Gas compression delays the onset of viscous fingering→

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Viscous fingering is a classical hydrodynamic instability that occurs when a low-viscosity fluid, such as a gas, is used to drive a much more viscous fluid, such as oil, from a confined geometry. In addition to being a particularly accessible example of spontaneous pattern formation, viscous fingering plays an important role in engineering applications including the underground sequestration of carbon dioxide, the operation of fuel cells, and the remediation of groundwater contamination.

In a pair of studies, we examined common but previously overlooked mechanism that can have a strong impact on these patterns. Specifically, we used a series of careful experiments and state-of-the-art numerical simulations to study the injection of air to displace oil from a thin gap between two parallel plates (i.e., a Hele-Shaw cell). As the air invades the gap, the air-oil interface forms an intricate branching pattern of viscous fingers. This process has been the focus of intense study for decades, but the simple fact that air and other gases are highly compressible was previously ignored. Compression causes the air to behave like a spring, pressurising as it is forced into the flow cell and then depressurising as the oil gradually flows out. We showed that this process of compression and expansion can both delay the onset of viscous fingering and reduce the intensity of the fingering pattern. And even when both fluids are liquids, some amount of compression is difficult to avoid — for example, because of large injection pressures, flexible tubing and other components, or the presence of small gas bubbles. Our pair of studies is the first to quantify the impact of compression on the formation of these classical patterns.

Read the papers:

  • Gas compression systematically delays the onset of viscous fingering. LC Morrow, C Cuttle, and CWM. Physical Review Letters, 131:224002, 2023. doi:10.1103/PhysRevLett.131.224002 | pdf.
  • Compression-driven viscous fingering in a radial Hele-Shaw cell. C Cuttle, LC Morrow, and CWM. Physical Review Fluids, 8:113904, 2023. doi:10.1103/PhysRevFluids.8.113904 | pdf. Editors' Suggestion.

Featured in Physics Magazine

Compression-driven expulsion of liquids→

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Using gas to drive a viscous liquid out of a confined geometry, such as from a narrow tube or channel or from a porous medium, is a classical problem in fluid dynamics. It is also a common feature of many practical applications, including the operation of fuel cells, the subsurface storage of carbon dioxide, and even the squeezing of ketchup out of a bottle. In all of these scenarios, the compression of the gas provides the driving force and the viscosity of the liquid provides the resistance. However, both the amount of compression and the amount of resistance are coupled to the amount of liquid that has been displaced. The tight coupling of these basic mechanical ingredients leads to surprising behavior, even in the simplest of settings. We studied this problem in a controlled way by compressing gas to drive oil from a capillary tube. Our results show that a steady rate of squeezing can generate a strongly unsteady flow, and there exists a critical threshold above which the flow abruptly transitions from smooth squirting to a violent burst.

Read the paper or the preprint

Featured in: University of Oxford | Department of Engineering Science | American Physical Society | The Daily Mail | Physics World | Ars Technica | FYFD | etc.

Deformable porous media→

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A deformable porous medium is one in which the solid skeleton deforms in response to the motion of the fluid(s). How can the "deformability" of a porous medium be defined and estimated? What are the key differences between a stiff (weakly deformable) porous medium and a soft (highly deformable) porous medium? Why are low-porosity media different? This short article addresses those questions and some others.

Gas invasion into a soft granular material→

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Gas migration through a soft, liquid-saturated granular material involves a strong coupling between the motion of the gas and the deformation of the material. This process is central to many natural and industrial systems, such as the generation and venting of gases from lake beds and waste ponds. We link grain-scale fluid and solid mechanics with macroscopic migration, trapping, and venting using high-resolution experiments and a simple mechanistic model. We find that the largest amount of trapping and the largest venting events occur at intermediate confining stress.

Read the paper: Lee et al., PRFluids 2020

Simulating fluid displacement→

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The simultaneous flow of multiple fluid phases through a porous solid occurs in many natural and industrial processes. Microscale physical mechanisms such as the relative affinity of the solid for the fluids (i.e., wettability), capillarity, and viscosity combine with pore geometry to produce a wide variety of macroscopic flow patterns. Pore-scale modeling is an essential tool to connect microscale mechanisms with macroscopic patterns, but quantitative comparisons between different models, and with experimental data, are lacking. Here, we perform an unprecedented comparison of state-of-the-art models from 14 leading groups with a recent experimental dataset. The results underscore the challenges of simulating multiphase flows through porous media, highlighting specific areas for further effort in what is already a flourishing field of research.

