A new microstructure-based constitutive model for human blood

A new constitutive equation for whole human blood is derived using ideas drawn from temporary polymer network theory to model the aggregation and disaggregation of erythrocytes in normal human blood at different shear rates. Each erythrocyte is represented by a dumbbell. The use of a linear spring law in the dumbbells leads to a multi-mode generalized Maxwell equation for the elastic stress and both the relaxation times and viscosities are functions of a time-dependent structure variable. An approximate constitutive equation is derived by choosing a single mode corresponding to the cell aggregate size where the largest number of cells are to be found. This size is identified in the case of steady flows. The model exhibits shear-thinning, viscoelasticity and thixotropy and these are clearly related to the microstructural properties of the fluid. Agreement with the experimental data of Bureau et al. [M. Bureau, J.C. Healy, D. Bourgoin, M. Joly, Rheological hysteresis of blood at low shear rate, Biorheology 17 (1980) 191–203] in the case of a simple triangular step shear rate flow is convincing.