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 semi-dilute 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

Plane irrotational flow against a porous plate

The standard hodograph approach to irrotational flow with a free surface, past a solid obstacle, was extended by Cumberbatch (Q. Jl Mech. appt. Math. 35 (1982)) to the case of a porous plate, or mesh. He introduced a sink distribution at the mesh, satisfying an integral equation of the second airfoil type. Explicit solutions can then be given by quadratures. The present paper shows how the solution to the above case, and also to the case of jet flow against a mesh, can be expressed much more simply, and even in closed form for suitable values of one parameter. Motivation comes from the attempt to model the motion of spray droplets being blown over a row of vines or trees

Motion of rigid aggregates under different flow conditions

The response of rigid aggregates to different flow fields was investigated theoretically using model clusters with realistic three-dimensional structure composed of identical spherical primary particles. The aim is to relate the main fluid dynamic properties of the system with the geometry and morphology of the aggregates. Our simulations were based on Stokesian dynamics. The dilute limit of a colloidal aggregate system was studied, where aggregates are very far from each other and hence mutual interaggregate interactions are negligible. The motion of aggregates was characterized in terms of translational mobility and angular velocity, and the ability of simple models, based on either simplified aggregate geometry or the concept of permeability, to capture the main features of the motion was examined