Mechanistic modelling of fluid permeation through compressible fiber beds

A mechanistic model is developed to describe fluid permeation through compressible fiber beds based on the micro-mechanical theories of compressibility of fiber assemblies recently advanced in textile science and engineering. The heterogeneous bed is assumed to be composed of a pile of homogeneous layers with properties depending upon position in the z-direction. The fiber network inside each layer is treated as an assembly of the unit cells with fiber segments between two adjacent fiber-to-fiber contact points as diagonals. Fiber segments in the unit cells experience either bending or slipping under a mechanical stress, which is accumulated from the drag forces in upstream layers and transmitted through fiber contact points. Individual bending and/or slipping behaviors of fiber segments are combined into the overall response of the fiber network. Porosity profile along the z-direction is thus obtained. The Kozeny-Carman equation is used to relate permeability to the porosity with the help of the Davies-Ingmason correlation. Besides the phenomenological relationship between flow rate, thickness of fiber bed and total hydraulic pressure drop, the model predicts the pressure-induced variations in the structural properties along the z-direction. Simulation results of the mechanistic model are presented. Experiments of water permeation through pulp fiber beds under steady-state conditions were performed with various bed formation conditions, and the flow rates and thicknesses of fiber beds were measured as a function of total hydraulic pressure drop. The model calculations are in good agreement with the experimental results.