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Re-entrant corner flow for PTT fluids in the natural stress basis

✍ Scribed by J.D. Evans; D.N. Sibley

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 646 KB
Volume: 157
Category: Article
ISSN: 0377-0257
DOI: 10.1016/j.jnnfm.2008.09.008

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✦ Synopsis

We revisit the situation of steady planar flow of Phan-Thien-Tanner (PTT) fluids around re-entrant corners of angles /˛where 1/2 ≤ ˛< 1. The model is considered in the absence of a solvent viscosity, under which a class of self-similar solutions has been identified with stress singularities of O(r -2(1-˛) ) and stream function behaviour O(r ˛(1+˛) ) (r being the radial distance from the corner). The asymptotic analysis is completed by providing a solution for the downstream boundary layer using natural stress variables. We show that the matching of the outer (core) solution into the downstream boundary layer imposes a restriction on the range of ˛∈ (2/3, 1) for which these self-similar solutions are applicable, i.e. they only hold for corner angles between 180 • and 270 • .

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