Dynamic viscosity of macromolecular liquids for a superposition of static and oscillating velocity gradients

Two coupled, inhomogeneous relaxation equations for the friction pressure tensor and the alignment tensor are derived within the framework of irreversible thermodynamics. These equations are solved for a specific geometry, viz. flow between flat plates, and for a velocity gradient of the form Γ0 + Γ1 cos Ωt with small Γ1. From the resulting relation between the (time-dependent) friction pressure tensor and the velocity gradient, the dynamic viscosity and the normal pressure can be inferred. The frequency dependence of the relevant viscosity coefficients is discussed. If Г0, the magnitude of the static part of the velocity gradient is large enough, a type of resonance behavior is found with the resonance frequency Ωres≈(1 + ξ)-1Γ0 where ξ is the ratio between the relation times of the friction pressure tensor and of the alignment tensor.