Flow-driven compaction of a fibrous porous medium

Abstract

A combined theoretical and experimental study is presented for the flow-induced compaction of a onedimensional fibrous porous medium near its gel point for deformation at low and high rates. The theory is based on a two-phase model in which the permeability is a function of local solid fraction, and the deformation of the solid is resisted by both a compressive yield stress and a rate-dependent bulk viscosity. All three material properties are parameterized and calibrated for cellulose fibres using sedimentation, permeation and filtration experiments. It is shown that the incorporation of rate-dependence in the solid stress significantly improves the agreement between theory and experiment when the drainage flow is relatively rapid. The model is extended to rates outside the range where it was calibrated to understand the dynamics of a standard test for pulp suspensions: the Canadian Standard Freeness test. The model adequately captures all of the experimental findings, including the score of the freeness test, which is found to be sensitively controlled by the bulk solid viscosity and to a lesser degree by the permeability law, but depends only weakly on the compressive yield stress.

Dewatering saturated, networked suspensions with a screw press

“…In steady state, mass conservation for each phase, Darcy's law, and stress balance are as follows [19,20,[13][14][15]…”

“…In consolidation theory, the network stressŜ is typically modeled via a φ-dependent isotropic plastic yield pressure,Ŝ = −p Y (φ)I, whenever network deformation occurs (∇ •û s = 0); otherwise, the magnitude ofŜ is smaller than p Y (φ) [13]. More generally, it is possible for such networks to exhibit rate-dependent behaviour once deformation occurs [19,20], and this extension to the effective network stress was found necessary to describe the behaviour of paper-making fibre suspensions [14,15]. We therefore writeŜ =ŜI, withŜ < 0 under compression, and set the mean solid network stress to bê…”

“…To model the screw press, we therefore adopt a two-phase formulation for the material [13], and break the press up into the two compartments. The formulation incorporates Darcy's law for the flow of the fluid; for the solid, we take the effective solid network stress to be given by a plastic compressive yield pressure (as in conventional compaction models [13]) and a rate-dependent viscous term that has proven critical in filtration studies of pulp suspensions [14,15]. Because the churning section has uniform pressure, no detailed model is needed to describe this complicated region; all that is required is the imposition of the conditions holding at the transition point.…”

A model for French-press experiments of dry snow compaction

“…Compaction occurs in a variety of natural and industrial processes, such as sedimentary basin formation, paper pulp dewatering, and particle flocculation, and has motivated numerous experiments and mathematical models (e.g. Landman et al, 1991;Fowler and Noon, 1999;Fowler, 2011;Hewitt et al, 2016a, b;Paterson et al, 2019). In this section, we describe the theory outlined by Hewitt et al (2016b).…”

Hydrodynamic instabilities in miscible fluids

“…After the seminal work by Hill [30], a further attempt to experimentally investigate fingering between miscible fluids has been reported by Wooding [37], who however did not discuss the linear stability problem that provides a prediction for the expected wavelength at the onset of the instability. Only some authors [26,31,38,39,40,33] have explored the initial growth of fingers and derived expressions for the incipient fingers with maximum growth rate or maximum amplitude [34]. In all cases but one [41], the introduced models predict that, as interfacial tension tends to zero, the finger wavelength tends to zero possibly with diverging growth rates.…”