Drag on fixed beds of fibres in slow flow

As a sequel to earlier work on viscous flow through random beds of fixed spheres, the flow through beds of fixed cylindrical fibres is studied by the same method. Several distributions of orientation are considered. The aim is to find the shielding radius and drag per unit length as a function of volume fraction occupied by the fibres, in the semidilute situation. The first approximation is obtained from the drag on a very long cylinder resulting from the uniform flow at infinity of a viscous fluid in the presence of Darcy resistance. Estimates are made of the effects of finite length, and of curvature of the fibres. Finally the effect of a neighbouring cylinder is considered, to obtain the second-stage approximation for straight fibres. Comparison is made with some experimental and numerical results for unidirectional fibres and for plane pads.