Relative flow porosity is defined as the fraction of the void volume in a porous medium through which fluid can flow under a macroscopic pressure gradient. In saturated paper, much of the void volume is occupied by water that cannot flow due to chemical or physical absorption and mechanical obstruction (isolated or dead-end pores). In partially saturated paper, surface tension effects further hinder fluid flow through the sheet. In this paper, we discuss various methods for examining relative flow porosity and present results of new experimental techniques based on in-plane flow measurements. The experimental approach involves radially injecting known volumes of aqueous, non-absorbing dye into the center of a compressed, saturated sheet restrained by solid surfaces. The volume of the sheet occupied by the dye is measured, as is the total porosity of the sheet. The ratio of injected dye volume to pore volume within the dyed region is an estimate of effective porosity.
We show that in unrefined, filler-free paper, effective porosity values are on the order of 40% or more. The relative porosity may be as high as 90% of the extra fiber pore volume. Data for both initially dry and initially saturated sheets are presented. A geometric theory exists to predict relative porosity in fibrous structures, but we find that this model predicts values for relative porosity much lower than we observe here. Using simple measures of the volume occupied by the swollen-fibers in a compressed mat, we find that most(on the order of 90%) of the extra fiber pores pace is available to flow.