Kinetics of polymer tumbling in shear flow: A coarse-grained description

We study the classic problem of dynamical evolution of a polymer in a shear flow. Interestingly, the polymer goes through several distinctly identifiable conformations during its passage from coiled to stretched states back and forth. We identify these conformations assumed by the polymer while tumbling and study the kinetics of the process in terms of the residence and recurrence times of individual conformations. The distribution of residence times exhibits exponentially decaying tails which helps us build an effective Markovian picture of the truly non-Markovian problem. We present the explicit W matrix for the coarse-grained evolution via a master equation and study its elements as a function of the Weissenberg number. We show that the timescales of decay of the autocorrelation function for the full Langevin dynamics compare quite well with the approximate results from the master equation approach.