Linear Polymers in the Turbulence Vortices

Abstract

LONG chain linear polymers in dilute aqueous solutions show several anomalies, particularly a reduction in turbulent skin friction. Attempts have been made to explain such anomalies in terms of visco-elasticity. It is, however, worth considering the possibility that the effects arise from a “spiral combing” of the macromolecules in the cores of the vortices which constitute the turbulence. If aligned at an angle to a cylindrical surface of slippage—with their front ends in the faster flow on the interior—these macromolecules would act as “sea anchors” bridging the streamlines of different velocities, thereby increasing the effective local viscosity in these cores, and thus making these cores act more nearly as rigid bodies. In a plane shear flow such an alignment is improbable, for there a macromolecule, even if it happened to have been stretched, would tend to be turned by the vorticity of that flow until it is aligned with a streamline, and becomes free to slip with respect to other macromolecules so aligned. But the rather unusual circumstances necessary to produce such “combing” at a fairly large angle to the pathlines—namely, a brief spurt of a strong shear, followed by some reduction of the tendency of the fluid to sweep (turn) a stretched macromolecule towards a pathline—are indeed experienced by a macromolecule which is close to a vortex at the moment of its birth. As the diffusing vortex spreads over the macromolecule, this macromolecule first experiences a spurt of shear accompanied by the vorticity of an opposite sense; and by the time it is engulfed by the core (the vorticity of which would tend to sweep this macromolecule towards a pathline) the vorticity of the core is already diminished by the diffusion. It is therefore conceivable that an occasional macromolecule might be stretched by the spurt of the shear enough to have its end “caught” in the manner suggested in Fig. 1. Such “rigidized cores” would be less likely to diffuse, turn, stretch and break up than the vortices which constitute the turbulence in a homogeneous fluid; and so would more likely be formed in longer sections, and act as “rollers”, namely, as more effective constituents of the vortex sheet formed by the turbulent layer. This explanation accounts also for other anomalies manifested by these solutions.