Search

Ice slabs are multi-meter thick layers of solid reforzen ice that form on top of the porous firn layer in Greenland’s wet snow zone. Recent observations in Northwest Greenland highlight the ability of this relict firn layer to store meltwater in its pores after surface meltwater drains rapidly through cracks in the overlying ice slab. Current fracture mechanics (i.e., LEFM) assumes that the stored elastic energy in an impermeable solid matrix is instantaneously dissipated by creating new crack surfaces, which only holds for impermeable solid media. To better understand the fate of meltwater in the porous firn layer beneath ice slabs, we develop a two-dimensional, poroelastic continuum model to quantify the stress and pressure changes in the porous firn during meltwater penetration.We extend Biot’s poroelastic theory to two-phase immiscible flow by introducing meltwater saturation as an extra variable. By coupling the fluid continuity and force balance equations, we resolve the spatiotemporal evolution of 1) matrix deformations and effective stresses, 2) the water saturation field, and 3) the water pressure field. We adopt a fracture criterion for the cohesive porous firn layer: the maximum tensile effective stress should exceed the material tensile strength to generate fractures. We study the maximum tensile effective stress induced by water injection as a function of firn’s mechanical and hydraulic properties (bulk modulus, porosity, and permeability), and the infiltration conditions (constant infiltration pressure or flow rate). Our results show that the maximum tensile effective stress in the firn layer is no more than a quarter of that predicted for an equivalent solid ice column, because the imposed load is mostly transmitted into the pore pressure. Therefore our model predicts that surface-to-bed hydrofracture is unlikely to form if meltwater can leak into the firn layer. In “Vulnerability of Firn to Hydrofracture, Part II: Greenland’s Ice Slab Regions”, we apply this model to assess the vulnerability of Greenland’s ice slab regions.

Ice flows in response to stresses according to the flow law that involves ice viscosity. An accurate description of effective ice viscosity is essential for predicting the mass loss of the Antarctic Ice Sheet, yet measurement of ice viscosity is challenging at a continental scale. Lab experiments of polycrystalline ice shows that the effective viscosity of ice obeys a power-law relation with the strain rate, known as Glen’s flow law. However, it remains unclear how processes at ice-shelf scales impact the effective viscosity of glacial ice. Here, we leverage the availability of remote-sensing data and physics-informed deep learning to infer the effective ice viscosity and examine the rheology, i.e. flow law, of glacial ice in Antarctic Ice Shelves. We find that the rheology of ice shelves differs substantially between the compression and extension zones. In the compression zone near the grounding line the rheology of ice closely obeys power laws with exponents in the range 1

Ice shelves, the floating extensions of ice sheets, can reduce the rate of sea level rise by buttressing the upstream grounded ice. However, calving, or the fracturing that creates icebergs, can cut out regions that were resisting flow, and allow for increased ice flux and thus sea level contribution. In this work, I focus on the transition from basal crevasses, or seawater-filled fractures on the bottom surface, to full thickness fractures called rifts. Using RACMO ice shelf surface temperatures and holding the ice-ocean interface at -2℃, I find good agreement between observed rifts on the Larsen C and Ross Ice Shelves and rifts predicted to evolve from basal crevasses through 2D Mode I Linear Elastic Fracture Mechanics (LEFM). I also explore the influence of ice shelf geometry in rift formation by solving the Shallow Shelf Approximation (SSA) equations for idealized ice shelves with COMSOL’s Finite Element Analysis software. Using the stress field outputs with LEFM’s rift initiation criteria, I find qualitative agreement in the rift orientation between the predicted unstable basal crevasses and the observed rifts on the left margin of Pine Island Ice Shelf.

The drainage efficiency of the subglacial water system evolves during the melt season. However, direct measurement of drainage efficiency under 1000-meters thick ice is challenging. We previously demonstrated that surface observations of rapid lake drainage induced uplifts can be used to assess subglacial transmissivity beneath the ice sheet. When a lake drains, the water reaches the interface between the ice and bed and forms a water-filled blister. This water then drains through the subglacial drainage system. In this study, we use mathematical models to examine the behavior of surface uplift relaxation resulting from different types of drainage systems, including a laminar water sheet, a turbulent water sheet, and a turbulent subglacial channel. Combined with surface GPS observations of five lakes, we showed that the model can be used to study the evolution of subglacial drainage efficiency.

