Flow of Viscoelastic Liquids: Comparison of Departures from Laminar Flow in Porous Beds and in Tubes
Authors: Jones W.M. , Maddock J.L. 
Published: December 2007

Abstract
The lowest value [Re]' of the Reynolds number at which streamline flow breaks down has been studied experimentally for the flow of "ordinary" liquids [water, glycerol solution, salt solution, turpentine] and of relaxing liquids [solutions of Cellofas in water and polyacrylamide in water] through a straight tube and in beds of glass beads. The tube was 30.3-cm long and 0.368-cm I.D., two sizes of beads were used—0.206-cm and 0.114-cm diameter —packed in brass tubes of diameter 1.59 cm and length 15.2 cm,. Most experiments were made at 25 1C, but some have also been made at 15C and 35C.
In both the tube and beads [Re]' is the same for all "ordinary" liquids, but [Re]' is between 6 and 12 per cent higher for the Cellofas solution, but only while it is degrading. In the case of the polyacrylamide solutions-departures from laminar flow, occur at a value of [Re]' which is about 9 per cent lower in the flow and about 32 per cent lower in porous bed flow; these departures in polyacrylamide flow are accompanied by pronounced drag reduction in the tube, but not in the porous beds. Lowering the temperature in the flow of polyacrylamide solutions lowers [Re]' in porous beds and increases drag reduction in the tubes.
Introduction
Jones and Williams showed that the value of the flow of gaseous carbon dioxide through tubes and through porous materials was different from the value of [Re]' in the flow of gaseous nitrogen through the same tube or porous material. The difference was attributed to the relaxation of a vibrational mode of the CO2 molecule either absorbing or emitting energy to the bulk motion of the gas, depending on the conditions of the experiment. As a consequence of the experiments and their interpretation, it was anticipated that very similar effects would occur in the flow of relaxing liquids through tubes and porous materials; preliminary experiments confirming these predictions are reported here. There were also theoretical reasons for expecting the onset of instabilities to be different in a relaxing liquid [see Thomas and Walters]; also, considerable drag reduction has been observed in the turbulent flow of such liquids through tubes [see Savins].
EXPERIMENTAL METHOD
The flows of "ordinary" liquids [water, 5 per cent weight-weight glycerol solution in water, 5 per cent weight-weight salt solution in water, and turpentine] and of relaxing liquids [a solution of Cellofas in water .005 weight-weight, and solutions of polyacrylamide in water ranging from .05 to .005 per cent weight-weight] through a straight tube 30.3-cm, long and 0.368-cm I.D. have been studied. The flow of water and of the glycerol solution and that of the relaxing liquids have also been studied in beds of glass beads. Two sizes of beads have been used—0.206- and 0.114-cm diameter—packed in brass tubes of diameter 1.59 cm and length 15.2 cm. The porosities of the beds were 0.382 and 0.369, respectively. All experiments were thermostatted initially to 25C +1C. Some experiments have been done at 15C and 35C to study the effect of temperature. The mass rate of flow of liquid (V rho) and the pressure difference [Delta p] across the tube or porous bed were measured.
The resistance Delta p to laminar flow through tubes is given by:
........................................(1)