On non‐Newtonian fluid flow in rough fractures

Flow of non‐Newtonian fluids between rough walls is of interest in several geophysical and industrial applications. In this work (mainly geared toward fractured media) a governing equation for creeping flow of a purely viscous power law fluid of flow behavior index n in a rough‐walled fracture is obtained, generalizing past results for a Newtonian fluid. An equivalent fracture aperture is defined, in analogy to the well‐known hydraulic aperture valid for n = 1. Tortuosity is introduced as a vectorial quantity, thereby distinguishing between true and apparent fracture aperture. Examples are provided to illustrate the utility of the proposed approach. It is demonstrated that tortuosity effects significantly decrease the equivalent fracture permeability. Depending on the specific geometry considered, the flow behavior index may or may not have a significant impact on the equivalent fracture permeability. When it does, the reduction effect due to tortuosity is enhanced as the flow behavior index decreases

Stability Analysis of Gravity Currents of a Power-Law Fluid in a Porous Medium

We analyse the linear stability of self-similar shallow, two-dimensional and axisymmetric gravity currents of a viscous power-law non-Newtonian fluid in a porous medium. The flow domain is initially saturated by a fluid lighter than the intruding fluid, whose volume varies with time astα. The transition between decelerated and accelerated currents occurs atα= 2 for two-dimensional and atα= 3 for axisymmetric geometry. Stability is investigated analytically for special values ofαand numerically in the remaining cases; axisymmetric currents are analysed only for radially varying perturbations. The two-dimensional currents are linearly stable forα 2 (two-dimensional accelerated currents) andα> 3 (axisymmetric accelerated currents) the linear stability analysis is of limited value since the hypotheses of the model will be violated

Direct Simulation of Micro-Component Water Consumption for the Evaluation of Potential Water Reuse in Households

A study on water/energy balances at the household scale is performed using Life Cycle Assessment (LCA) to estimate Greenhouse Gas (GHG) emissions and impacts resulting from multiple scenarios incorporating various options for: (i) component sizing, (ii) energy usage, and (iii) water reuse. Sustainability indicators are evaluated to select feasible options, while reducing whole life cycle GHG emissions. Water reuse schemes using rainwater are strongly dependent on rainfall availability and require significant tank volumes. Schemes using only gray water are more compact but more energy for treatment is needed before usage. Schemes obtained by combining both options perform better in terms of reliability and sustainability

Shear-Thinning Fluid Flow in Variable-Aperture Channels

Non-Newtonian fluid flow in a single fracture is a 3-D nonlinear phenomenon that is often averaged across the fracture aperture and described as 2-D. To capture the key interactions between fluid rheology and spatial heterogeneity, we adopt a simplified geometric model to describe the aperture variability, consisting of adjacent one-dimensional channels with constant aperture, each drawn from an assigned aperture distribution. The flow rate is then derived under the lubrication approximation for the two limiting cases of an external pressure gradient that is parallel/perpendicular to the channels; these two arrangements provide upper and lower bounds to the fracture conductance. The fluid rheology is described by the Prandtl–Eyring shear-thinning model. Novel closed-form results for the flow rate and hydraulic aperture are derived and discussed; different combinations of the parameters that describe the fluid rheology and the variability of the aperture field are considered. The flow rate values are very sensitive to the applied pressure gradient and to the shape of the distribution; in particular, more skewed distribution entails larger values of a dimensionless flow rate. Results for practical applications are compared with those valid for a power-law fluid and show the effects on the fracture flow rate of a shear stress plateau

PROPAGATION OF GRAVITY CURRENTS OF NON-NEWTONIAN POWER-LAW FLUIDS IN POROUS MEDIA

A comprehensive analytical and experimental framework is presented to describe gravity-driven motions of rheologically complex fluids through porous media. These phenomena are relevant in geophysical, environmental, industrial and biological applications. The fluid is characterized by an Ostwald-DeWaele constitutive equation with behaviour index n. The flow is driven by the release of fluid at the origin of an infinite porous domain. In order to represent several possible spreading scenarios, we consider: i) different domain geometries: plane, radial, and channelized, with the channel shape parameterized by ; ii) instantaneous or continuous injection, depending on the time exponent of the volume of fluid in the current, ; iii) horizontal or inclined impermeable boundaries. Systematic heterogeneity along the streamwise and/or transverse direction is added to the conceptualization upon considering a power-law permeability variation governed by two additional parameters  and . Scalings for current length and thickness are derived in self similar form coupling the modified Darcy’s law accounting for the fluid rheology with the mass balance equation. The speed, thickness, and aspect ratio of the current are studied as a function of model parameters; several different critical values of  emerge and govern the type of dependency, as well as the tendency of the current to accelerate or decelerate and become thicker or thinner at a given point. The asymptotic validity of the solutions is limited to certain ranges of model parameters. Experimental validation is performed under constant volume, constant and variable flux regimes in tanks/channels filled with transparent glass beads of uniform or variable diameter, using shear-thinning suspensions and Newtonian mixtures. The experimental results for the length and profile of the current agree well with the self-similar solutions at intermediate and late times

