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

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

On the need of a scale-dependent material characterization to describe the mechanical behavior of 3D printed Ti6Al4V custom prostheses using finite element models

Additive manufacturing is widely used in the orthopaedic industry for the high freedom and flexibility in the design and production of personalized custom implants made of Ti6Al4V. Within this context, finite element modeling of 3D printed prostheses is a robust tool both to guide the design phase and to support clinical eval-uations, possibly virtually describing the in-vivo behavior of the implant. Given realistic scenarios, a suitable description of the overall implant's mechanical behavior is unavoidable. Considering typical custom prostheses' designs (i.e. acetabular and hemipelvis implants), complex designs involving solid and/or trabeculated parts, and material distribution at different scales hinder a high-fidelity modeling of the prostheses.Moreover, uncertainties in the production and in the material characterization of small parts approaching the accuracy limit of the additive manufacturing technology still exist.While recent works suggest that the mechanical properties of thin 3D-printed parts may be peculiarly affected by specific processing parameters (i.e. powder grain size, printing orientation, samples' thickness) as compared to conventional Ti6Al4V alloy, the current numerical models make gross simplifications in describing the complex material behavior of each part at different scales.The present study focuses on two patient-specific acetabular and hemipelvis prostheses, with the aim of experimentally characterizing and numerically describing the dependency of the mechanical behavior of 3D printed parts on their peculiar scale, therefore, overcoming one major limitation of current numerical models. Coupling experimental activities with finite element analyses, the authors initially characterized 3D printed Ti6Al4V dog-bone samples at different scales, representative of the main material components of the investigated prostheses. Afterwards, the authors implemented the characterized material behaviors into finite element models to compare the implications of adopting scale-dependent vs. conventional scaleindependent approaches in predicting the experimental mechanical behavior of the prostheses in terms of their overall stiffness and the local strain distribution. The material characterization results highlighted the need for a scale-dependent reduction of the elastic modulus for thin samples compared to the conventional Ti6Al4V, which is fundamental to properly describe the overall stiffness and local strain distribution on the prostheses.The presented works demonstrate how an appropriate material characterization and a scale-dependent ma-terial description is needed to develop reliable FE models of 3D printed implants characterized by a complex material distribution at different scales

Morpho-Physiological and Biochemical Responses of Hydroponically Grown Basil Cultivars to Salt Stress

Depending on duration and magnitude, abiotic stresses interfere with plant metabolic processes and may severely impact developmental and qualitative attributes. In this study, in addition to characterizing three different cultivars of basil (‘Anise’, ‘Cinnamon’, and ‘Lemon’) grown under hydroponics, we appraised the impact of NaCl salt stress (60 mM) on morphophysiological and nutraceutical properties of the basil crop. Salt stress significantly reduced fresh yield (51.54%, on average) and photosynthetic parameters (ACO2, E, and gs) in all cultivars by raising tissue concentrations of Na+ and Cl−. In addition to reducing the concentration of nitrate (77.21%), NaCl salt stress increased the concentrations of key bioactive molecules, notably carotenoids (lutein and β-carotene), phenolic acids, and flavonoid derivatives, thus resulting in a higher antioxidant activity of salt-treated basil plants compared to the untreated ones. Analysis by UHPLC revealed that cichoric acid was the most abundant polyphenolic compound in all basil cultivars, with the highest values recorded in ‘Cinnamon’

CRTC1â MAML2 fusion in mucoepidermoid carcinoma of the breast

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147797/1/his13779_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147797/2/his13779.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147797/3/his13779-sup-0001-TableS1.pd

Direct targets of Klf5 transcription factor contribute to the maintenance of mouse embryonic stem cell undifferentiated state