Hydrofracture and rapid lake drainage can transport surface meltwater to the bed of the Greenland Ice Sheet, thereby coupling surface mass balance processes and dynamic mass loss. Vertical hydrofracture is widely assumed to occur in the ablation zone, where abundant surface runoff that can fill fractures. However, in Greenland, the runoff line has expanded into the accumulation zone due to the development of ice slabs in the firn. It remains unclear whether surface runoff from these ice slab regions also drains locally to the bed. Recent observations in Northwest Greenland suggest that when meltwater penetrates ice slabs via surface fractures, it leaks off into a relict firn layer and does not initiate unstable vertical hydrofracture that propagates throughout the ice thickness. At the same time, buried supraglacial lakes have been observed to drain to the ice sheet bed this same region. Therefore, to assess the mass balance impact of ice slab expansion, it is important to understand if and when surface-to-bed hydrofracture may occur in these regions.In “Vulnerability of Firn to Hydrofracture, Part I: Poromechanical Modeling”, we developed an analytic expression for the maximum tensile effective stress within the firn layer beneath a water-filled fracture in an ice slab. Here we apply this model to Greenland’s ice slab regions. We use an ensemble of in situ and remote sensing observations to constrain the physical, mechanical, and hydraulic parameters in our model. We then run a Monte Carlo analysis to constrain the physically-plausible range of maximum tensile effective stress in the firn for two scenarios: a water-filled crevasse in an ice slab or a supraglacial lake over a fractured ice slab. Our results show that the maximum stress in the firn layer is always less than in an equivalent solid ice column, and typically remains compressive, because the imposed load is partially accommodated by a change in pore pressure. An overlying lake further stabilizes the system by increasing the lithostatic stress that acts to close the fracture. Therefore, in Greenland, the relict firn layer can be an important stabilizing factor that suppresses surface-to-bed hydrofracture under ice slabs, despite the abundance of both surface crevassing and meltwater.

Tropical cyclones (TCs) are responsible for large-scale loss of life and property, and billions of dollars worth of damage annually. Forecasting is typically accomplished through the use of dynamical models which directly integrate the governing equations of motion. These forecasts, and especially intensity forecasts, rely on accurate initial conditions obtained by assimilating real-time observational data. However, current methods used to generate these initial conditions are computationally expensive and limited, and TC intensity forecasts have much room for improvement. Here, we show that a Physics-Informed Neural Network can provide a promising alternative for data assimilation for TC initial conditions. Using synthetic training data sparsely sampled from hurricanes simulated in a forecast model, a PINN is able to accurately reconstruct full 2- and 3-dimensional wind and pressure fields of a TC. We also demonstrate how a set of sparse, real-time observations, can be used to accurately reconstruct Hurricane Ida. Our results demonstrate how recent advances in computational capabilities and deep learning can be applied to TC data assimilation, offering an accurate and efficient complement to existing data assimilation methods.

On the Greenland Ice Sheet, hydrofracture connects the supraglacial and subglacial hydrologicsystems, coupling surface runoff dynamics and ice velocity. Over the last two decades, the growthof low-permeability ice slabs in the firn above the equilibrium line has expanded Greenland’s runoffzone, but the vulnerability of these regions to hydrofracture is still poorly understood. Observationsfrom Northwest Greenland suggest that when meltwater drains through crevasses in ice slabs, itis stored in the underlying relict firn layer and does not reach the ice sheet bed. Here, we useporomechanics to investigate whether water-filled crevasses in ice slabs can propagate verticallythrough a firn layer. Based on numerical simulations, we develop an analytical estimate of the waterinjection-induced effective stress in the firn given the water level in the crevasse, ice slab thickness,and firn properties. We find that the firn layer reduces the system’s vulnerability to hydrofracturebecause much of the hydrostatic stress is accommodated by a change in pore pressure, rather thanbeing transmitted to the solid skeleton. This result suggests that surface-to-bed hydrofracture willnot occur in ice slab regions until all pore space proximal to the initial flaw has been filled with solidice.

