Enhancement of drag and mixing in a dilute solution of rodlike polymers at low Reynolds numbers

We study the dynamics of a dilute solution of rigid rodlike polymers in a viscous fluid at low Reynolds numbers by means of numerical simulations of a simple rheological model. We show that the rotational dynamics of polymers destabilizes the laminar flow and causes the emergence of a turbulent-like chaotic flow with a wide range of active scales. This regime displays an increased flow resistance, corresponding to a reduced mean flow at fixed external forcing, as well as an increased mixing efficiency. The latter effect is quantified by measuring the decay of the variance of a scalar field transported by the flow. By comparing the results of numerical simulations of the model in two and three dimensions, we show that the phenomena observed are qualitatively independent on the dimensionality of the system, but the effects of polymer are, in general, stronger in two dimensions. This dimensional effect is explained in terms of the different rotational degrees of freedom of the rods.