Hydrodynamic changes of the depletion layer of dilute polymer solutions near a wall

The system studied in this work is a dilute solution of rod‐like molecules under simple shear flow and near a hard wall. The time evolution of the probability density function is described by a diffusion equation; particle trajectories that correspond to this equation are generated by stochastic methods. Several algorithms are presented to handle the constraints imposed by the presence of the wall. In good agreement with recent experimental work on xanthan solutions, for high shear rates we observe an increase in the thickness of the depletion layer near the wall. For low to intermediate shear rates, however, we find a transient decrease of the depletion layer thickness that has not been observed experimentally. Based on the results of our simulations, we present a simple procedure to determine a few, well defined characteristic parameters from the experimental density profiles.