Cylindrical cell model for the hydrodynamics of particle assemblages at intermediate reynolds numbers

The spherical cell model for transport in assemblages of spheres, which stems from the low Reynolds number hydrodynamics, has a serious physical limitation when extended to the range of intermediate Reynolds numbers. Spherical symmetry cannot persist around a sphere, given a definite direction of convection. The boundary conditions of the spherical cell model are inappropriate and a cubic cell model would best represent the system. However, in order to avoid undue mathematical difficulties peculiar to three‐dimensional problems, a cylindrical cell model is proposed. A numerical solution of the Navier‐Stokes equations expressed in vorticity‐stream function variables has been performed in conjunction with the cylindrical cell model for various values of porosity and Reynolds number. A much better agreement of the drag coefficient with experimental results is obtained by the cylindrical cell model than by the spherical cell model.