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Preprint 3-2016

Apparent Slip for an upper convected Maxwell Fluid

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Author(s) : Andreas Münch , Barbara Wagner , L. Pamela Cook , Richard Braun

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 3-2016

MSC 2000

76A05 Non-Newtonian fluids
34E05 Asymptotic expansions
76A20 Thin fluid films

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.

Keywords : Wormlike micelle solutions, thin-film approximation, sharp-interface limit, matched asymptotic expansions

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