Abstract
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, λ. 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), r, has a maximum estimated as λ -1 . This PDF shows an exponential tail for large T and a small-r 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.
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