The literature was searched for experiments and theories related to low-Reynolds-number flow through fibrous porous media, particularly highly porous structures. Experimental data were found for a wide range of materials, from polymer chains to fiberglass, and the results collapse reasonably well when the appropriate dimensionless co-ordinates are employed. Of the theories, accurate solutions of Stokes equation are available for regular arrays of parallel rods, either aligned with or normal to the flow. For irregular arrays and three-dimensional media, approximate permeabilities can be calculated from several flow models.

The permeability of fibrous porous media

Slow flow past periodic arrays of cylinders with application to heat transfer

Developing a new form of permeability and Kozeny-Carman constant for homogeneous porous media by means of fractal geometry

Laminar viscous flow through regular arrays of parallel solid cylinders

A model problem is analysed to study the microscopic flow near the surface of two-dimensional porous media. In the idealized problem we consider axial flow through infinite and semi-infinite lattices of cylindrical inclusions. The effect of lattice geometry and inclusion shape on the permeability and surface flow are examined. Calculations show that the definition of a slip coefficient for a porous medium is meaningful only for extremely dilute systems. Brinkman's equation gives reasonable predictions for the rate of decay of the mean velocity for certain simple geometries, but fails for to predict the correct behaviour for media anisotropic in the plane normal to the flow direction.

Microscopic flow near the surface of two-dimensional porous media. Part 1. Axial flow

The increasing complexity of heat transfer and process situations which involve fluid flow has demanded the frequent use of flow passages of unusual geometrical configuration. The present investigation is concerned with one such novel configuration, namely the longitudinal flow between solid cylindrical rods which are arranged in regular array. A schematic diagram of the situation under study. The rods may be located either in triangular or square array. The flow will be taken to be laminar and fully developed. The aim of this analysis is to determine the pressure drop, shear stress, and velocity-distribution characteristics of the system. The starting point of this study is the basic law of momentum conservation. The resulting differential equation has been solved in an approximate, but almost exact, manner by the use of truncated trigonometric series. Results are obtained over a wide range of porosity values for both the triangular and square arrays. Heat transfer has not been considered. The configuration under investigation has potential application in compact heat exchangers for nuclear reactors and other situations. Further the results should also be of interest in the theory of flow through unconsolidated porous beds (ia, 9a). The only related analytical work known to the authors is that of Emersleben (S), who considered only the square array. His rather involved solution, based on complex zeta functions, appears to be valid only at high porosities. Experiments covering a porosity range of 0.093 to 0.984 have been made by Sullivan (4) using parallel-oriented fibers, most of the tests being for fibers in random array. These previous investigations will be compared with the present theory in a later section.

A. L. Loeffler

Papers

Longitudinal Laminar Flow Between Cylinders Arranged in Regular Array