An elastic theory of drag reduction

This explanation has been rather generally accepted. However, it is now open to some question in recent experiments with polymer injection at the center of a pipe, one finds drag reduction in conditions where wall effects are not involved (McComb and Rabie, 1979 Bewersdorff, 1982, 1984). 

This observation prompted Tabor and the present author to try a completely different approach (Tabor and de Gennes, 1986) namely to discuss first the properties of homogeneous, isotropic, three-dimensional turbulence without any wall effect. 

In Section 4.3 we return to wall turbulence, and try to set up a modified version of the Lumley approach, where, at each distance y from the wall, we have a cascade, but it is truncated elastically. This gives a law for the minimum eddy size r versus distance y which is qualitatively different from Lumley s viscous effect. But the net result is still an enhancement of the intermediate buffer layer . We expect drag reduction from this, although we have not carried out the detailed analog of Lumley s matching. 

In Section 4.4 we list some more general systems which can show drag reduction on turbulent flow. Some of the systems are dominantly elastic while others are probably dominantly viscous. 

Our whole discussion is very qualitative. But, even at this modest level, it leads to a surprisingly rich classification of possible cascades and flows. For instance, in bulk turbulence, we have three control parameters (a) the dissipation per unit mass e (b) the polymer chain length, or equivalently the number of monomers per chain N (c) the monomer concentration c (or the number of coils/cm, Cp = c/N). 

---

The various theories explaining drag reduction may be divided into three categories first, an explanation in which the increase in extensional viscosity for the polymer solution is the main ingredient second, a theory that stresses the importance of anisotropic effects introduced by the extended polymer molecules and third, a proposed explanation in which elastic effects are responsible for drag reduction. 

---