topic: response functions of viscoelastic layers in large amplitude oscillatory shear. Motivated by questions concerning protective biological layers, we focus on boundary stresses in a parallel plate geometry with imposed oscillatory strain or stress. These features are gleaned from resolution and analysis of coupled standing waves of deformation and stress. We identify a robust non-monotone variation in boundary stress signals with respect to all experimental controls: viscoelastic moduli of the layer, layer thickness, and driving frequency. This structure of peaks and valleys in boundary values of shear and normal stress indicates redundant mechanisms for stress communication (by tuning to the peaks) and stress filtering (by tuning to the valleys). In this paper, we first restrict to a single-mode non-linear Maxwell model for the viscoelastic layer, where analysis renders a transparent explanation of the phenomena. We then consider a Giesekus constitutive model of the layer, where analysis is supplanted by numerical simulations of coupled non-linear partial differential equations. Parametric studies of wall stress values from standing waves confirm persistence of the Maxwell model phenomena. The analysis and simulations rely on and extend our recent studies of shear waves in a micro parallel plate rheometer S.M. Mitran, M.G. Forest, L. Yao, B. Lindley, D. Hill, Extenstions of the Ferry shear wave model for active linear and nonlinear microrheology, J. Non-Newtonian Fluid Mech. 154 (2008) 120–135; D.B. Hill, B. Lindley, M.G. Forest, S.M. Mitran, R. Superfine, Experimental and modeling protocols from a micro-parallel plate rheometer, UNC Preprint, 2008]. |
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