| Περίληψη: | Many deaths are the result of cardiovascular diseases associated with unusual blood rheological properties in the circulatory system [Yilmaz and Gundogdu (2008)]. Therefore, understanding the rheological behavior of blood is paramount in providing insights on the causes of various diseases and the tailor-design of the transport of drug directly to the infected area [Yilmaz and Gundogdu (2008)]. Blood is mainly a suspension of elastic particulate cells, among which red blood cells (RBCs) dominate, in plasma, usually considered as a Newtonian fluid. Red blood cells tend to aggregate in the presence of plasma proteins, forming structures known as rouleaux which can be decomposed upon the applied tension induced by the flow. In this master thesis, we derive a constitutive rheological model for human blood which accounts for the formation and dissociation of rouleaux using the generalized bracket formulation of non-equilibrium thermodynamics [Beris and Edwards (1994)]. Similar to the model derived by Owens and coworkers [Owens (2006); Fang and Owens (2006); Moyers-Gonzalez et al. (2008)] through polymer network theory, each rouleau in our model is represented as a dumbbell; the corresponding structural variable is the conformation tensor of the dumbbell. The kinetics of rouleau formation and dissociation is treated as in German et al. (2013) by assuming a set of reversible reactions, each characterized by a forward and a reverse rate constant. The final set of evolution equations for the microstructure of each rouleau and the expression for the stress tensor turn out to be very similar to those of Owens and co-workers. However, by explicitly considering a mechanism for the formation and breakage of rouleaux, our model further provides expressions for the aggregation and disaggregation rates appearing in the final transport equations, which in the kinetic theory-based network model of Owens were absent and had to be specified separately. Despite this, the two models are found to provide similar descriptions of the experimental data collected by Mehri et al. (2013) on the size distribution of rouleaux.
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