Ice shelves are floating extensions of grounded ice and play a crucial role in slowing ice discharge into the ocean. Ice flows in response to stresses according to the flow law, which is essential for predicting the mass loss of ice sheet. Laboratory experiments have shown that polycrystalline ice obeys Glen’s flow law, a power-law relation between the stress and strain rate that has been applied to ice-sheet models for decades. However, it remains unclear how processes at ice-shelf scales impact the flow law, i.e. rheology, of glacial ice. Here, we reveal the rheology of glacial ice in Antarctic Ice Shelves leveraging the availability of remote-sensing data and physics-informed deep learning. We find that the rheology of ice shelves differs substantially between the compression and extension zones. In the compression zone near the grounding line the rheology of ice closely obeys power laws with exponents in the range 1 < n < 3, consistent with prior laboratory experiments. In the extension zone, which comprises most of the total ice-shelf area, the rheology deviates from laboratory findings and does not follow a clear trend. Our result highlights a need to examine the impact of ice-shelf scale processes on glacial rheology.

Dissolution and dissociation of CO2 in an aqueous phase induce diffusiophoretic motion of suspended particles with a nonzero surface charge. We report CO2-driven diffusiophoresis of colloidal particles and bacterial cells in a circular Hele-Shaw geometry. Combining experiments and model calculations, we identify the characteristic length and time scales of CO2-driven diffusiophoresis in relation to system dimensions and CO2 diffusivity. The motion of colloidal particles driven by a CO2 gradient is characterized by measuring the average velocities of particles as a function of distance from the CO2 sources. In the same geometrical configurations, we demonstrate that the directional migration of wild-type V. cholerae and a mutant lacking flagella, as well as S. aureus and P. aeruginosa, near a dissolving CO2 source is diffusiophoresis, not chemotaxis. Such a directional response of the cells to CO2 (or an ion) concentration gradient shows that diffusiophoresis of bacteria is achieved independent of cell shape, motility and the Gram stain (cell surface structure). Long-time experiments suggest potential applications for bacterial diffusiophoresis to cleaning systems or anti-biofouling surfaces, by reducing the population of the cells near CO2 sources.

Greenland supraglacial lakes sometimes drain to the ice-sheet base only hours to days apart in time, leading to the hypothesis that stress transmission following one drainage may be sufficient to induce hydro-fracture-driven drainages of other lakes. However, available observations characterizing the time- and length-scales of drainage-induced stress perturbations are insufficient to evaluate this hypothesis, hindering our understanding of whether lower-elevation lake drainages could generate stress changes that initiate hydro-fracture beneath lakes in inland ice-sheet regions. Here, we invert ice-sheet surface displacement observations from a dense Global Positioning System (GPS) array deployed around three supraglacial lakes in the Greenland Ice Sheet ablation zone to estimate the space-time history of slip and opening along pre-defined planes within an elastic half-space that best reproduces GPS observations during two rapid drainage events. We then use these slip and opening estimates to forward model ice-sheet surface stresses across all three neighboring lake basins and investigate stress transmission between the basins. We find that drainage of a central lake places neighboring basins in either tensional or compressional surface stress relative to their individual hydro-fracture scarp orientations, which, respectively, promotes or inhibits hydro-fracture initiation beneath those lakes. Surface-stress-change direction is asymmetric across the lake-draining fracture of the central lake and highly dependent on where surface uplift occurs. On elastic timescales, lake-drainage-induced stresses within the extent of the GPS array in the inland direction remain low within ~3 km of the central lake. This short length-scale for stress coupling in the inland direction is consistent with idealized lake-drainage scenarios for different lake volumes and ice-sheet thicknesses. Our observations and idealized-model results support the stress-transmission hypothesis for inducing hydro-fracture-driven drainage of lakes located within the region of uplift produced by the initial drainage, but refute this hypothesis for distal lakes not located down the subglacial hydraulic catchment from the initial drainage.

We study the relaxation dynamics of a fluid-filled blister between an elastic sheet and a porous substrate using laboratory experiments and a mathematical model. The dynamics are controlled by the deformation of the elastic sheet, the viscous stresses in the pores, and the capillary pressure at the liquid-air interface due to imbibition. We identify two regimes of drainage, where for thick sheets and more permeable substrates, drainage is primarily due to the stresses in the deformed elastic sheet, and for thin sheets and less permeable substrates, drainage is driven by the imbibition of the liquid into the pore space.

