Thermodynamically consistent thixotropic viscoelastic modeling of human blood from a conformational free energy

Abstract

Structural thixotropic viscoelastic models describe the rheology of human blood accurately, but their structural kinetics are postulated, so their compatibility with the second law of thermodynamics is not guaranteed. We present ROUGE (ROUleaux model Guided by free Energy), a tensorial model of blood that describes the deformation of individual red blood cells and of rouleaux with two conformation tensors, and the degree of aggregation with a scalar variable. A single postulated Helmholtz free energy determines the stress, the relaxation of all three variables, and the entropy generation, so the model satisfies the second law in any flow. To build it, we extend a simplified formulation of nonequilibrium thermodynamics, which accounts for conformational energy and entropy, to microstructures described by several structural variables of different kinds. The coupling between aggregation and rouleaux deformation is motivated by the Langmuir adsorption of fibrinogen and is restricted so that the quiescent, fully aggregated state is the stable minimum of the free energy. Fits to published data for step-ups and step-downs in shear rate show that the fibrinogen binding sites remain far from saturation, so that the free energy has no adjustable parameters. They also show that rouleaux breakdown requires no empirical shear-activation term: the structure is destroyed in proportion to the work done by the flow on the aggregates, and a single structural time produces both breakdown within seconds and an algebraic recovery over tens of seconds. The resulting model has five well-determined parameters, and its fitted solvent viscosity coincides with that of plasma.