Mathematical model of the velocity field external to a tank-treading red cell

The velocity field external to a stationary ellipsoidal particle with continuously rotating surface motion driven by a surrounding shear flow is calculated. The configuration is intended to model the so-called "tank-treading" behavior of mammalian erythrocytes (red cells) when suspended in shear flow. The boundary-value problem posed is based on the model developed by Keller & Skalak (7) and is solved by adapting Jeffrey's general solution (9) for the Stokes flow about a rigid, freely rotating ellipsoid immersed in an unbounded viscous flow. Streamlines and velocity profiles in the plane of symmetry are obtained by numerical computations. The flow pattern reveals two free stagnation points near the ends of the particle and the streamlines branching from these points delineate a region of closed streamlines surrounding the particle and two recirculating wakes extending to infinity both upstream and downstream of the particle. The presence of the wakes suggests a mechanism for enhanced diffusion of smaller solute particles in the surrounding fluid.