Affiliations: Laboratoire de Biorhéologie et d’Hydrodynamique Physicochimique (Laboratoire Associé au CNRS LA 343.), Université Paris VII, 2 Place Jussieu, 75251 Paris cedex 05, France
Note: [] Accepted by: Editor S. Oka
Abstract: A Maxwell-type equation, which involves both time-dependent viscosity η(t) and elastic modulus G(t) is proposed as governing the shear stress difference σ′=σ−σy, where σ and σy are total and yield shear stresses respectively. A (reaction kinetics) equation for a structure variable λ is written which describes the evolution of blood structure (network ⇄ rouleau ⇄ RBC) in stress formation and stress relaxation measurements and which also depends on the (constant) applied shear rate γ˙1. The time dependent viscosity is assumed to involve the solution λ(t,γ˙1) of the rate equation in the same manner than its equilibrium value λeq(γ˙1) enters in a viscosity equation η(λeq) yet proposed by one of the authors. A simple relation G(λ) completes the structural description. General solutions σ(t) of the Maxwell-type equation are discussed in the case of stress relaxation (after the cessation of steady flow) and stress formation (under constant shear rate). Especially, the latter exhibits the well-known “overshoot” behavior. Moreover, the long time behavior of the former allows the quantification of the yield shear stress. Lastly one example of application to blood measurements is discussed.
