Numerical research on the 3D fiber orientation distribution in arbitrary planar flows

The fiber orientation distribution in a fiber suspension flow was investigated by a finite difference scheme in spherical coordinates. The diffusivity was transformed between Cartesian and spherical coordinates through tensor analysis to obtain efficiency. It is found that under simple shear flow condition the diffusivity in the azimuthal direction, Dr, has greater effect on the orientation distribution than that in the colatitude direction, Drθθ.