Mathematics Colloquium

 

In this talk a mechanistic theory is developed to describe segregation in blood and other confined multicomponent suspensions. It incorporates the two key phenomena arising in these systems at low Reynolds number: hydrodynamic pair collisions and wall-induced migration. The theory predicts that the cell-free layer thickness follows a master curve relating it in a specific way to confinement ratio and volume fraction. Results from experiments and detailed simulations with different parameters (flexibility of different components in the suspension, viscosity ratio, confinement, among others) collapse onto the same curve.  In simple shear flow, several regimes of segregation arise, depending on the value of a ``margination parameter'' M. Most importantly, there is a critical value of M below which a sharp ``drainage transition'' occurs:  one component is completely depleted from the bulk flow to the vicinity of the walls. Direct simulations also exhibit this transition as the size or flexibility ratio of the components changes. Results are presented for both Couette and plane Poiseuille flow. Experiments performed in the laboratory of Wilbur Lam indicate the physiological and clinical importance of these observations.