Finite Extension of Polymers in Turbulent Flow

The statistics of polymers advected by a turbulent flow are investigated. To limit the polymer lengths above to coil-stretch transition, a FENE-P type relaxation law is used. The turbulence is modeled by a random strain, delta-correlated in time and with Gaussian statistics. The distribution of polymer lengths for both the coiled and stretched states are derived, from which are obtained analytical expressions for the moments of the distribution. The polymer stress on the fluid decreases linearly with the inverse of the Deborah number. The degradation (breaking) of the polymers is also discussed, showing that even for large Deborah number some polymers can remain unbroken.