Hydraulic transmissivity inferred from ice-sheet relaxation following Greenland supraglacial lake drainages.

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 [Formula: see text] to 215 ± 90.2 [Formula: see text]) as the melt season progresses, suggesting significant changes in basal hydrology beneath the lakes driven by seasonal meltwater input.

CO2-Driven diffusiophoresis for maintaining a bacteria-free surface.

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.

Vulnerability of Antarctica's ice shelves to meltwater-driven fracture.

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.

Bubble Bursting: Universal Cavity and Jet Profiles.

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 La=ργR_{0}/µ^{2}, where ρ, µ, γ, 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 (tt_{0}) both obey a |t-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.

Foam-driven fracture.

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.

Suppressing viscous fingering in structured porous media.

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.

Fluid-driven cracks in an elastic matrix in the toughness-dominated limit.

The dynamics of fluid-driven cracks in an elastic matrix is studied experimentally. We report the crack radius R(t) as a function of time, as well as the crack shapes w(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 (Lai et al. 2015 Proc. R. Soc. A 471, 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 modulus E of the gelatin, viscosity µ of the fracturing liquid and the injection flow rate Q, 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 radius R(t)∝t(2/5) and the half maximum crack thickness W(t)∝t(1/5) The experimental results are in good agreement with the predictions of the toughness scaling laws: the experimental data for crack radius R(t) for a wide range of parameters (E,µ,Q) collapse after being rescaled by the toughness scaling laws, and the rescaled crack shapes w(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'.

Elastic Relaxation of Fluid-Driven Cracks and the Resulting Backflow.

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.