Stability of plane Poiseuille flow of slightly viscoelastic fluids

Abstract

In many practical situations involving fluid flow, turbulence or eddying occurs near solid surfaces, and resistance to motion is largely associated with this turbulence. Large reductions in turbulent frictional resistance; for example, of the pressure drop in pipe flows, can sometimes be achieved by dissolving small quantities of certain substances in the liquid. The first clear scientific description of the phenomenon which now bears his name was given by Toms (1949). The additive substances usually have very high molecular weights, of the order of 10⁶, and are effective in concentrations of the order of ten to one hundred parts per million by weight. In these very low concentrations the solution has a viscosity, μ, which is independent of shear rate and indistinguishable from that of the solvent alone. Here, then, are fluids which are essentially the same as the solvent (usually water) in their values of density and viscosity, which are normally regarded as the relevant fluid parameters, yet they behave in a radically different way.