Flow-induced compaction of a deformable porous medium

Estimating the interfacial permeability for flow into a poroelastic medium

Boundary conditions between a porous solid and a fluid has been a long-standing problem in modeling porous media. For deformable poroelastic materials such as hydrogels, the question is further complicated by the elastic stress from the solid network. Recently, an interfacial permeability condition has been developed from the principle of positive energy dissipation on the hydrogel-fluid interface. Although this boundary condition has been used in flow computations and yielded reasonable predictions, it contains an interfacial permeability η as a phenomenological parameter. In this work, we use pore-scale models of flow into a periodic array of solid cylinders or parallel holes to determine η as a function of the pore size and porosity. This provides a means to evaluate the interfacial permeability for a wide range of poroelastic materials, including hydrogels, foams and biological tissues, to enable realistic flow simulations.

A theory of hydrogel mechanics that couples swelling and external flow

Two aspects of hydrogel mechanics have been studied separately in the past. The first is the swelling and deswelling of gels in a quiescent solvent bath triggered by an environmental stimulus such as a change in temperature or pH, and the second is the solvent flow around and into a gel domain, driven by an external pressure gradient or moving boundary. The former neglects convection due to external flow, whereas the latter neglects solvent diffusion driven by a gradient in chemical potential. Motivated by engineering and biomedical applications where both aspects coexist and potentially interact with each other, this work presents a poroelasticity model that integrates these two aspects into a single framework, and demonstrates how the coupling between the two gives rise to novel physics in relatively simple one-dimensional and two-dimensional flows.

In-situ measurement of the internal compaction of a soft material caused by permeation flow

HYPOTHESIS

The compaction of hydrogel films under permeation flow can be measured, in-situ, by tracking the internal displacements of their structure, thereby revealing the internal deformation profile. Additionally, monitoring the permeation flow rate and applied pressure over time enables determination of variations in the hydrogel's permeability due to flow-induced compaction. Hydrogels are soft porous materials capable of containing high amounts of water within their polymeric matrix. Flow-induced internal deformation can modify the hydrogel's permeability and selectivity, which are important attributes in separation processes, both industrial (e.g., membrane-based water purification) and natural (mucous filters in suspension feeders and intestinal lining) systems. Measuring the flow-induced compaction in thin hydrogels films can reveal the interplay between flow and permeability. However, the micro-scale internal compaction remains uncharted for due to experimental challenges.

EXPERIMENTS

A technique is demonstrated for analyzing the compaction and stratification of permeable soft materials, in-situ, created by a pressure-driven permeation flow. To this end, the internal deformations within a soft material layer are calculated, based on tracking the positions of fluorescent micro-tracers that are embedded within the soft material. We showcase the capabilities of this technique by examining a hundred-micron-thick calcium-alginate cake deposited on a nanofiltration membrane, emphasizing the achieved micro-scale resolution of the local compaction measurements.

FINDINGS

The results highlight the possibility to examine thin hydrogel films and their internal deformation produced by flow-induced stresses when varying the flow conditions. The method enables the simultaneous calculation of the soft material's permeance, as the pressure-driven flow conditions are continuously monitored. In summary, the proposed method provides a powerful tool for characterizing the behaviour of permeable soft materials under permeation conditions, with potential applications in engineering, biophysics and material science.

Technique for studying in high resolution poromechanical deformation of a rocklike medium

Pressurized fluid injection into underground rocks occurs in applications like carbon sequestration, hydraulic fracturing, and wastewater disposal and may lead to human-induced earthquakes and surface uplift. The fluid injection raises the pore pressure within the porous rocks, while deforming them, yet this coupling is rarely captured by experiments. Moreover, experimental studies of rocks are usually limited to postmortem inspection and cannot capture the complete deformation process in time and space. In this Letter we will present a unique experimental system that can capture the spatial distribution of poromechanical effects in real time by using an artificial rocklike transparent medium mimicking the deformation of sandstone. We will demonstrate the system abilities through a fluid injection experiment, showing the nonuniform poroelastic expansion of the medium and the corresponding poroelastic model that captures completely the results without any fitting parameters. Moreover, our results demonstrate and validate the underlying assumptions of the poroelastic theory for fluid injection in rocklike materials, which are relevant for understanding human-induced earthquakes and injection induced surface uplift.

A method for measuring fluid pressure and solid deformation profiles in uniaxial porous media flows

Flow through rigid, reactive, or deformable porous media has relevance to the dynamical behavior studied across a broad range of problems in science and engineering. Here, we describe an apparatus designed to simultaneously measure the pervadic pressure profile, fluid volume flux, and deformation in an evolving poroelastic medium. We demonstrate the apparatus in measurements of flow-induced compression of a soft latex foam. The approach can be used in both rigid and reactive porous media.

The breakdown of Darcy's law in a soft porous material

We perform direct numerical simulations of the flow through a model of deformable porous medium. Our model is a two-dimensional hexagonal lattice, with defects, of soft elastic cylindrical pillars, with elastic shear modulus G, immersed in a liquid. We use a two-phase approach: the liquid phase is a viscous fluid and the solid phase is modeled as an incompressible viscoelastic material, whose complete nonlinear structural response is considered. We observe that the Darcy flux (q) is a nonlinear function - steeper than linear - of the pressure-difference (ΔP) across the medium. Furthermore, the flux is larger for a softer medium (smaller G). We construct a theory of this super-linear behavior by modelling the channels between the solid cylinders as elastic channels whose walls are made of material with a linear constitutive relation but can undergo large deformation. Our theory further predicts that the flow permeability is an universal function of ΔP/G, which is confirmed by the present simulations.

From arteries to boreholes: steady-state response of a poroelastic cylinder to fluid injection

The radially outward flow of fluid into a porous medium occurs in many practical problems, from transport across vascular walls to the pressurization of boreholes. As the driving pressure becomes non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid has an increasingly strong impact on the flow. For very large pressures or very soft materials, as is the case for hydraulic fracturing and arterial flows, this coupling can lead to large deformations and, hence, to strong deviations from a classical, linear-poroelastic response. Here, we study this problem by analysing the steady-state response of a poroelastic cylinder to fluid injection. We consider the qualitative and quantitative impacts of kinematic and constitutive nonlinearity, highlighting the strong impact of deformation-dependent permeability. We show that the wall thickness (thick versus thin) and the outer boundary condition (free versus constrained) play a central role in controlling the mechanics.

Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids

Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However, it ignores interfacial stress and only applies to very dilute composites-i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori-Tanaka multiphase approximation scheme, we extend Eshelby's theory to treat a composite with interfacial stress in the non-dilute limit. In particular, we calculate the elastic moduli of composites comprised of a compliant, elastic solid hosting a non-dilute distribution of identical liquid droplets. The composite stiffness depends strongly on the ratio of the droplet size, R, to an elastocapillary lengthscale, L. Interfacial tension substantially impacts the effective elastic moduli of the composite when [Formula: see text]. When R<3L/2 (R=3L/2) liquid inclusions stiffen (cloak the far-field signature of) the solid.