Theory of Margination in Blood and Other Multicomponent Suspensions

A mechanistic theory is developed to describe distribution and segregation of particles in confined multicomponent suspensions such as blood. It incorporates the two key phenomena arising in these systems at low Reynolds number: hydrodynamic pair collisions and wall-induced migration. In simple shear flow, an analytical relationship is found for the depletion layer or “cell-free layer” thickness of deformable-particle suspensions in terms of confinement ratio and volume fraction. Based on this result, a master curve collapsing a wide variety of experimental and direct simulation results can be found. In multicomponent suspensions 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.