Tumbling motion of a single chain in shear flow: a crossover from Brownian to non-Brownian behavior.

We present the numerical results for the dynamics of a single chain in steady shear flow. The chain is represented by a bead-spring model and the smoothed profile method is used to accurately account for the effects of thermal fluctuations and hydrodynamic interactions acting on beads due to host fluids. It was observed that the chain undergoes tumbling motions and that its dimensionless frequency F=6pietasigma3nu/kBT depends only on the Peclet number Pe with a power law F proportional to Pealpha, where kB is the Boltzmann constant, T is the temperature, and sigma is the diameter of the beads. The exponent alpha clearly changes from 2/3 to 1 around the critical Peclet number, Pec, indicating that the crossover reflects the competition of thermal fluctuation and shear flow. The presented numerical results agree well with our theoretical analysis based on Jeffrey's work.