Stress growth at inception of steady shearing flow from rotarance theory

Rotarance theory explains the contributions to the non-Newtonian behavior of a complex fluid with, and only with, the physics of orientation of its particles in suspension. These particles may be prolate, like straight chain polymers, or spherically symmetric, like the tridumbbell due to Giesekus, or oblate, like a ring, or a planar star. In this work, we continue the empowerment of rotarance theory by arriving at the analytical expression for another of its canonical rheological material functions: stress growth following the sudden inception of steady shear flow (also known simply as stress growth). We do so for the shear stress response, along with both normal stress difference responses. We find that in stress growth, the greater the ratio of the macromolecular moments departs from unity, be this departure prolate (I3/I1<1) or oblate (I3/I1>1), the greater the overshoots of both the shear stress and the normal stress differences. The canonical experimental observations of shear rate dependent overshoots are thus recovered, as are the well-known analytical results for the rigid dumbbell or multi-bead rod (I3/I1=0). We find that oblate macromolecules (such as rigid rings or planar stars) produce far greater overshoots than prolate (straight chains).