Surface meltwater reaching the base of the Greenland Ice Sheet transits through drainage networks, modulating the flow of the ice sheet. Dye and gas-tracing studies conducted in the western margin sector of the ice sheet have directly observed drainage efficiency to evolve seasonally along the drainage pathway. However, the local evolution of drainage systems further inland, where ice thicknesses exceed 1000 m, remains largely unknown. Here, we infer drainage system transmissivity based on surface uplift relaxation following rapid lake drainage events. Combining field observations of five lake drainage events with a mathematical model and laboratory experiments, we show that the surface uplift decreases exponentially with time, as the water in the blister formed beneath the drained lake permeates through the subglacial drainage system. This deflation obeys a universal relaxation law with a timescale that reveals hydraulic transmissivity and indicates a two-order-of-magnitude increase in subglacial transmissivity (from 0.8 ± 0.3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{m}}{{\rm{m}}}^{3}$$\end{document}mm3 to 215 ± 90.2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{m}}{{\rm{m}}}^{3}$$\end{document}mm3) as the melt season progresses, suggesting significant changes in basal hydrology beneath the lakes driven by seasonal meltwater input., Hydraulic transmissivity under the 1km-thick Greenland Ice Sheet was inferred by ice-sheet uplift relaxation after rapid lake drainage events. A two-order-of-magnitude increase in hydraulic transmissivity was found throughout the melt season.

Dissolution and dissociation of CO2 in an aqueous phase induce diffusiophoretic motion of suspended particles with a nonzero surface charge. We report CO2-driven diffusiophoresis of colloidal particles and bacterial cells in a circular Hele-Shaw geometry. Combining experiments and model calculations, we identify the characteristic length and time scales of CO2-driven diffusiophoresis in relation to system dimensions and CO2 diffusivity. The motion of colloidal particles driven by a CO2 gradient is characterized by measuring the average velocities of particles as a function of distance from the CO2 sources. In the same geometrical configurations, we demonstrate that the directional migration of wild-type V. cholerae and a mutant lacking flagella, as well as S. aureus and P. aeruginosa, near a dissolving CO2 source is diffusiophoresis, not chemotaxis. Such a directional response of the cells to CO2 (or an ion) concentration gradient shows that diffusiophoresis of bacteria is achieved independent of cell shape, motility and the Gram stain (cell surface structure). Long-time experiments suggest potential applications for bacterial diffusiophoresis to cleaning systems or anti-biofouling surfaces, by reducing the population of the cells near CO2 sources.

Surface meltwater reaching the base of the Greenland Ice Sheet transits through drainage networks, modulating the flow of the ice sheet. Dye-tracing studies indicate that drainage efficiency evolves seasonally along the drainage pathway. However, the local evolution of drainage systems further inland, where ice thicknesses exceed 1000 m, remains largely unknown. Here, we develop a novel method to infer transmissivity of the drainage system based on surface uplift relaxation following rapid lake drainage events. Combining field observations of five lake drainage events with a mathematical model and laboratory experiments, we show that the surface uplift decreases exponentially with time, as the water in the blister formed beneath the drained lake permeates through the subglacial drainage system. This deflation obeys a universal relaxation law with a timescale that reveals hydraulic transmissivity and indicates a two-order-of-magnitude increase in subglacial transmissivity as the melt season progresses, suggesting significant changes in basal hydrology beneath the lakes.

Atmospheric warming threatens to accelerate the retreat of the Antarctic Ice Sheet by increasing surface melting and facilitating ‘hydrofracturing’1–7, where meltwater flows into and enlarges fractures, potentially triggering ice-shelf collapse3–5,8–10. The collapse of ice shelves that buttress11–13 the ice sheet accelerates ice flow and sea-level rise14–16. However, we do not know if and how much of the buttressing regions of Antarctica’s ice shelves are vulnerable to hydrofracture if inundated with water. Here we provide two lines of evidence suggesting that many buttressing regions are vulnerable. First, we trained a deep convolutional neural network (DCNN) to map the surface expressions of fractures in satellite imagery across all Antarctic ice shelves. Second, we developed a stability diagram of fractures based on linear elastic fracture mechanics to predict where basal and dry surface fractures form under current stress conditions. We find close agreement between the theoretical prediction and the DCNN-mapped fractures, despite limitations associated with detecting fractures in satellite imagery. Finally, we used linear elastic fracture mechanics theory to predict where surface fractures would become unstable if filled with water. Many regions regularly inundated with meltwater today are resilient to hydrofracture—stresses are low enough that all water-filled fractures are stable. Conversely, 60 ± 10 per cent of ice shelves (by area) both buttress upstream ice and are vulnerable to hydrofracture if inundated with water. The DCNN map confirms the presence of fractures in these buttressing regions. Increased surface melting17 could trigger hydrofracturing if it leads to water inundating the widespread vulnerable regions we identify. These regions are where atmospheric warming may have the largest impact on ice-sheet mass balance. Using a neural network trained on continent-wide data and a fracture model, the ice shelves in Antarctica that may be prone to hydrofracturing under further atmospheric warming are identified.

