Extensional flow of dilute polymer solutions

Abstract

The behaviour of dilute polymer solutions in sink flow, viz., radial flow toward a point, was investigated experimentally and theoretically. Solutions of polyethylene oxide, in the drag-reducing concentration range, were pushed through a 60° conical channel at Reynolds numbers of order 10². Preliminary studies revealed a range of flow conditions in which the flow was free of secondary motion yet non-Newtonian effects were significant. Measurements of pressure differential between two radial positions yielded the non-Newtonian normal stress developed in the radial direction; the magnitude was the same order as the Newtonian stress, i.e., as the dynamic pressure ½ρV².

Several fluid models were analysed to determine the stress generated by each in sink flow. It was found that a solution of Rouse–Zimm flexible macromolecules produces a stress which is three orders of magnitude below the observed level, and that macro-molecules with finite extension fall short by two orders. A suspension of elongated particles, of the type analysed by Batchelor, was also considered, but application to the present case was difficult because of the small scale required by the theory. Consequently, the theory was extended to include particles the size of the flow field, and an order-of-magnitude analysis revealed that for such particles to produce the desired stress, the aspect ratio must be $O(10^{\frac{7}{2}})$, and the cross dimension is likely O(0·1)μm. Electron micrographs of freeze-dried samples of the polymer solutions showed the solute in the form of an irregular network of apparently undissolved strands, with diameters in the O(0·1)μm range.