Turbulent dynamics of polymer solutions

We study properties of dilute polymer solutions. The probability density function (PDF) of polymer end-to-end extensions R in turbulent flows is examined. We show that if the value of the Lyapunov exponent lambda is smaller than the inverse molecular relaxation time 1/tau then the PDF has a strong peak at the equilibrium size Ro and a power tail at R much greater than R-0. This confirms and extends the results of J. L. Lumley [Symp. Math. 9, 315 (1972)]. There is no essential influence of polymers on the flow in this regime. At A lambda tau > 1 the majority of molecules is stretched to the linear size R-op much greater than R-0, which can be much smaller than the maximal length of the molecules due to their back reaction.