Molecularly based criteria for shear banding in transient flow of entangled polymeric fluids.

Dissipative particle dynamics simulations of polymeric melts in a start-up of shear flow as a function of ramp time to its steady state value is studied. Herein, we report the molecular findings showing the effect of ramp time on the formation of shear banded structures and chain relaxation behavior. Specifically, it is shown that shear banding emerges at a rapid start-up; however, homogeneous shear prevails when the deformation rate ramp time is sufficiently slow. This finding is in full consistency with prior continuum level linear stability analysis of shear banding in start-up of shear flows as well as experimental observations of entangled DNA and polymer solutions. Further, it has been revealed that the ratio of the longest chain orientation relaxation time to that of the time for the imposed deformation rate to reach its steady state value plays a central role in determining whether local strain inhomogeneities that lead to the formation of shear banded flow structures are created. In addition, we have shown that the gradient of the number of entanglements along the velocity gradient direction should reach a critical value for the creation of localized strain inhomogeneity. Moreover, the relation between the local process leading to shear banded flows and the relaxation mechanism of the chain is discussed. Overall, a molecular picture for the interrelation between the longest chain orientation and stress relaxation time, local inhomogeneities, and shear banding has been proposed and corroborated with extensive analysis.