Normal Stress Coefficient in Solutions of Macromolecules

Abstract

IN a previous note¹, the most general possible stress versus strain-velocity relations for an incompressible visco-inelastic fluid have been given. They involve two physical parameters for the fluid, Θ and Ψ Θ is the viscosity and Ψ is a new parameter which we shall term the ‘normal stress coefficient'. These relations must also be valid for a visco-elastic fluid in steady-state laminar flow. From a phenomenological point of view, Θ and Ψ may be constants or they may depend on the strain-velocity invariants. If the fluid is in a steady state of laminar flow, parallel to the x-axis, the velocity gradient being parallel to the y-axis, both tangential and normal components of stress, t_xy and t_ZZ exist at any point of the fluid, where t_xy= Θ _x and t_ZZ = — 1/2 Ψx² x is the velocity gradient in the fluid.