A study of the permeability of pulp and paper

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Studies of anisotropic permeability with applications to water removal in fibrous webs

An analytical study is devised for the problem of bimodal porous flow across a periodic array of permeable cylindrical inclusions. Such a configuration is particularly relevant for porous media systems of dual granulometry, an idealization often taken, e.g. in the modelling of membranes and fibrous applications. The double-porosity system is governed by the Stokes–Brinkman–Darcy equations, the most general description in this class of flow problems characterized by the permeabilities of the surrounding matrix and inclusions, their porosities and the relative volume fraction. We solve this problem with the Kuwabara cell model and lubrication approach, providing analytical solutions for the system effective permeability in closed analytical form. The ensemble of results demonstrates the self-consistency of the bimodal solutions in eight possible limit configurations and supports the validity of the Beavers–Joseph interface stress jump condition for transmission from the open Stokes flow to low-permeable Darcy region. At the same time, these solutions bring further insight on the relative significance of the governing parameters on the effective permeability, with a focus on the role of the effective viscosity (porosity) distribution. Furthermore, although the cell model is restricted to relatively small volume fractions in open flow, its validity extends in less-permeable background flow inside Brinkman/Brinkman description. In turn, the lubrication approximation remains more adequate in the opposite limit of the dense impermeable inclusions. These conclusions are drawn from comparisons with the numerical solutions obtained with the developed lattice Boltzmann model and the standard finite element method. The two methods principally differ in the treatment of the interface conditions: implicit and explicit, respectively. The purpose of this task is therefore twofold. While the numerical schemes help quantifying the validity limits of the theoretical approach, the analytical solutions offer a non-trivial benchmark for numerical schemes in highly heterogeneous soil.

Stokes–Brinkman–Darcy Solutions of Bimodal Porous Flow Across Periodic Array of Permeable Cylindrical Inclusions: Cell Model, Lubrication Theory and LBM/FEM Numerical Simulations

Paper permeability is commonly expressed in terms of gas flow rates through a sheet. This practice is useful for comparing similar sheets, but does not truly characterize the interaction of flowing fluid with the porous structure and provides no direct information about flow in a wet sheet. The standard engineering definition of permeability provides a more useful parameter, though one less easily measured. The standard definition is based on Darcy's law (1), which, for one-dimensional flow, states that the velocity of fluid flow through a saturated porous medium is directly proportional to the pressure gradient: An extensive set of data for in-plane and transverse permeability has been obtained. We focus on recent results for hardwood and softwood kraft pulps which are consistent with measurements in other pulp types. Anisotropic permeability data are discussed in terms of practical implications and theoretical considerations such as pore structure. The new data give insight into two-dimensional flows which may occur in practical papermaking and nonwovens processes. The observed tendency for fiber networks to have high in-plane permeabilities is especially relevant in water removal processes. For example, in-plane flows can reduce the water removal capacity of a press. Saturated permeability data are also directly correlated with impulse drying performance. As a measure of water removal performance, saturated permeability data are much more relevant than freeness data. A variety of factors can influence the saturated transverse or in-plane permeability of a fibrous network. We consider the effects of compression, fines content, basis weight, yield, and different disintegration and refining methods. In addition, the effects of hornification from drying and partial hornification from wet pressing were quantified. Partial water removal by pressing results in some hornification, increasing the permeability of the resaturated sheet. The permeability of a dried and resaturated sheet increased more than the permeability of a sheet formed from dried and reslushed fibers.

Studies of anisotropic permeability with applications to water removal in fibrous webs. II: Water removal and other factors affecting permeability

Presentation d'une technique d'etude de l'anisotropie de la permeabilite du papier aux liquides. On procede a une injection laterale de fluide dans un disque de papier lamine initialement sec. La limite du fluide en mouvement est photographiee et les resultats concernant la permeabilite sont obtenus par une analyse d'image combinee aux solutions approchees du probleme d'ecoulement. Le degre d'anisotropie dans le plan du papier ne semble pas changer avec le gonflement des fibres.

Using edge-flow test to examine the in-plane anisotropic permeability of paper

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George Ronald Brown

Papers

Creeping flow of fluids through assemblages of elliptic cylinders and its application to the permeability of fiber mats