Stretching of polymer in a random flow: Effect of a shear rate

The role of increasing shear rate on polymer extension and angular statistics in a random flow is studied. Large polymer extension results from a random part of a velocity field, whereas a shear component suppresses it although the coil-stretch transition occurs even at the highest shear rates. The universality in the limiting slope of a decay of a polymer extension probability distribution function (PDF) at the highest values of the Weissenberg number and at different contributions of the shear component is found. In the presence of the strong shear component, a tail of the PDF of polymer extension becomes significantly broadened in comparison to an isotropic random flow. With the increasing shear rate a PDF of a polymer out-of-the-shear-plane angle θ changes from uniform at small shear to peaked around a zero angle with an algebraic tail ~ θ-2 at the large shear rates, in accord with theory and numerical simulations.