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Main Title: Apparent Slip for an upper convected Maxwell Fluid
Author(s): Münch, Andreas
Wagner, Barbara
Cook, L. Pamela
Braun, Richard
Type: Research Paper
Abstract: In this study the flow field of a nonlocal, diffusive upper convected Maxwell (UCM) fluid with a polymer in 4 a solvent undergoing shearing motion is investigated for pressure driven planar channel flow and the free boundary problem 5 of a liquid layer on a solid substrate. For large ratios of the zero shear polymer viscosity to the solvent viscosity, it is shown 6 that channel flows exhibit boundary layers at the channel walls. In addition, for increasing stress diffusion the flow field away 7 from the boundary layers undergoes a transition from a parabolic to a plug flow. Using experimental data for the wormlike 8 micelle solutions CTAB/NaSal and CPyCl/NaSal, it is shown that the analytic solution of the governing equations predicts 9 these signatures of the velocity profiles. Corresponding flow structures and transitions are found for the free boundary problem of a thin layer sheared along a solid substrate. Matched asymptotic expansions are used to first derive sharp-interface models 11 describing the bulk flow with expressions for an apparent slip for the boundary conditions, obtained by matching to the flow in 12 the boundary layers. For a thin film geometry several asymptotic regimes are identified in terms of the order of magnitude of 13 the stress diffusion, and corresponding new thin film models with a slip boundary condition are derived.
Subject(s): wormlike micelle solutions
thin-film approximation
sharp-interface limit
matched asymptotic expansions
Issue Date: 4-Feb-2016
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 76A05 Non-Newtonian fluids
34E05 Asymptotic expansions
76A20 Thin fluid films
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2016, 03
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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