Onset of Instabilities and Reduction of Drag in the Flow of Relaxing Liquids through Tubes and Porous Beds

Abstract

Jones and Williams^1,2 showed that the onset of instabilities in the flow of gaseous carbon dioxide through tubes and through porous materials occurred at a value of the Reynolds number Re which was different from the value of Re when instabilities occurred 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 carbon dioxide molecule, the vibrational mode 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 (that is, visco-elastic) liquids through tubes and porous materials; preliminary experiments confirming these predictions are reported here. (There are also theoretical reasons for expecting the onset of instabilities to be different in a relaxing liquid, compare Thomas and Walters³; considerable drag reduction has also been observed in the turbulent flow of such liquids through tubes⁴.)