Read the paper: Zhao et al., PNAS 2019

From arteries to boreholes: Fluid injection into a poroelastic cylinder

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The radially outward flow of fluid into a porous medium occurs in many practical problems, from transport across vascular walls to the pressurisation of boreholes in the subsurface. When the injection pressure is large and/or the material is soft, the solid structure will deform and this can have a strong impact on the flow. Here, we study the response of a poroelastic cylinder to sudden fluid injection across a series of two papers, focusing first on the steady state and then on the transient evolution. In both cases, we examine the relative importance of nonlinearity, geometry, constraint, and driving method in determining the amount of deformation, the magnitude of the resulting stresses, the relationship between flow rate and driving pressure, and the rate at which the deformation evolves.

Read the papers: Auton & MacMinn, RSPA 2017 and Auton & MacMinn, RSPA 2018

Dynamics of swelling and drying in gels→

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Polymeric hydrogels swell by absorbing a remarkable amount of water. These materials are widely used in a variety of engineering applications, and predicting the rates of swelling and drying is a key aspect of designing for these applications, but these processes are complex and highly nonlinear. Using a mathematical model and a series of experiments, we showed here that swelling and drying are inherently transient and strikingly different. These results pave the way for more sophisticated prediction and control of swelling and drying.

Read the paper: Bertrand et al., PRApplied 2016

Wettability control on multiphase flow in porous media→

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The simultaneous flow of multiple fluid phases through a porous solid occurs in many natural and industrial processes—for example, rainwater infiltrates into soil by displacing air, and carbon dioxide is stored in deep saline aquifers by displacing brine. It has been known for decades that wetting—the affinity of the solid to one of the fluids—can have a strong impact on the flow, but the microscale physics and macroscopic consequences remain poorly understood. Here, we study this in detail for the first time by systematically varying the wetting properties of a microfluidic porous medium. Our high-resolution images reveal the fundamental control of wetting on multiphase flow, elucidate the inherently 3D pore-scale mechanisms, and help explain the striking macroscopic displacement patterns that emerge.

Read the paper and watch some videos: Zhao et al., PNAS 2016

Talk at the Isaac Newton Institute→

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Watch Chris talk about large-deformation poroelasticity and swelling at a workshop on "Melt in the Mantle" at the Isaac Newton Institute in Cambridge, UK. It was a fascinating and interdisciplinary event focused on the physics of flow, transport, and deformation in the multiphase systems. Don't miss the other talks:

  • Workshop 1 - From Foundations to State-of-the-Art in Magma/Mantle Dynamics
  • Workshop 2 - From the Grain to the Continuum: Two Phase Dynamics of a Partially Molten, Polycrystalline Aggregate
  • Workshop 3 - From the Continuum to the Tectonic: the Magma/Mantle Dynamics of Planet Earth

Large deformations of a soft porous material→

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In porous materials, deformation of the solid skeleton is mechanically coupled to flow of the interstitial fluid. Soft porous materials such as soils, gels, and biological tissues often experience very large deformations. Here, we provide an overview of the physics of poromechanical coupling and the mathematical theory of large-deformation poroelasticity, and then study the importance of large deformations in the context of two uniaxial model problems.

Read the paper and download the associated MATLAB code: MacMinn et al., PRApplied 2016.

Fluid-driven deformation of porous materials→

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Fluid flow can deform a porous material if the pressure is large enough, or if the material is soft enough. These poromechanical deformations occur across biophysics and geophysics, from the mechanics of human tissues to the recovery of oil and gas, but they are notoriously difficul to study in a laboratory setting. Here, we achieved this by injecting fluid into a packing of soft particles.

Left: Injection of fluid (arrows) into a packing of soft particles deforms the packing, opening a cavity around the injection port. Bands of shear failure (red patches) lead to wedge-like displacement patterns reminiscent of flower petals (white to blue).

Read the paper and watch some videos: MacMinn et al., PRX 2015.