VISCOUS FLOW IN A CYLINDRICAL TUBE CONTAINING A LINE OF SPHERICAL PARTICLES.

Three cases of viscous flow in a circular cylindrical tube containing an infinite line of spherical particles equally spaced along the axis of the tube are considered: axial translation of the particles, flow past a line of stationary particles, flow of fluid and particles under an imposed pressure gradient. The fluid is taken to be incompressible, Newtonian and the linearized equations of creeping flow are used. The case is an idealization of blood flow in capillaries where the diameter of the red blood cells is of the same order as the diameter of the capillary itself. The results may also be of interest in sedimentation, fluidized beds, and groundwater flow. An exact solution in the form of an infinite series of singularities at the center of each sphere is developed and evaluated numerically for a range of sphere radius to tube radius of zero to 0.9. The drag on each sphere, the pressure drop and typical streamline patterns are given. The results show that the drag and pressure drop for a given size of sphere decrease as the spacing between spheres increases and for spacings more than one tube diameter, there is little interaction between spheres. (Author)