Creep in macromolecular solutions according to rigid dumbbell kinetic theory

Abstract

A macromolecular solution is represented by the simple model of rigid dumbbells suspended in a Newtonian fluid with Brownian motion included. Hydrodynamic interaction is not taken into account. It is found that for this model there will be recoil after the cessation of steady shearing flow. The ultimate shear recovery S∞ is developed as a power series in κ−, the shear rate prior to the cessation of the steady shear flow: $$S_\infty = (\theta _0 /2\eta _0 ) \kappa ^\user1{ - } + O(\kappa ^\user1{ - } )^3$$ where η0 and θ0 values of the viscosity and primary normal stress functions respectively at zero-shear rate. The coefficient of the term in (κ−)3 is calculated. In addition, the behavior of the normal stresses during the recoil process is found; during recoil τ22−τ33 has the opposite sign from τ11−τ22.