On the stretching of dilute polymer solutions

Abstract

Recently Champagne, Harris, and Corrsin ( 2 ) have measured turbulence properties in a nearly homogeneous shear flow where far downstream of a shear-turbulence generator, the turbulence has reached a nearly homogeneous asymptotic condition with constant values of the mean velocity gradient and the one-point turbulence moments. The present note interprets the experimental results in terms of Phillips' hypothesis. The experimentally measured value of the eddy viscosity ve is found to be 0.0144 sq. ft./sec. The Eulerian space-time correlation of CONSTITUTIVE EQUATIONGordon and Schowalter recently presented a modification of the dumbbell theory of dilute polymer solutions ( 1 2 ) , based on a structured fluid theory of Ericksen ( 1 3 ) . Gordon and Everage used this result to obtain an explicit constitutive equation ( 1 4 ) , namely

Cavitation suppression by polymer additives: Concentration effect and implication on drag reduction

“…The basic mechanisms involved in both these hydrodynamic phenomena may therefore have much in common. For example, extremely high viscoelastic resistance of polymers to elongational strains has been proposed as a possible explahation for drag reduction (Lumley, 1969;Everage and Gordon, 1971;Ting, 1972). In the case of jet cavitation, it may be possible that the stress-strain balance was also strongly affected by the presence of the polymer additives.…”

Some limitations on the detection of high elongational stress effects in dilute polymer solutions

“…It was later pointed out, however, that, although the steady-state stress levels may be large, the transient behavior can be quite different.28 Recent investigations have, therefore, proposed constitutive equations which are more adaptable to the treatment of transient flows. [17][18][19] Such a model will be used for the discussion presented here. In this continuum model,lg which is based on the bead-spring molecular theories of Rouse and Zimm, the total stress u is related to the strain rate tensor d by where p is the hydrostatic pressure, t s is the solvent viscosity, and d n ) is the nth mode stress deviator satisfying In eq.…”

Network models of concentrated polymer solutions derived from the yamamoto network theory

“…(4), it is convenient to diagonalize the tensor r* = r -ED by introducing a tensor T such that T-'-r*.T = V, where V is diagonal. Furthermore we transform the coordinates to a new frame p = ( p ,~, z ) The transformed value of this scalar quantity is simply (11) x 2 + y 2 + 2 2 = p2-2 w p q + q z + 2 2 where…”