Hydrogel as a Medium for Fluid-Driven Fracture Study

In this paper we describe how to construct polyacrylamide hydrogels to study the processes linked with hydraulic fracturing. These transparent, linearly elastic and brittle gels permit fracturing at low pressures and speeds allowing accurate measurements to be obtained. In the context of hydraulic fracturing, the broad range of modulus and fracture energy values that are attainable allow experimental exploration of particular regimes of importance. We also describe how material properties may be deduced from hydraulic fracturing experiments. Lastly, we analyse the fracture surface patterns that emerge from fluid-driven cracks occurring within the medium. These patterns are similar to those that have been observed in other materials and we comment on their fractal-like nature

Entrainment in two coalescing axisymmetric turbulent plumes

AbstractA model of the total volume flux and entrainment occurring in two coalescing axisymmetric turbulent plumes is developed and compared with laboratory experiments. The dynamical evolution of the two plumes is divided into three regions. In region 1, where the plumes are separate, the entrainment in each plume is unaffected by the other plume, although the two plumes are drawn together due to the entrainment of ambient fluid between them. In region 2 the two plumes touch each other but are not yet merged. In this region the total entrainment is a function of both the dynamics of the touching plumes and the reduced surface area through which entrainment occurs. In region 3 the two plumes are merged and the entrainment is equivalent to that in a single plume. We find that the total volume flux after the two plumes touch and before they merge increases linearly with distance from the sources, and can be expressed as a function of the known total volume fluxes at the touching and merging heights. Finally, we define an ‘effective’ entrainment constant, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\alpha _{eff}$, as the value of $\alpha$ needed to obtain the same total volume flux in two independent plumes as that occurring in two coalescing plumes. The definition of $\alpha _{eff}$ allows us to find a single expression for the development of the total volume flux in the three different dynamical regions. This single expression will simplify the representation of coalescing plumes in more complex models, such as in large-scale geophysical convection, in which plume dynamics are not resolved. Experiments show that the model provides an accurate measure of the total volume flux in the two coalescing plumes as they evolve through the three regions.The authors gratefully acknowledge the National Science Foundation (Grant OCE- 0824636) and the Office of Naval Research (Grant N00014-09-1-0844) for their support of the 2013 WHOI Geophysical Fluid Dynamics Summer School where this project was initiated. Support to CC was given by the National Science Foundation project OCE- 1130008. CC wishes to thank Jason Hyatt for improving the clarity of this manuscript.This is the author accepted manuscript. The final version is available from CUP at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9300855&fileId=S0022112014003899

Displacement ventilation: a viable ventilation strategy for makeshift hospitals and public buildings to contain COVID-19 and other airborne diseases.

The SARS-CoV-2 virus has so far infected more than 31 million people around the world, and its impact is being felt by all. Patients with diseases such as COVID-19 should ideally be treated in negative pressure isolation rooms. However, due to the overwhelming demand for hospital beds, patients have been treated in general wards, hospital corridors and makeshift hospitals. Adequate building ventilation in hospitals and public spaces is a crucial factor to contain the disease (Escombe et al. 2007 PLoS Med. 4; Escombe et al. 2019 BMC Infect. Dis. 19, 88 (doi:10.1186/s12879-019-3717-9); Morawska & Milton 2020 Clin. Infect. Dis. ciaa939. (doi:10.1093/cid/ciaa939)), to exit lockdown safely, and reduce the chance of subsequent waves of outbreaks. A recently reported air-conditioner-induced COVID-19 outbreak caused by an asymptomatic patient, in a restaurant in Guangzhou, China (Lu et al. 2020 Emerg. Infect. Dis. 26) exposes our vulnerability to future outbreaks linked to ventilation in public spaces. We argue that displacement ventilation (either mechanical or natural ventilation), where air intakes are at low level and extracts are at high level, is a viable alternative to negative pressure isolation rooms, which are often not available on site in hospital wards and makeshift hospitals. Displacement ventilation produces negative pressure at the occupant level, which draws fresh air from outdoors, and positive pressure near the ceiling, which expels the hot and contaminated air out. We acknowledge that, in both developed and developing countries, many modern large structures lack the openings required for natural ventilation. This lack of openings can be supplemented by installing extract fans. We have also discussed and addressed the issue of the 'lock-up effect'. We provide guidelines for such mechanically assisted, naturally ventilated makeshift hospitals

