Current models of filtration and expression model the solid phase as an elastic medium with non-linear behavior [1-3]. However, many materials such as wood pulp fibers are substantially porous in themselves giving rise to void spaces within the fibrous medium on two distinct scales. For instance, the cell walls of papermaking pulp fibers are known to contain nanoscale pores of sizes in the range of 10-50 nm in the radial direction and micron sized pores in the axial direction [4, 5, 6]. This is in addition to the interfiber pores within the fibrous mat which are in the range of 2-50 microns in size. Since the fibers are compressible, they expel water into the interfiber pore space under compression. The interaction of the expression phenomenon at the micro (or nano) scale with the overall consolidation of the medium determines the response of the fibrous media and its final structure.
In this paper, we develop a mathematical model to describe consolidation on this dual scale with suitable 'averaged' consolidation coefficients or diffusivities. The model is then solved numerically to obain predictions of dewatering rates and fibrous medium porosity distributions under different loading conditions.
We compared our results with experimental data obtained by consolidation under specific loading conditions applied to a fibrous material using an Instron machine.
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