(350a) Unequal Granular Temperature Model for Motion of Platelets to the Wall and Red Blood Cells to the Center

The motion of platelets to the wall and red blood cells to the center is explained by the unequal granular temperature kinetic theory. The migration of platelets to walls of the blood vessels in the presence of red blood cells is caused by the high granular pressure produced by the random oscillations of the red blood cells and the dissipation of platelet random energy at the walls. The motion of red blood cells from the wall to the center was computed using a slightly modified model of Gidaspow and Huang ( Annals of Biomedical Engineering 37, No 8,1534-1545, 2009). At the wall the shear has the highest value. This produces a high granular pressure and temperature which drive the red blood cells towards the center.Granular temperature is simply the average of the variances of the particle velocities in the three directions (  D. Gidaspow, Multiphase Flow and Fluidization,  Academic Press ,1994 : D. Gidaspow and V.Jiradilok, Computational Techniques, Nova Science, 2009 ) The particle velocities can be measured using a CCD camera and their standard deviations computed. To test the validity and the accuracy of the kinetic theory model, a two story riser was built at IIT with a splash plate on top of the riser to obtain symmetry. The particle velocities were parabolic and the particle concentrations were uniform at the center of the 7.6 cm tube and high at the wall. Granular temperatures can be approximated by the fourth order parabolic equation obtained by solving the granular temperature equation for elastic particles. In the fully developed reasonably dilute flow, the granular pressure can be approximated by an ideal equation of state .In developed flow, the radial variation of this pressure is zero. This approximation allowed us to obtain a very simple expression for the platelet distribution in terms of its inlet concentration. This analytical solution agreed with the experiments of Aarts, et al ( Arteriosclerosis 8.No 6, 819-824, 1988 ).