THEORY OF AIR-FLOW THROUGH FILTERS MODELED AS ARRAYS OF PARALLEL FIBERS

Existing theories of fluid flow through fibrous filters modelled as arrays of parallel fibres are reviewed and a new theory is described, which has the unique property of giving, in a simple analytical form, a continuous stream function through arrays of fibres. The method, which depends on Stokes flow conditions, is based on the variational principle and minimization procedures and is first applied to the simplest array, which is rectangular in structure. The theory is then generalized to arrays of lower symmetry predicting, in accordance with experiment, that the flow pattern is highly dependent on the structure but the pressure drop is only weakly dependent.