The effect of double diffusion on entrainment in turbulent plumes

We investigate experimentally the effect of double diffusion in the salt-fingering configuration on entrainment in turbulent plumes. Plumes over a range of source buoyancy fluxes and source density ratios are examined. When the plumes are double diffusive ( ) the entrainment coefficient is not constant, with an up to 20 % reduction from the value found for single-diffusive plumes, that is, plumes with . The scale of reduction is found to be in direct relation to the source density ratio and is inversely related to the distance travelled by the plume, indicating that double-diffusive effects decrease as the plume evolves. We propose an explanation for the observed reduction in the entrainment coefficient on the basis of differential diffusion hindering large-scale engulfment at the edge of the plume.We acknowledge funding from the EPSRC under the Programme Grant EP/K034529/1 ‘Mathematical Underpinnings of Stratified Turbulence’ (MUST), and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant no. 742480 ‘Stratified Turbulence And Mixing Processes’ (STAMP). M.D. is supported by the Gates Cambridge Scholarship

Experimental exploration of fluid-driven cracks in brittle hydrogels

Hydraulic fracturing is a procedure by which a fracture is initiated and propagates due to pressure (hydraulic loading) applied by a fluid introduced inside the fracture. In this study, we focus on a crack driven by an incompressible Newtonian fluid, injected at a constant rate into an elastic matrix. The injected fluid creates a radial fracture that propagates along a plane. We investigate this type of fracture both theoretically and experimentally. Our experimental apparatus uses a brittle and transparent polyacrylamide hydrogel matrix. Using this medium, we examine the rate of radial crack growth, fracture aperture, shape of the crack tip and internal fluid flow field. Our range of experimental parameters allows us to exhibit two distinct fracturing regimes, and the transition between these, in which the rate of radial crack propagation is dominated by either viscous flow within the fracture or the material toughness. Measurements of the profiles near the crack tip provide additional evidence of the viscosity-dominated and toughness-dominated regimes, and allow us to observe the transition from the viscous to the toughness regime as the crack propagates. Particle image velocimetry measurements show that the flow in the crack is radial, as expected in the viscous regime and in the early stages of the toughness regime. However, at later times in the toughness regime, circulation cells are observed in the flow within the crack that destroy the radial symmetry of the flow field.</jats:p

Regime transitions and energetics of sustained stratified shear flows

We describe the long-term dynamics of sustained stratified shear flows in the laboratory. The stratified inclined duct (SID) experiment sets up a two-layer exchange flow in an inclined duct connecting two reservoirs containing salt solutions of different densities. This flow is primarily characterised by two non-dimensional parameters: the tilt angle of the duct with respect to the horizontal, \unicode[STIX]{x1D703} (a few degrees at most), and the Reynolds number $Re$, an input parameter based on the density difference driving the flow. The flow can be sustained with constant forcing over arbitrarily long times and exhibits a wealth of dynamical behaviours representative of geophysically relevant sustained stratified shear flows. Varying \unicode[STIX]{x1D703} and $Re$ leads to four qualitatively different regimes: laminar flow; mostly laminar flow with finite-amplitude, travelling Holmboe waves; spatio-temporally intermittent turbulence with substantial interfacial mixing; and sustained, vigorous interfacial turbulence (Meyer &amp; Linden, J. Fluid Mech., vol. 753, 2014, pp. 242–253). We seek to explain the scaling of the transitions between flow regimes in the two-dimensional plane of input parameters (\unicode[STIX]{x1D703},Re). We improve upon previous studies of this problem by providing a firm physical basis and non-dimensional scaling laws that are mutually consistent and in good agreement with the empirical transition curves we inferred from 360 experiments spanning \unicode[STIX]{x1D703}\in [-1^{\circ },6^{\circ }] and $Re\in [300,5000]$. To do so, we employ state-of-the-art simultaneous volumetric measurements of the density field and the three-component velocity field, and analyse these experimental data using time- and volume-averaged potential and kinetic energy budgets. We show that regime transitions are caused by an increase in the non-dimensional time- and volume-averaged kinetic energy dissipation within the duct, which scales with \unicode[STIX]{x1D703}Re at high enough angles. As the power input scaling with \unicode[STIX]{x1D703}Re is increased above zero, the two-dimensional, parallel-flow dissipation (power output) increases to close the budget through an increase in the magnitude of the exchange flow, incidentally triggering Holmboe waves above a certain threshold in interfacial shear. However, once the hydraulic limit of two-layer exchange flows is reached, two-dimensional dissipation plateaus and three-dimensional dissipation at small scales (turbulence) takes over, at first intermittently, and then steadily, in order to close the budget and follow the \unicode[STIX]{x1D703}Re scaling. This general understanding of regime transitions and energetics in the SID experiment may serve as a basis for the study of more complex sustained stratified shear flows found in the natural environment.EPSRC Doctoral Prize EPSRC Programme Grant EP/K034529/1 ERC Horizon 2020 Grant No 74248

