On the turbulent flow of dilute polymer solutions

Abstract

This paper is concerned with the problem of explaining the anomalous decrease in turbulent skin friction observed in the turbulent flow of very dilute polymer solutions. The experimental evidence for dilute solutions is summarized. The polymer molecule in solution is examined from a theoretical point of view, using the Rouse model. It is found that the model predicts that the molecule will locally store energy as a function of the local strain rate of the solution. The experimental evidence is reexamined and it is concluded that the anomalous decrease in turbulent momentum transport results because the molecules manage to alter the energy balance of the small disturbances at the edge of the viscous sublayer. By slightly altering this balance the molecules allow viscous dissipation to destroy disturbances which would have had sufficient energy to grow had the molecules not been present. By decreasing the number of small disturbances which grow per unit area and time and move out from the edge of the viscous sublayer, the addition of polymer molecules ultimately changes the structure of the turbulence in the outer part of the boundary layer. This change results in lower Reynolds stresses and hence lower turbulent momentum transport. With the help of the relation for local energy storage derived from the Rouse model, parameters are developed to characterize the phenomenon. These parameters appear to be useful in understanding the experimental evidence to date.