Distribution of blood components in the Poiseuille flow

The thermodynamic approach is used to describe the stationary distributions of blood components in a cylindrical Poiseuille flow. Based on it, a method is described for numerical modelling of the distribution of blood components over the blood vessel cross-section. Dispersed phases are represented by a combination of cellular components (red blood cells, white blood cells, etc.), blood plasma is considered as a low molecular weight dispersion medium. The distributions are obtained on the basis of the invariance condition of mechanochemical potentials (the sum of the chemical potential and mechanical energy) of the components, which is fulfilled at stationary equilibrium in stationary external fields of different nature. The calculation is reduced to a numerical search for a solution to a system of transcendental equations corresponding to the continuity of the medium. This system has a unique solution that describes the consistent distributions of all the components of a multiphase flow over the cross-section. It is shown that at the Poiseuille flow, the distributions of the individual dispersed phases can have up to three symmetrical extrema, the position of which is determined by the flow conditions (shear rate, vessel diameter, blood composition). As a demonstration of the model’s capabilities, the distribution of blood components (erythrocytes, platelets, lymphocytes) for vessels with a diameter of 0.1 to 5 mm at shear rates from 1 to 100 s-1 is given. It is shown that there is a very complex relationship between flow parameters (shear rate, diameter of a blood vessel) and blood composition. Unlike most hydrodynamic models of two-phase flows, the thermodynamic approach allows one to consider the distributions of an arbitrary set of dispersed and low molecular weight blood components, including foreign ones.