Research data supporting "Regime transitions and energetics of sustained stratified shear flows"

We provide the following data: 1. The three-component velocity and density fields in space and time (u, v, w, ρ)(x, y, z, t) for all 16 experiments listed in table 2 of the paper; 2. The MATLAB codes used to compute and plot the energetics of the above data, as explained in the paper and shown in figures 10, 11, 14, 15, 16. 3. Movies showing all the flow fields and the spanwise vorticity in a number of slices allowing for an advanced visualisation of the 4D data to complement figures 3-4; 4. Plots of the mass flux and volume flux for each experiment; 5. A README.pdf file giving more information about the data, its format and usage instructions

The effect of an indoor-outdoor temperature difference on transient cross-ventilation

We examine the effect of an indoor-outdoor temperature difference on the transient wind-driven cross-ventilation of a room. Laboratory experiments are performed in a water flume using a reduced-scale model room. For solely wind-driven cross-ventilation with no initial temperature difference between the room and the external fluid, the ventilation rate is constant. In experiments, the mean dye concentration decays exponentially, which is expected when the room remains well-mixed. When there is an initial temperature difference but no wind, the buoyancy-driven exchange-ventilation results lie between a model that assumes the room is well-mixed and a new model that assumes no mixing between the incoming flow and the room. When both wind and buoyancy drive the flow, the relative importance of these two effects can be described by a Froude number, Fr. For buoyancy-dominated ventilation (Fr1), a temperature difference slightly reduces the ventilation rate, but only by up to 6%, a change that can be neglected in most applications. Two processes compete to ventilate the room in combined cases: the removal of fluid from a lower layer by flow through the windows and the erosion of an upper layer by entrainment into the jet that crosses the room. The relative rates of these two processes depend on the geometry of the room.This work is supported by the Engineering and Physical Sciences Research Council (EPSRC) Grand Challenge grant Managing Air for Green Inner Cities (MAGIC) [grant number EP/N010221/1]

A comparison of entrainment in turbulent line plumes adjacent to and distant from a vertical wall

EPSRC (R008957/1) EPSRC (K034529/1) ERC (742480

On the origin of the circular hydraulic jump in a thin liquid film

For more than a century, it has been believed that all hydraulic jumps are created due to gravity. However, we found that thin-film hydraulic jumps are not induced by gravity. This study explores the initiation of thin-film hydraulic jumps. For circular jumps produced by the normal impingement of a jet onto a solid surface, we found that the jump is formed when surface tension and viscous forces balance the momentum in the film and gravity plays no significant role. Experiments show no dependence on the orientation of the surface and a scaling relation balancing viscous forces and surface tension collapses the experimental data. Experiments on thin film planar jumps in a channel also show that the predominant balance is with surface tension, although for the thickness of the films we studied gravity also played a role in the jump formation. A theoretical analysis shows that the downstream transport of surface tension energy is the previously neglected, critical ingredient in these flows and that capillary waves play the role of gravity waves in a traditional jump in demarcating the transition from the supercritical to subcritical flow associated with these jumps.Commonwealth Scholarship Commission, EPSRC grant EP/K50375/