Turbulence induced change in the conformation of polymer molecules

Abstract

An investigation into the conformation of a polymer molecule exposed to a stochastic flow field is made utilizing a cumulant expansion. The study begins by considering the full Kirkwood–Riseman n-bead chain with an arbitrary connector potential as a model for the polymer molecule, digressing to the two-bead dumbbell molecule for detailed calculations. It is found that the effect of the stochastic velocity field on the molecule can be interpreted as a ‘‘renormalization’’ of the connector potential. The introduction of this renormalized potential greatly simplifies the mathematics and lends an intuitive understanding to the effect of the turbulence on the polymer. It is shown that this analysis will recover the anomalous tendency of the radius of gyration to become infinite for the special case of a Hookean potential which has been observed by previous investigators. Further, this study involves the Eulerian velocity–velocity correlation function rather than the Lagrangian correlation used in the previous studies.