STOKES FLOW THROUGH A SYSTEM OF PARALLEL INFINITE CYLINDERS WITH AXES ORIENTED AT AN ANGLE TO THE DIRECTION Of MEAN FLOW

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Abstract
Theoretical models based on Stokes flow of air through a fibrous filter predict a significantly higher pressure drop than experimentally measured values. This discrepancy persists even when the interaction of the flow between) neighboring fibers is accounted for. Various authors have attributed this discrepancy to the inhomogeneity of the fiber distribution within the filter and to the possibility that some fibers are partially orientation in the directon of mean flow. It has been shown that fiber density inhomogeneity does indeed contribute to this discrepancy In this paper, the effect on the flow and subsequent pressure drop when the fibers are oriented at an angle to the directon of mean flow is studied. The solution of the three dimensional equation for creeping, incompressible flow in a doubly periodic, infinite lattice of infinite circular cylinders when there is a constant mean flow whose direction makes an acute angle with the axes of the cylinders is given. If the volume fraction of fibers is small, the periodic boundary conditions can be replaced by requiring zero vorticity at the outer boundary of an imagined cylindrical cell of fluid surrounding one of the cylinders. The resulting parallel and transverse problems have known solutions and give an approximate solution to the flow through the periodic lattice. The resulting drag is used to compute the dimensionless pressure drop across a filter for several values of the volume fraction of fiber and is compared to the experimentally determined formula of Davies. It is shown that the average drag over a uniform distribution of fiber orientations yields a pressure drop which is significantly closer to the experimental values of Davies than that resulting from strictly transverse flow.