Slow flow through a periodic array of spheres

Slow flow through a periodic array of spheres is studied theoretically, and the drag force by the fluid on a sphere forming the periodic array is calculated using a modification of the method developed by Hashimoto (1959). Results for the complete range of volume fraction c of spheres are given for simple cubic, body-centered cubic, and face-centered cubic arrays and these agree well with the corresponding values reported by previous investigators. Also, series expansions for the drag force to 0(c¹⁰) are derived for each of these cubic arrays. The method is also applied to determine the drag force to 0(c³) on infinitely long cylinders in square and hexagonal arrays.