A model for motion and sedimentation of cylindrical red-cell aggregates during slow blood flow in narrow horizontal tubes

When blood flows slowly in a narrow tube, red-cell aggregation results in formation of an approximately cylindrical “core” of red cells, which moves as a rigid body. The core is denser than the surrounding fluid, and sedimentation is observed in horizontal tubes. To model this, the Stokes flow of a fluid surrounding a long solid cylinder (the core) contained in a long hollow cylinder (the tube) is considered. The cylinder axes are parallel but not coincident. An exact analytic expression for the resistance coefficient for motion perpendicular to the axes is given. This coefficient increases rapidly with the ratio of core radius to tube radius, and core eccentricity. The predicted rate of sedimentation is comparable to that observed experimentally. The apparent viscosity of a two-phase medium consisting of a core of aggregated particles and surrounding pure fluid is calculated. For a core radius corresponding to experimental conditions, the apparent viscosity increases rapidly with increasing eccentricity of the core.