We undertake an experimental investigation into the instabilities that emerge when a shear-thinning fluid intrudes a less viscous Newtonian fluid axisymmetrically in a lubricated Hele-Shaw cell. Pre-formed lubrication layers of Newtonian fluid that separate the shear-thinning fluid from the cell walls are incorporated into the experimental design. Provided the lubrication layers remain effective at reducing shear stress, so that extensional stresses dominate the flow of the intruding fluid, the instabilities evolve to form branch-like structures, which exhibit fracturing or tearing behaviour at their troughs. Thicker lubrication layers enable the branches to propagate radially outwards, whilst thinner, less effective ones hinder their development and progression. In the absence of lubrication layers, the shear-thinning fluid spreads radially and remains axisymmetric. For lubricated flows, we show that the number of branches is dependent primarily on the strain rate at the radial distance where they first emerge, and that the number of branches decreases with increasing strain rate.

The dynamics of soft porous media involves complex interactions between fluid flow and elasticity. The recent paper by Fiori et al. (J. Fluid Mech., vol. 974, 2023, A2) highlights phenomena relating to the periodic loading of such poro-elastic media, including hysteresis and the localisation of deformation at high frequencies. These effects could result in rectification and steady streaming in many important applications.

We consider the multidirectional swelling and drying of hydrogels formed from super-absorbent polymers and water, focusing on the elastic deformation caused by differential swelling. By modelling hydrogels as instantaneously incompressible, linear-elastic materials and considering situations in which there can be large isotropic strains (arising from swelling) while deviatoric strains remain small, it is possible to describe accurately a wider range of gel states than traditional linear elastic theories allow. An equation is derived relating the displacement field to the polymer fraction in such hydrogels, permitting the shape of the swelling gel to be determined as it evolves in time, using the formulation of Part 1 to find the local polymer fraction. We discuss the boundary conditions to be applied at the surfaces of a gel, both on the bulk elastic stress and on the pervadic (pore) pressure in the interstices. Similarities between the equation for the displacements and the equations of classical plate theory are investigated by considering a model problem of a slender cylinder with its base immersed in water drying by evaporation into the surrounding air. In this problem, there is differential drying along the axis of the cylinder, as the base remains swollen while the top dries. The results of our displacement formulation agree qualitatively with experiments that we have conducted, and provide a physical interpretation of the forced biharmonic equation describing the displacement field.

We introduce a new approach for modelling the swelling, drying and elastic behaviour of hydrogels, which leverages the tractability of classical linear-elastic theory whilst incorporating nonlinearities arising from large swelling strains. Relative to a reference state of a fully swollen gel, in which the polymer scaffold may only comprise less than $1\,\%$ of the total volume, a constitutive model for the Cauchy stress tensor is presented, which linearises around small deviatoric strains corresponding to shearing deformations of the material whilst allowing for a nonlinear relation between stress and isotropic strains. Such isotropic strains are considered only to be a consequence of losses and gains of water, while the hydrogel is taken to be instantaneously incompressible. The dynamics governing swelling and drying are described by coupling the interstitial flow of the water through the porous gel with the elastic response of the gel. This approach allows for a complete description of gel behaviour using only three macroscopic polymer-fraction-dependent parameters: an osmotic modulus, a shear modulus and a permeability. It is shown how these three material parameters can, in principle, be determined experimentally using a simple rheometry experiment in which a gel is compressed between two plates surrounded by water and the total force on the top plate is measured. To illustrate our approach, we solve for the swelling of a gel under horizontal confinement and for a partially dried hydrogel bead placed in water.

We describe a theoretical and experimental study of an axisymmetric viscous gravity current with a constant flux, confined to the space between two horizontal parallel plates. The effect of confinement results in two regions of flow: an inner region where the fluid is in contact with both plates and an outer annular region where the fluid forms a gravity current along the lower plate. We present a simple theoretical model that describes the flow dynamics by a single dimensionless parameter $J$, which is the ratio of the characteristic height of an unconfined gravity current to the height of the confined space. Theoretical height profiles display the same characteristics as unconfined gravity currents until $J \approx 0.48$, where a rapid change in behaviour occurs as confinement comes into effect. For larger values of $J$, the confined viscous gravity current gradually tends to Hele-Shaw flow, with the transition essentially complete by $J \approx 2$. We compare the findings from our theoretical model with the results of a series of experiments using golden syrup with various fluxes and gap spacings. Although the data aligns with the major aspects of the model, it is clear that other physics is at play and a single non-dimensional parameter is not sufficient to capture the flow behaviour fully. We speculate on the factors absent in our model that may be responsible for this mismatch.

A new facility has been developed to investigate the directional solidification of transparent aqueous solutions forming mushy layers in a quasi-two-dimensional system. Experiments have been conducted on NaCl–H2O solutions by translating a Hele-Shaw cell at prescribed rates between fixed heat exchangers providing a temperature gradient of approximately 1°C mm−1. The mush–liquid interface remained planar at all freezing velocities larger than 8 μm s−1, while steepling occurred at lower velocities. No significant undercooling of the mush–liquid interface was detected at freezing velocities up to 12 μm s−1. Mathematical predictions of the steady-state temperature profile and mushy-layer thickness as functions of freezing rate are in excellent agreement with experimental measurements.

We present experiments and theory relating to transpiration through unrestrained hydrogel beads in contact with a water reservoir below and air above. Experimentally, we find that saturated hydrogel beads shrink until a steady state is reached in which water flows continuously through the beads. The size of the bead in steady state is sensitive to the evaporation rate, which depends on the relative humidity and speed of the surrounding air, and to the pressure head imposed by the fluid reservoir. Specifically, the bead size decreases with increasing pressure head or evaporation rate. Our one-dimensional model proposes that transport in the hydrogel is driven by gradients in osmotic pressure, caused by gradients in polymer concentration in the hydrogel that correspond to gradients in swelling. If the evaporation rate or the pressure head changes, the adjustment of this gradient requires the bead to change shape and size. Smaller beads have larger gradients of osmotic pressure, which drive higher transpiration rates and can draw water against larger pressure heads.

