Blood viscoelasticity and thixotropy from stress formation and relaxation measurements: a unified model

A Maxwell-type equation, which involves both time-dependent viscosity eta (t) and elastic modulus G(t) is proposed as governing the shear stress difference sigma' = sigma - sigma Y, where sigma and sigma Y are total and yield shear stresses respectively. A (reaction kinetics) equation for a structure variable lambda is written which describes the evolution of blood structure (network in equilibrium rouleau in equilibrium RBC) in stress formation and stress relaxation measurements and which also depends on the (constant) applied shear rate gamma 1. The time dependent viscosity is assumed to involve the solution lambda (t, gamma 1) of the rate equation in the same manner than its equilibrium value lambda eq(gamma 1) enters in a viscosity equation eta [lambda eq] yet proposed by one of the authors. A simple relation G[lambda] completes the structural description. General solutions sigma (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.