Lagrangian stretching and polymeric stress: unification of two disparate branches of continuum mechanics

Polymeric flows are common in industrial, biological, and natural processes ranging from enhanced oil recovery to drug delivery to biofilm transport.  The stretching of polymeric chains induces large polymeric stress which controls the flow dynamics and transport in polymeric flows. However, the measurement of polymeric stress is challenging. The Lagrangian stretching field is an easily computed Lagrangian coherent structure (LCS) that represents the hidden skeleton of the flow and behaves as a strong transport barrier. We have theoretically obtained a general relationship between the polymeric stress and the stretching fields for weak flows and also extended it for special flows having strong kinematics. Further, we have numerically shown a strong correlation between the stress and stretching fields for complex geometries and chaotic flows. Thus, this work unifies two disparate branches of continuum mechanics and establishes a simple framework to determine the topology of polymeric stress using a readily measured velocity field.