Slip Backflow of Polymers in Elastic Fractures for Subsurface Heat Recovery

This research delves into the complexities of backflow phenomena in finite-length and flat-walled fractures with elastic walls, specifically focusing on power-law fluids, whose shear-thinning behavior distinguishes them from Newtonian fluids. We model the backflow process under the lubrication approximation and by incorporating the linear Navier slip law. We numerically examine the influence of parameters such as slip length, fluid rheology, and external pressure on the backflow propagation of the carrier fluid. Our findings underscore the significant role played by the rheological index in determining the fracture closure rate. Additionally, our investigations highlight the marked effect of external pressure variations on pressure distribution within the fracture. Notably, the friction coefficient at the fracture walls, as denoted by a dimensionless slip number, exhibits limited influence on the fundamental dynamics of the problem. These insights advance our understanding of power-law fluid backflow and have wide-ranging applications across various engineering disciplines

Porous gravity currents: A survey to determine the joint influence of fluid rheology and variations of medium properties

We develop a model to grasp the combined effect of rheology and spatial stratifications on two- dimensional non-Newtonian gravity-driven flow in porous media. We consider a power-law constitutive equation for the fluid, and a monomial variation of permeability and porosity along the vertical direction (transverse to the flow) or horizontal direction (parallel to the flow). Under these assumptions, similar- ity solutions are derived in semi-analytical form for thin gravity currents injected into a two-dimensional porous medium and having constant or time-varying volume. The extent and shape of the porous domain affected by the injection is significantly influenced by the interplay of model parameters. These describe the fluid (flow behaviour index n ), the spatial heterogeneity (coefficients β, γ, δ, ω for variations of per- meability and porosity in the horizontal or vertical direction), and the type of release (volume exponent α). Theoretical results are validated against two sets of experiments with α= 1 (constant inflow) con- ducted with a stratified porous medium (simulated by superimposing layers of glass beads of different diameter) and a Hele-Shaw analogue for power-law fluid flow, respectively. In the latter case, a recently established Hele-Shaw analogy is extended to the variation of properties parallel to the flow direction. Comparison with experimental results shows that the proposed model is able to capture the propagation of the current front and the current profile

Digital reconstruction of the Ceprano calvarium (Italy), and implications for its interpretation

The Ceprano calvarium was discovered in fragments on March 1994 near the town of Ceprano in southern Latium (Italy), embedded in Middle Pleistocene layers. After reconstruction, its morphological features suggests that the specimen belongs to an archaic variant of H. heidelbergensis, representing a proxy for the last common ancestor of the diverging clades that respectively led to H. neanderthalensis and H. sapiens. Unfortunately, the calvarium was taphonomically damaged. The postero-lateral vault, in particular, appears deformed and this postmortem damage may have infuenced previous interpretations. Specifcally, there is a depression on the fragmented left parietal, while the right cranial wall is warped and angulated. This deformation afected the shape of the occipital squama, producing an inclination of the transverse occipital torus. In this paper, after X-ray microtomography (μCT) of both the calvarium and several additional fragments, we analyze consistency and pattern of the taphonomic deformation that afected the specimen, before the computer-assisted retrodeformation has been performed; this has also provided the opportunity to reappraise early attempts at restoration. As a result, we ofer a revised interpretation for the Ceprano calvarium’s original shape, now free from the previous uncertainties, along with insight for its complex depositional and taphonomic history

Stimulation of S1PR5 with A-971432, a selective agonist, preserves blood-brain barrier integrity and exerts therapeutic effect in an animal model of Huntington's disease

Huntington's disease (HD) is themost common neurodegenerative disorder for which no effective cure is yet available. Although several agents have been identified to provide benefits so far, the number of therapeutic options remains limited with only symptomatic treatment available. Over the past few years, we have demonstrated that sphingolipid-based approachesmay open the door to newandmore targeted treatments for the disease. In this study, we investigated the therapeutic potential of stimulating sphingosine-1-phosphate (S1P) receptor 5 by the new selective agonist A-971432 (provided by AbbVie) in R6/2mice, a widely used HD animalmodel. Chronic administration of low-dose (0.1mg/kg) A-971432 slowed down the progression of the disease and significantly prolonged lifespan in symptomatic R6/2mice. Such beneficial effects were associated with activation of pro-survival pathways (BDNF, AKT and ERK) and with reduction of mutant huntingtin aggregation. A-971432 also protected blood-brain barrier (BBB) homeostasis in the same mice. Interestingly, when administered early in the disease, before any overt symptoms, A-971432 completely protected HDmice fromthe classic progressivemotor deficit and preserved BBB integrity. Beside representing a promising strategy to take into consideration for the development of alternative therapeutic options for HD, selective stimulation of S1P receptor 5may be also seen as an effective approach to target brain vasculature defects in the disease