Blood exhibits a non-Newtonian rheology, i.e., its shear-rate to shear-stress relationship is non-linear, i.e., one has to apply a threshold force, the so-called yield-stress before it moves at all. This particularity is due to the composition of blood and the particular qualities of its components (Boron et al., 2005). For our purpose we will consider that blood consists mainly of plasma with near-Newtonian flow properties and red blood cells (RBC) thus leading to a two-phase flow behavior where the plasma acts as the carrier phase and the RBC as suspended therein liquid-drop-like carried phase (Pinkowski, Lilienblum, 2015). At low shear rates (low velocity gradients) RBC tend to form rouleaux structures and these primary, randomly scattered rouleaux tend also to group together to form secondary rouleaux structures (Kulicke, 1986). Fibrinogen adhered to the vessel wall forms together with these secondary rouleaux fibrinogen filaments leading to increased viscosity at low shear rates. These fibrinogen filaments can be considered as precursors of blood clots. The key component in hemostasis is an elongated glycoprotein in the plasma that through activation by thrombin self-assembles into a first fibrin clot (Brown, J.H. et al. 2000).