Stresses in Dilute Solutions of Bead–Nonlinear-Spring Macromolecules. I. Steady Potential and Plane Flows

Abstract

The mechanics of a dilute solution of bead–nonlinear‐spring molecules are investigated in various steady homogeneous flows. A new type of nonlinear spring (“linear locked”) with a finite end‐to‐end distance is introduced which allows closed solutions of the diffusion equation to be found. Hence, only a simple numerical calculation of stresses is necessary. In a steady shear flow we find a viscosity decreasing with shear rate, and in an extensional flow there is a limiting upper viscosity for large extension rates. Neither of these realistic results holds for the Rouse model. In a shear flow the first normal stress difference is positive, and the second normal stress difference is zero. In general steady plane flow it is shown there is a critical kinematic condition separating states of large and small dissipation for highly extensible molecules. The role of polydispersity in molecular weights is briefly considered.