Analytical Analysis of the Conformational and Rheological Properties of Flexible Active Polar Linear Polymers under Shear Flow

Abstract: The conformational and rheological properties of active polar linear polymers (APLPs) under linear shear flow are studied analytically. We describe a discrete APLP as an inextensible flexible Gaussian bead-spring chain supplemented by active forces along the bonds. The linear, non-Hermitian equations of motion are solved by an eigenfunction expansion in terms of a biorthogonal basis set. The model reveals an intimate coupling between activity and shear flow, which implies activity-enhanced polymer conformational and rheological properties. Compared to a passive polymer, we find a significantly enhanced shrinkage transverse to the flow direction with increasing shear rate, with a power-law exponent $-4/3$, compared to the passive values of $-2/3$. This conformational change is tightly linked with a strongly amplified shear-thinning behavior, where the shear viscosity exhibits the same power law. The characteristic shear rate for the onset of these effects is determined by the activity. In the asymptotic limit of large activities, the shear-induced features become independent of activity and equal to those of passive polymers.