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On the mechanisms for drag reduction: A viscoelastic evaluation based on a bead‐spring model
Author(s) -
Ting R. Y.
Publication year - 1972
Publication title -
journal of applied polymer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.575
H-Index - 166
eISSN - 1097-4628
pISSN - 0021-8995
DOI - 10.1002/app.1972.070161211
Subject(s) - viscoelasticity , drag , constitutive equation , mechanics , newtonian fluid , viscosity , dissipation , generalized newtonian fluid , dumbbell , classical mechanics , extensional viscosity , stress relaxation , flow (mathematics) , spring (device) , turbulence , relaxation (psychology) , physics , thermodynamics , shear rate , finite element method , shear viscosity , medicine , kinetics , physical therapy , social psychology , psychology
Two possible drag reduction mechanisms were examined by studying the viscoelastic effects of polymer solutions for the separate cases of oscillatory shear flow and elongational flow. The constitutive equation used was based on a modified dumbbell molecular model which predicts non‐Newtonian viscosity and both the primary and the secondary normal stress differences. It can be shown that when this constitutive equation is arranged in the form of the Oldroyd model, the latter becomes a special case of this more general equation. The present results show that viscoelastic effects on the mean local rate of energy dissipation of a fluid element in an oscillatory motion are negligibly small. However, such effects introduce very large increases in the elongational viscosity as the stretching rate exceeds a certain limiting value and the flow time exceeds the terminal relaxation time of the fluid. The relative merits of these findings as possible explanations of turbulent drag reduction are briefly discussed.