Compressional dynamics of fibrous porous media II: gelling and Freeness

We present a model for flow-induced compaction of a fibrous porous medium near its gel point, that is, the smallest solid fraction at which fibres (on average) interact mechanically. The solid network’s compressive yield stress and permeability is calibrated experimentally for a particular cellulose pulp suspension in the low-solidity limit, and the effect of rate-dependence is elucidated via a comparison of the two-phase model to experimental PIV measurements of the solid-phase velocity. A standardised industrial testing device for examining pulp suspensions at low solid-fractions called the “Canadian Standard Freeness” tester and the corresponding “freeness score” is described. The model results compare well with the device, and the dependence of the freeness score on the material properties of the pulp network is elucidated and compared to the freeness scores of a catalogue of pulps whose properties are only known at higher solid-fractions.