Presentation file for the invited talk given by W. Roger Buck at Analog Modeling for Tectonic Processes 2020 Workshop

In hydraulic fracturing, water is injected at high pressure to crack shale formations. More sustainable techniques use aqueous foams as injection fluids to reduce the water use and wastewater treatment of conventional hydrofractures. However, the physical mechanism of foam fracturing remains poorly understood, and this lack of understanding extends to other applications of compressible foams such as fire-fighting, energy storage, and enhanced oil recovery. Here we show that the injection of foam is much different from the injection of incompressible fluids and results in striking dynamics of fracture propagation that are tied to the compressibility of the foam. An understanding of bubble-scale dynamics is used to develop a model for macroscopic, compressible flow of the foam, from which a scaling law for the fracture length as a function of time is identified and exhibits excellent agreement with our experimental results.

After a bubble bursts at a liquid surface, the collapse of the cavity generates capillary waves, which focus on the axis of symmetry to produce a jet. The cavity and jet dynamics are primarily controlled by a nondimensional number that compares capillary inertia and viscous forces, i.e., the Laplace number $\mathrm{La}=\ensuremath{\rho}\ensuremath{\gamma}{R}_{0}/{\ensuremath{\mu}}^{2}$, where $\ensuremath{\rho}$, $\ensuremath{\mu}$, $\ensuremath{\gamma}$, and ${R}_{0}$ are the liquid density, viscosity, interfacial tension, and the initial bubble radius, respectively. In this Letter, we show that the time-dependent profiles of cavity collapse ($tl{t}_{0}$) and jet formation ($tg{t}_{0}$) both obey a $|t\ensuremath{-}{t}_{0}{|}^{2/3}$ inviscid scaling, which results from a balance between surface tension and inertia forces. Moreover, we present a scaling law, valid above a critical Laplace number, which reconciles the time-dependent scaling with the recent scaling theory that links the Laplace number to the final jet velocity and ejected droplet size. This leads to a self-similar formula which describes the history of the jetting process, from cavity collapse to droplet formation.

Finger-like protrusions that form along fluid−fluid displacement fronts in porous media are often excited by hydrodynamic instability when low-viscosity fluids displace high-viscosity resident fluids. Such interfacial instabilities are undesirable in many natural and engineered displacement processes. We report a phenomenon whereby gradual and monotonic variation of pore sizes along the front path suppresses viscous fingering during immiscible displacement, that seemingly contradicts conventional expectation of enhanced instability with pore size variability. Experiments and pore-scale numerical simulations were combined with an analytical model for the characteristics of displacement front morphology as a function of the pore size gradient. Our results suggest that the gradual reduction of pore sizes act to restrain viscous fingering for a predictable range of flow conditions (as anticipated by gradient percolation theory). The study provides insights into ways for suppressing unwanted interfacial instabilities in porous media, and provides design principles for new engineered porous media such as exchange columns, fabric, paper, and membranes with respect to their desired immiscible displacement behavior., Proceedings of the National Academy of Sciences of the United States of America, 115 (19), ISSN:0027-8424, ISSN:1091-6490

Cracks filled with fluid propagation when the pressurized fluid is injected into the crack. Subsequently, when the fluid inlet is exposed to a lower pressure, the fluid flows backwards (backflow) and the crack closes due to the elastic relaxation of the solid. Here we study the dynamics of the crack closure during the backflow. We find that the crack radius remains constant and the fluid volume in the crack decreases with time in a power-law manner at late times. The balance between the viscous stresses in the fluid and elastic stresses in the fluid and the elastic stresses in the solid yields a scaling law that agrees with the experimental results for different fluid viscosities, Young's moduli of the solid, and initial radii of the cracks. Furthermore, we visualize the time-dependent crack shapes, and the convergence to a universal dimensionless shape demonstrates the self-similarity of the crack shapes during the backflow process.

