Polymer statistics in a random flow with mean shear

We consider the dynamics of a polymer with finite extensibility placed in a chaotic flow with large mean shear, to explain how the polymer statistics changes with Weissenberg number, Wi , the product of the polymer relaxation time and the Lyapunov exponent of the flow, λ̄. The probability distribution function (PDF) of the polymer orientation is peaked around a shear-preferred direction, having algebraic tails. The PDF of the tumbling time (separating two subsequent flips), τ , has a maximum estimated as λ̄−1. This PDF shows an exponential tail for large τ and a small-τ tail determined by the simultaneous statistics of the velocity PDF. Four regimes of Wi are identified for the extension statistics: one below the coil–stretched transition and three above the coil–stretched transition. Emphasis is given to explaining these regimes in terms of the polymer dynamics.