Shallow, gravity-driven flow in a poro-elastic layer

Hewitt, Duncan R.; Neufeld, Jerome A.; Balmforth, N. J.

doi:10.1017/jfm.2015.361

Cited by 21 publications

(26 citation statements)

References 39 publications

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“…Note that variations in permeability do not enter at this order because Eqs. (19) and (25) together imply that ||∇p/(M/L)|| = ||(∇ · σ )/(M/L)|| ∼ . This latter scaling should also be viewed as a constraint: Imposing pressure or stress gradients of size approaching M/L will drive a deformation that violates the assumption 1, invalidating the linear theory.…”

Section: Discussionmentioning

confidence: 97%

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Large Deformations of a Soft Porous Material

2016

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Compressing a porous material will decrease the volume of the pore space, driving fluid out. Similarly, injecting fluid into a porous material can expand the pore space, distorting the solid skeleton. This poromechanical coupling has applications ranging from cell and tissue mechanics to geomechanics and hydrogeology. The classical theory of linear poroelasticity captures this coupling by combining Darcy's law with Terzaghi's effective stress and linear elasticity in a linearized kinematic framework. Linear poroelasticity is a good model for very small deformations, but it becomes increasingly inappropriate for moderate to large deformations, which are common in the context of phenomena such as swelling and damage, and for soft materials such as gels and tissues. The well-known theory of large-deformation poroelasticity combines Darcy's law with Terzaghi's effective stress and nonlinear elasticity in a rigorous kinematic framework. This theory has been used extensively in biomechanics to model large elastic deformations in soft tissues, and in geomechanics to model large elastoplastic deformations in soils. Here, we first provide an overview and discussion of this theory with an emphasis on the physics of poromechanical coupling. We present the large-deformation theory in an Eulerian framework to minimize the mathematical complexity, and we show how this nonlinear theory simplifies to linear poroelasticity under the assumption of small strain. We then compare the predictions of linear poroelasticity with those of large-deformation poroelasticity in the context of two uniaxial model problems: Fluid outflow driven by an applied mechanical load (the consolidation problem) and compression driven by a steady fluid throughflow. We explore the steady and dynamical errors associated with the linear model in both situations, as well as the impact of introducing a deformation-dependent permeability. We show that the error in linear poroelasticity is due primarily to kinematic nonlinearity, and that this error (i) plays a surprisingly important role in the dynamics of the deformation and (ii) is amplified by nonlinear constitutive behavior, such as deformation-dependent permeability.arXiv:1510.03455v3 [physics.flu-dyn]

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Section: Discussionmentioning

confidence: 97%

“…As a result, replacing x with X in Eqs. (19), (21), (24), and (25) will result in a Lagrangian interpretation of the linear model that is still valid to first order in . These two models are equivalent in the limit of → 0, but they will always differ at order 2 and diverge from each other as the deformation grows.…”

Section: Discussionmentioning

confidence: 99%

Large Deformations of a Soft Porous Material

2016

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“…In the limit of a rigid till, the till reduces to a standard incompressible porous medium. In the shallow limit, we need only consider the vertical force balance on the till, which is dominated by the vertical normal stress Σ (see, e.g., Hewitt et al (2015a)). The stress Σ can be decomposed into the isotropic fluid pore pressure p and an 'effective' network stress σ, giving Σ = p + σ (cf.…”

Section: The Tillmentioning

confidence: 99%

“…where M = K + 4G/3 1 is the stiffness (or, more precisely, the p-wave modulus, defined in terms of the bulk and shear moduli of the till K and G; see Hewitt et al (2015a)).…”

Section: The Tillmentioning

confidence: 99%

The influence of a poroelastic till on rapid subglacial flooding and cavity formation

2018

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We develop a model of the rapid propagation of water at the contact between elastic glacial ice and a poroelastic subglacial till, motivated by observations of the rapid drainage of supraglacial lakes in Greenland. By treating the ice as an elastic bending beam, the fluid dynamics of contact with the subglacial hydrological network, which is modelled as a saturated poroelastic till, can be examined in detail. The model describes the formation and dynamics of an axisymmetric subglacial cavity, and the spread of pore pressure, in response to injection of fluid. A combination of numerical simulation and asymptotic analysis is used to describe these dynamics for both a rigid and a deformable porous till, and for both laminar and turbulent fluid flow. For constant injection rates and laminar flow, the cavity is isostatic and its spread is controlled by bending of the ice and suction of pore water in the vicinity of the ice–till contact. For a deformable till, this control can be modified: generically, a flexural wave that is initially trapped in advance of the contact point relaxes over time by diffusion of pore pressure ahead of the cavity. While the dynamics are found to be relatively insensitive to the properties of the subglacial till during injection with a constant flux, significant dependence on the till properties is manifest during the subsequent spread of a constant volume. A simple hybrid turbulent–laminar model is presented to account for fast injection rates of water: in this case, self-similar turbulent propagation can initially control the spread of the cavity, but there is a transition to laminar control in the vicinity of the ice–till contact point as the flow slows. Finally, the model results are compared with recent geophysical observations of the rapid drainage of supraglacial lakes in Greenland; the comparison provides qualitative agreement and raises suggestions for future quantitative comparison.

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“…1,[9][10][11] Surface-effect pumps include all devices making use of spontaneous capillary forces and substrate wicking to passively induce fluid flow. 12 Further, force-field pumps are usually defined as nonmechanical including electro-osmotic, 3,13 electrowetting, 14 poroelastic, 15 electrodynamic, thermocapillary and gravitydriven pumps. 1,3,16,17 Common metrics for performance comparison in microfluidic applications include: operational fluid volumes, flow rates, directionality, persistence time, flow pattern control, fluid capacity, recirculation, optical accessibility, power requirements, heat transfer, and cost of implementation.…”

Section: Introductionmentioning

confidence: 99%

Closed-loop feedback control for microfluidic systems through automated capacitive fluid height sensing

et al. 2018

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Precise fluid height sensing in open-channel microfluidics has long been a desirable feature for a wide range of applications. However, performing accurate measurements of the fluid level in small-scale reservoirs (<1 mL) has proven to be an elusive goal, especially if direct fluid-sensor contact needs to be avoided. In particular, gravity-driven systems used in several microfluidic applications to establish pressure gradients and impose flow remain open-loop and largely unmonitored due to these sensing limitations. Here we present an optimized self-shielded coplanar capacitive sensor design and automated control system to provide submillimeter fluid-height resolution (∼250 μm) and control of small-scale open reservoirs without the need for direct fluid contact. Results from testing and validation of our optimized sensor and system also suggest that accurate fluid height information can be used to robustly characterize, calibrate and dynamically control a range of microfluidic systems with complex pumping mechanisms, even in cell culture conditions. Capacitive sensing technology provides a scalable and cost-effective way to enable continuous monitoring and closed-loop feedback control of fluid volumes in small-scale gravity-dominated wells in a variety of microfluidic applications.

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Shallow, gravity-driven flow in a poro-elastic layer

Cited by 21 publications

References 39 publications

Large Deformations of a Soft Porous Material

Large Deformations of a Soft Porous Material

The influence of a poroelastic till on rapid subglacial flooding and cavity formation

Closed-loop feedback control for microfluidic systems through automated capacitive fluid height sensing

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