Abstract
Conditions are presented for the appearance of weak tangential discontinuities of the velocity profile in isothermal Phan-Thien-Tanner viscoelastic medium flows through plane slit channels and narrow pipes.
References
N. Phan-Thien and R.I. Tanner, “A New Constitutive Equation Derived from Network Theory,” J. Non-Newtonian Fluid Mech. 2(4), 353–365 (1977).
R.I. Tanner and S. Nasseri, “Simple Constitutive Models for Linear and Branched Polymers,” J. Non-Newtonian Fluid Mech. 116, 1–17 (2003).
W.M. Brondani, H.T. Coradin, A.T. Franco, et al., “Numerical Study of a PTT Viscoelastic Fluid Flow through a Concentric Annular,” in Proc. 19th Intern. Congr. Mechanical Engineering (Brasilia, DF, 2007).
A. Bogaerds, G. Peters, M. Hulsen, and F. Boaijors, Stability Analysis of Viscoelastic Fountain Flow(Techn. Univ. Eindhoven, Eindhoven, 2002).
P.J. Oliveira, “Asymmetric Flows of Viscoelastic Fluids in Symmetric Planar Expansion Geometries,” J. Non-Newton. Fluid Mech. 114, 33–63 (2003).
V. Ganvir, “Extrudate Swell of Linear and Branched Polyethylene,” J. Non-Newton. Fluid Mech. 166(1), 12–24 (2011).
L.M. Quinzani, G.H. McKinley, R.A. Brown, and R.C. Armstrong, “Modeling the Rheology of Polyisobutylene Solutions,” J. Rheol. 34, 705–748 (1990).
L.M. Quinzani, R.C. Armstrong, and R.A. Brown, “Use of Coupled Birefringence and LDV Studies of Flow through a Planar Contraction to Test Constitutive Equations for Concentrated Polymer Solutions,” J. Rheol. 39, 157–165 (1995).
W.L. Raiford, L.M. Quinzani, P.J. Coates, et al., “LDV Measurements of Viscoelastic Flow Transitions in Abrupt Axisymmetric Contractions: Interaction of Inertia and Elasticity,” J. Non-Newton. Fluid Mech. 32, 39–68 (1989).
O.I. Skulskii and S.N. Aristov, Mechanics of Anomalously Viscous Fluids (Scientific Publishing Center “Regular and Chaotic Dynamics”, Moscow-Izhevsk, 2004) [in Russian].
M.A. Alves, F.T. Pinho, and P.J. Oliveira, “Study of Steady Pipe and Channel Flows of a Single-Mode Phan-Thien-Tanner Fluid,” J. Non-Newton. Fluid Mech. 101, 55–76 (2001).
P.J. Oliveira and F.T. Pinho, “Analytical Solution for Fully Developed Channel and Pipe Flow of Phan-Thien-Tanner Fluids,” J. Fluid Mech. 387, 271–280 (1999).
L.L. Ferras, J.M. Nobrega, and F.T. Pinho, “Analytical Solutions for Channel Flow of Phan-Thien-Tanner and Giesekus Fluids under Slip,” J. Non-Newton. Fluid Mech. 171–172, 97–105 (2012).
D.O.A. Cruz, F.T. Pinho, and P.J. Oliveira, “Analytical Solutions for Fully Developed Laminar Flow of Some Viscoelastic Liquids with a Newtonian Solvent Contribution”, J. Non-Newton. Fluid Mech. 132, 28–35 (2005).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © D.V. Ananyev, E.K. Vachagina, A.I. Kadyirov, A.A. Kainova, G.T. Osipov, 2014, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2014, Vol. 49, No. 5, pp. 17–26.
Rights and permissions
About this article
Cite this article
Ananyev, D.V., Vachagina, E.K., Kadyirov, A.I. et al. Determination of existence conditions for the solutions with a weak discontinuity for simplest viscoelastic fluid flows. Fluid Dyn 49, 576–584 (2014). https://doi.org/10.1134/S0015462814050032
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462814050032