The dynamics of fluid-driven cracks in an elastic matrix is studied experimentally. We report the crack radiusR(t) as a function of time, as well as the crack shapesw(r,t) as a function of space and time. A dimensionless parameter, the pressure ratio Δpf/Δpv, is identified to gauge the relative importance between the toughness (Δpf) and viscous (Δpv) effects. In our previous paper (Laiet al.2015Proc. R. Soc. A471, 20150255. (doi:10.1098/rspa.2015.0255)), we investigated the viscous limit experimentally when the toughness-related stresses are negligible for the crack propagation. In this paper, the experimental parameters, i.e. Young’s modulusEof the gelatin, viscosityμof the fracturing liquid and the injection flow rateQ, were chosen so that the viscous effects in the flow are negligible compared with the toughness effects, i.e. Δpf/Δpv≫1. In this limit, the crack dynamics can be described by the toughness-dominated scaling laws, which give the crack radiusR(t)∝t2/5and the half maximum crack thicknessW(t)∝t1/5. The experimental results are in good agreement with the predictions of the toughness scaling laws: the experimental data for crack radiusR(t) for a wide range of parameters (E,μ,Q) collapse after being rescaled by the toughness scaling laws, and the rescaled crack shapesw(r,t) also collapse to a dimensionless shape, which demonstrates the self-similarity of the crack shape. The appropriate choice of the viscous or toughness scaling laws is important to accurately describe the crack dynamics.This article is part of the themed issue ‘Energy and the subsurface’.

We investigate experimentally the steady flows in a cylinder containing two immiscible liquids, with the primary fluid being driven by the upper boundary rotating at constant speeds. The system exhibits interesting interplays between the flow fields and the morphology of the interface, with evidence showing that the remarkable flattop structure is a consequence of the vortex breakdown discovered decades ago, and that the deformability of the interface also feedbacks positively to the development of the vortices. Monitoring the topological structure of the flow fields defines the base states and transitions behind the morphology, whereas our survey over different aspect ratios also reveals rich phenomena of surface instabilities accompanying these steady states.

The Daya Bay Reactor Neutrino Experiment has measured a non-zero value for the neutrino mixing angle $\theta_{13}$ with a significance of 5.2 standard deviations. Antineutrinos from six 2.9 GW$_{\rm th}$ reactors were detected in six antineutrino detectors deployed in two near (flux-weighted baseline 470 m and 576 m) and one far (1648 m) underground experimental halls. With a 43,000 ton-GW_{\rm th}-day livetime exposure in 55 days, 10416 (80376) electron antineutrino candidates were detected at the far hall (near halls). The ratio of the observed to expected number of antineutrinos at the far hall is $R=0.940\pm 0.011({\rm stat}) \pm 0.004({\rm syst})$. A rate-only analysis finds $\sin^22\theta_{13}=0.092\pm 0.016({\rm stat})\pm0.005({\rm syst})$ in a three-neutrino framework., Comment: 5 figures. Version to appear in Phys. Rev. Lett

The Daya Bay Reactor Neutrino Experiment is designed to determine precisely the neutrino mixing angle $\theta_{13}$ with a sensitivity better than 0.01 in the parameter sin$^22\theta_{13}$ at the 90% confidence level. To achieve this goal, the collaboration will build eight functionally identical antineutrino detectors. The first two detectors have been constructed, installed and commissioned in Experimental Hall 1, with steady data-taking beginning September 23, 2011. A comparison of the data collected over the subsequent three months indicates that the detectors are functionally identical, and that detector-related systematic uncertainties exceed requirements., Comment: 24 pages, 36 figures

When a pressurized fluid is injected into an elastic matrix, the fluid generates a fracture that grows along a plane and forms a fluid-filled disc-like shape. We report a laboratory study of such a fluid-driven crack in a gelatin matrix, study the crack shape as a function of time and investigate the influence of different experimental parameters such as the injection flow rate, Young’s modulus of the matrix and fluid viscosity. We choose parameters so that effects of material toughness are small. We find that the crack radius R ( t ) increases with time t according to t α with α =0.48±0.04. The rescaled experimental data at long times for different parameters collapse based on scaling arguments, available in the literature, showing R ( t )∝ t 4/9 from a balance of viscous stresses from flow along the crack and elastic stresses in the surrounding matrix. Also, we measure the time evolution of the crack shape, which has not been studied before. The rescaled crack shapes collapse at longer times and show good agreement with the scaling arguments. The gelatin system provides a useful laboratory model for further studies of fluid-driven cracks, which has important applications such as hydraulic fracturing.