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

Crossover from viscous fingering to fracturing in cohesive wet granular media: a photoporomechanics study

We study fluid-induced deformation and fracture of cohesive granular media, and apply photoporomechanics to uncover the underpinning grain-scale mechanics. We fabricate photoelastic spherical particles of diameter d = 2 mm, and make a monolayer granular pack with tunable intergranular cohesion in a circular Hele-Shaw cell that is initially filled with viscous silicone oil. We inject water into the oil-filled photoelastic granular pack, varying the injection flow rate, defending-fluid viscosity, and intergranular cohesion. We find two different modes of fluid invasion: viscous fingering, and fracturing with leak-off of the injection fluid. We directly visualize the evolving effective stress field through the particles' photoelastic response, and discover a hoop effective stress region behind the water invasion front, where we observe tensile force chains in the circumferential direction. Outside the invasion front, we observe compressive force chains aligning in the radial direction. We conceptualize the system's behavior by means of a two-phase poroelastic continuum model. The model captures granular pack dilation and compaction with the boundary delineated by the invasion front, which explains the observed distinct alignments of the force chains. Finally, we rationalize the crossover from viscous fingering to fracturing by comparing the competing forces behind the process: viscous force from fluid injection that drives fractures, and intergranular cohesion and friction that resist fractures.

Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits

Microfluidic devices manufactured from soft polymeric materials have emerged as a paradigm for cheap, disposable and easy-to-prototype fluidic platforms for integrating chemical and biological assays and analyses. The interplay between the flow forces and the inherently compliant conduits of such microfluidic devices requires careful consideration. While mechanical compliance was initially a side-effect of the manufacturing process and materials used, compliance has now become a paradigm, enabling new approaches to microrheological measurements, new modalities of micromixing, and improved sieving of micro- and nano-particles, to name a few applications. This topical review provides an introduction to the physics of these systems. Specifically, the goal of this review is to summarize the recent progress towards a mechanistic understanding of the interaction between non-Newtonian (complex) fluid flows and their deformable confining boundaries. In this context, key experimental results and relevant applications are also explored, hand-in-hand with the fundamental principles for their physics-based modeling. The key topics covered include shear-dependent viscosity of non-Newtonian fluids, hydrodynamic pressure gradients during flow, the elastic response (deformation and bulging) of soft conduits due to flow within, the effect of cross-sectional conduit geometry on the resulting fluid-structure interaction, and key dimensionless groups describing the coupled physics. Open problems and future directions in this nascent field of soft hydraulics, at the intersection of non-Newtonian fluid mechanics, soft matter physics, and microfluidics, are noted.

Capillary and viscous fracturing during drainage in porous media

Detailed understanding of the couplings between fluid flow and solid deformation in porous media is crucial for the development of novel technologies relating to a wide range of geological and biological processes. A particularly challenging phenomenon that emerges from these couplings is the transition from fluid invasion to fracturing during multiphase flow. Previous studies have shown that this transition is highly sensitive to fluid flow rate, capillarity, and the structural properties of the porous medium. However, a comprehensive characterization of the relevant fluid flow and material failure regimes does not exist. Here, we used our newly developed multiphase Darcy-Brinkman-Biot framework to examine the transition from drainage to material failure during viscously stable multiphase flow in soft porous media in a broad range of flow, wettability, and solid rheology conditions. We demonstrate the existence of three distinct material failure regimes controlled by nondimensional numbers that quantify the balance of viscous, capillary, and structural forces in the porous medium, in agreement with previous experiments and granular simulations. To the best of our knowledge, this study is the first to effectively decouple the effects of viscous and capillary forces on fracturing mechanics. Last, we examine the effects of consolidation or compaction on said dimensional numbers and the system's propensity to fracture.

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.

Theory of the flow-induced deformation of shallow compliant microchannels with thick walls

Long, shallow microchannels embedded in thick, soft materials are widely used in microfluidic devices for lab-on-a-chip applications. However, the bulging effect caused by fluid-structure interactions between the internal viscous flow and the soft walls has not been completely understood. Previous models either contain a fitting parameter or are specialized to channels with plate-like walls. This work is a theoretical study of the steady-state response of a compliant microchannel with a thick wall. Using lubrication theory for low-Reynolds-number flows and the theory for linearly elastic isotropic solids, we obtain perturbative solutions for the flow and deformation. Specifically, only the channel's top wall deformation is considered, and the ratio between its thickness t and width w is assumed to be (t/w)²≫1. We show that the deformation at each stream-wise cross section can be considered independently, and that the top wall can be regarded as a simply supported rectangle subject to uniform pressure at its bottom. The stress and displacement fields are found using Fourier series, based on which the channel shape and the hydrodynamic resistance are calculated, yielding a new flow rate-pressure drop relation without fitting parameters. Our results agree favourably with, and thus rationalize, previous experiments.

From arteries to boreholes: transient response of a poroelastic cylinder to fluid injection

The radially outward flow of fluid through a porous medium occurs in many practical problems, from transport across vascular walls to the pressurization of boreholes in the subsurface. When the driving pressure is non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid can control both the steady state and the transient mechanics of the system. Very large pressures or very soft materials lead to large deformations of the solid skeleton, which introduce kinematic and constitutive nonlinearity that can have a non-trivial impact on these mechanics. Here, we study the transient response of a poroelastic cylinder to sudden fluid injection. We consider the impacts of kinematic and constitutive nonlinearity, both separately and in combination, and we highlight the central role of driving method in the evolution of the response. We show that the various facets of nonlinearity may either accelerate or decelerate the transient response relative to linear poroelasticity, depending on the boundary conditions and the initial geometry, and that an imposed fluid pressure leads to a much faster response than an imposed fluid flux.