(221i) An Inhomogeneous, Nonequilibrium Thermodynamics Approach to Modeling Blood Rheology

Colloidal suspensions often exhibit complex behavior under flow sometimes including variable viscosity, inhomogeneous, stress-induced, particle migration, and transient memory effects. Modeling these effects can be difficult due to the nonequilibrium nature of flowing material and the need for comprehensive models which relate the macroscopic behavior to microscopic interactions. Nevertheless, models for complex colloidal suspensions have widespread use in both industrial and clinical settings. Blood, primarily a suspension of red blood cells (RBCs) in an aqueous plasma, is one example of a complex colloidal material. Under shear, blood exhibits pseudoplasticity, viscoelasticity, and thixotropy. These effects arise from both the tendency of RBCs to reversibly form coin stack microstructures called rouleaux at low shear rates and the ability of RBCs to deform and stretch at high shear rates. Moreover, inhomogeneous separation concentration of RBCs from plasma can occur for blood flow driven by gradients in the shear under Poiseuille and/or excluded by the wall effects under both Poiseuille and Couette conditions. Moreover, to fully describe the flow of blood in complex geometries, a full tensorial approach is required that accounts for both the complex rheological behavior and the potential for inhomogeneous phase separation.

In this work, we present a transient and inhomogeneous constitutive model for blood rheology based on nonequilibrium thermodynamic principles. The model incorporates physically meaningful parameters and can track the transient behavior of variables that are indicative of the current structure state within the blood. The model is fit to experimental rheology data for healthy human blood and used to predict additional stress and concentration data at physiologically relevant flow conditions for shear flow and Poiseuille flow in a microchannel. While the model was developed for blood, it is likely that the principles used in the derivation can be applied to a wide range of complex colloidal suspensions.