Constrained recoil after cessation of steady shearing flow from polymer rotarance theory

Abstract

Herein, we add another canonical rheological material function to our recent series of these derived from rotarance theory. By rotarance , we mean the hydrodynamic resistance to rotation felt by macromolecules in suspension. We thus use the physics of macromolecular orientation, and only this physics, to derive analytical expressions for (i) the ultimate shear recovery and (ii) both normal stress difference responses, in constrained recoil following cessation of steady shearing flow (called simply creep recovery ). By constrained , we mean that both the shear stress is released suddenly, and thereafter, the fluid remains confined between sliding plates with constant gap. The recoil phenomenon in polymeric liquids returns the fluid towards (but never completely to) its initial state. We call the final state, this ultimate shear strain, the ultimate shear recovery . Whereas recoil is absent in Newtonian fluids, it presents in elastic liquids. As with all known results from rotarance theory, we find creep recovery depends on macromolecular structure, and specifically, on the ratio of macromolecular moments of inertia, I ₃ / I ₁ . We recover well the well-known results for creep recovery for the rigid dumbbell (where I ₃ / I ₁ = 0), as we must.