Viscous flow in a cylindrical tube containing a line of spherical particles

The viscous, creeping flow through a cylindrical tube of a liquid, which contains rigid, spherical particles, is investigated analytically. The spheres are located on the axis of the cylinder and are equally spaced. Solutions are derived for particles in motion and fixed, with and without fluid discharge. Numerical results are presented for the drag on each sphere and the mean pressure drop for a wide range of sizes and spacings of the spheres. The study is motivated by possible application to blood flow in capillaries, where red blood cells represent particles of the same order of magnitude as the diameter of the capillary itself. The results may also be of interest in other applications, such as sedimentation and fluidized beds. It is shown that there is little interaction between particles if the spacing is more than one tube diameter, and that the additional pressure drop over that for Poiseuille flow is less than 50% if the sphere diameter is less than 0·8 of the tube diameter.