We consider the solidification of idealised two-component mixtures comprising a solvent or suspending fluid and dissolved solute molecules or suspended colloidal particles, each considered as hard spheres. We review some fundamental thermodynamic ideas regarding relative motion between species and phase equilibria in such mixtures to show how the related solid–liquid phase diagrams depend on the size of the spheres. Using similarity solutions, we first describe freezing of the solvent to form a pure solid (here referred to as ‘ice’), with the solute rejected from the solid forming a boundary layer or dense particle layer ahead of the freezing front. We extend ideas of constitutional supercooling to the case of colloidal suspensions and show that, for a given temperature difference driving solidification, constitutional supercooling occurs only for an intermediate range of particle sizes. Constitutional supercooling promotes the formation of a mushy layer in which segregated ice separates regions of concentrated solute or particles on the microscale. We formulate a continuum model of the mushy layer that relies on a key observation that the regelative motion of concentrated clusters of particles is independent of the size and geometry of the cluster. Our modelling begins with a description of relative motion as a Fickian diffusive process. However, at high particle concentrations, we show that it is more convenient and more computationally tractable to use an equivalent formulation in terms of Darcy flow of the solvent. Within a mushy layer these diffusive fluxes correspond directly to the regelative flux of particle clusters at a rate determined by the local temperature and temperature gradient.

We present a fluid-mechanical explanation of the formation of sedimentary wedges deposited at ice-stream grounding zones. We model both ice and till as layers of viscous fluid spreading under gravity into an inviscid ocean. To test the fundamentals of our theory, we perform a series of laboratory experiments in which we find that a similar wedge of underlying, less viscous fluid accumulates spontaneously around the grounding line. We formulate a simple local condition relating wedge slopes, which determines wedge geometry. It expresses a balance of fluxes of till either side of the grounding line and involves upstream and downstream gradients of till thicknesses as well as the upper surface gradient of the ice. It shows that a wedge will form, that is the upstream till thickness gradients are positive, when the flux of till driven by the glaciostatic pressure gradient of the overlying ice is greater than the flux of till ahead of the grounding zone. This is related to the unloading of the till as the ice sheet crosses the grounding line.

Introduction: eCTAS is a real time electronic triage decision-support tool designed to improve patient safety and quality of care by standardizing the application of the Canadian Triage and Acuity Scale (CTAS). The tool dynamically calculates a recommended CTAS score based on the presenting complaint, vital signs and selected clinical modifiers. The primary objective was to assess consistency of CTAS score distributions across 35 emergency departments (EDs) by 16 presenting complaints pre and post eCTAS implementation. Methods: This retrospective cohort study used population-based administrative data from January 2016 to December 2018 from all hospital EDs in Ontario that had implemented eCTAS with at least 9 months of data. Following a 3-month stabilization period, we compared data for 6 months post-eCTAS implementation to the same 6-month period the previous year (pre-implementation) to account for potential seasonal variation, patient volume and case-mix. We included triage encounters of adult (≥18 years) patients if they had one of 16 pre-specified high-volume, presenting complaints. A paired-samples t-test was used to determine consistency by estimating the absolute difference in CTAS distribution for each presenting complaint, by each hospital, pre and post eCTAS implementation, compared to the overall average of the 35 EDs. Results: There were 183,231 triage encounters in the pre-eCTAS cohort and 179,983 in the post-eCTAS cohort from 35 EDs across the province. Triage scores were more consistent with the overall average after eCTAS implementation in 6 (37.5%) presenting complaints: chest pain (cardiac features) (p < 0.001), extremity weakness/symptoms of cerebrovascular accident (p < 0.001), fever (p < 0.001), shortness of breath (p < 0.001), syncope (p = 0.02), and hyperglycemia (p = 0.03). Triage consistency was similar pre and post eCTAS implementation for the presenting complaints of altered level of consciousness, anxiety/situational crisis, confusion, depression/suicidal/deliberate self-harm, general weakness, head injury, palpitations, seizure, substance misuse/intoxication or vertigo. Conclusion: A standardized, electronic approach to performing triage assessments increased consistency in CTAS scores across many, but not all, high-volume CEDIS complaints. This does not reflect triage accuracy, as there are no known benchmarks for triage accuracy. Improvements in consistency were greatest for sentinel presenting complaints with a minimum allowable CTAS score.

The stress balance within an ice shelf is key to the resistance, or buttressing, it can provide and in part controls the rate of ice discharge from the upstream ice sheet. Unconfined ice shelves are widely assumed to provide no buttressing. However, theory and laboratory-scale analogue experiments have shown that unconfined, floating viscous flows generate buttressing via hoop stresses. Hoop stress results from the viscous resistance to spreading perpendicular to the flow direction in a diverging flow. We build on theoretical work to explore the controls on the magnitude of hoop-stress buttressing, deducing that buttressing increases with increasing effective viscosity and increasing divergence. We use an idealised model calibrated to unconfined sections of Antarctic ice shelves and find that many shelves have low effective viscosity, most likely due to extensive damage resulting from high extensional stresses. Therefore, they are unable to sustain the large hoop stresses required to resist flow. Some ice shelves that are surrounded by sea ice year-round have a greater effective viscosity and can provide buttressing, suggesting that sea ice reduces fracturing. However, we find that most unconfined ice shelves provide insignificant buttressing today, even when hoop stresses are considered in the stress balance.