APPARENT SLIP FOR AN UPPER CONVECTED MAXWELLFLUID

作者：Munch Andreas^*; Wagner Barbara; Cook L Pamela; Braun Richard J

来源：SIAM Journal on Applied Mathematics, 2017, 77(2): 537-564.

DOI：10.1137/16M1056869

• wormlike micelle solutions
• thin-film approximation
• sharp-interface limit
• matched asymptotic expansions

In this study the flow field of a nonlocal, diffusive upper convected Maxwell fluid in a solvent undergoing shearing motion is revisited for pressure driven planar channel flow and the free boundary problem of a liquid layer on a solid substrate is investigated. For large ratios of the zero shear polymer viscosity to the solvent viscosity, channel flows exhibit boundary layers at the channel walls. In addition, for increasing stress diffusion the flow field away from the boundary layers undergoes a transition from a parabolic to a plug flow. 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 describing the bulk flow with expressions for an apparent slip for the boundary conditions, obtained by matching to the flow in the boundary layers. For a thin-film geometry several asymptotic regimes are identified in terms of the order of magnitude of the stress diffusion, and corresponding new thin-film models with a slip boundary condition are derived.

• 出版日期2017