Molecular shape in homogeneous flows: predictions of the rouse model

An analysis of the Rouse model is used to predict the shape of flexible, free-draining polymers in homogeneous flows. The derivation is based on the Lodge-Wu/Booij-Van Wiechen solutions [1,2] for the configurational distribution function of a Rouse chain, which consists of a free-draining string of beads connected by Hookean springs. Much of the theoretical development parallels the one used by Saab et al. [3,4] to predict link orientations for the same molecular model; rather than solving for link orientation, however, we solve for bead location. The function P_v(U, t), which describes the spatial distribution of bead v about the chain center of mass in the presence of hydrodynamic forces, is a key development of this contribution. Various averages evaluated from this function can be employed to study details of a deformed molecule's configuration. The model predicts that spatial distortion in flow is a highly nonuniform function of location in the chain; hydrodynamic forces have a greater influence on the beads near the ends of the chain than on those near the center.