<p>Abstract</p> <p>Background</p> <p>A growing body of evidence has shown that Krüppel-like transcription factors play a crucial role in maintaining embryonic stem cell (ESC) pluripotency and in governing ESC fate decisions. Krüppel-like factor 5 (Klf5) appears to play a critical role in these processes, but detailed knowledge of the molecular mechanisms of this function is still not completely addressed.</p> <p>Results</p> <p>By combining genome-wide chromatin immunoprecipitation and microarray analysis, we have identified 161 putative primary targets of Klf5 in ESCs. We address three main points: (1) the relevance of the pathways governed by Klf5, demonstrating that suppression or constitutive expression of single Klf5 targets robustly affect the ESC undifferentiated phenotype; (2) the specificity of Klf5 compared to factors belonging to the same family, demonstrating that many Klf5 targets are not regulated by Klf2 and Klf4; and (3) the specificity of Klf5 function in ESCs, demonstrated by the significant differences between Klf5 targets in ESCs compared to adult cells, such as keratinocytes.</p> <p>Conclusions</p> <p>Taken together, these results, through the definition of a detailed list of Klf5 transcriptional targets in mouse ESCs, support the important and specific functional role of Klf5 in the maintenance of the undifferentiated ESC phenotype.</p> <p>See: <url>http://www.biomedcental.com/1741-7007/8/125</url></p

Combined effect of rheology and confining boundaries on spreading of gravity currents in porous media

One-dimensional flows of gravity currents within horizontal and inclined porous channels are investigated combining theoretical and experimental analysis to evaluate the joint effects of channel shape and fluid rheology. The parameter b governs the shape of the channel cross section, while the fluid rheology is characterised by a power-law model with behaviour index n. Self-similar scalings for current length and height are obtained for horizontal and inclined channels when the current volume increases with time as t^alpha. For horizontal channels, the interplay of model parameters a; n, and b governs the front speed, height, and aspect ratio of the current (ratio between the average height and the length). The dependency is modulated by two critical values of a; ab ¼ n=ðn þ 1Þ and an ¼ ð2b þ 1Þ=b. For all channel shapes, ab discriminates between currents whose height decreases (a < ab) or increases (a > ab) with time at a particular point. For all power-law fluids, an discriminates between decelerated currents, with timedecreasing aspect ratio (a < an), and accelerated currents, with time-increasing aspect ratio (a > an). Only currents with time-decreasing height (a < ab) and aspect ratio (a < an) respect model assumptions asymptotically; the former constraint is more restrictive than the latter. For inclined channels, a numerical solution in self-similar form is obtained under the hypothesis that the product of the channel inclination h and the slope of the free-surface is much smaller than unity; this produces a negligible error for h > 2 , and is acceptable for h > 0:5 . The action of gravity in inclined channels is modulated by both the behaviour index n and the shape factor b. For constant flux, the current reaches at long times a steady state condition with a uniform thickness profile. In steep channels and for sufficiently long currents, the free-surface slope becomes entirely negligible with respect to channel inclination, and the constant thickness profile depends only on n. Theoretical results are validated by comparison with experiments (i) in horizontal and inclined channels with triangular or semicircular cross-section, (ii) with different shear-thinning fluids, and (iii) for constant volume and constant flux conditions. The experimental results show good agreement with theoretical predictions in the long-time regime. Our analysis demonstrates that self-similar solutions are able to capture the essential long-term behaviour of gravity currents in porous media, accounting for diverse effects such as non-Newtonian rheology, presence of boundaries, and channel inclination. This provides a relatively simple framework for sensitivity analysis, and a convenient benchmark for numerical studies

Porous Gravity Currents of Non-Newtonian Fluids within Confining Boundaries

Motion of non-Newtonian gravity currents in horizontal impermeable channels filled with a porous material is investigated theoretically and experimentally. A constant or time-variable volume of fluid, characterized rheologically by the Ostwald-de Waele constitutive equation, is released from a point source into a channel of uniform cross-section, whose boundary height is described by a monomial relationship. The mathematical problem is formulated and solved at the Darcy scale coupling the local mass balance equation with a modified Darcy\u2019s law, taking into account the nonlinearity of the rheological equation. The resulting non-linear ODE is integrated numerically in the general case; for the release of a constant volume, a closed-form analytical solution is derived. Earlier results for Newtonian currents inside confining boundaries and power-law currents in two-dimensional geometry are generalized. The experiments were conducted in a transparent channel of semi-circular cross-section filled with uniform size glass ballotini. The position of the current front, recorded by a photo camera, was generally in a good agreement with the theory. The propagation of the current is described by L\propto t^F2 where F2 is a scalar depending on (i) the time exponent of the volume of fluid in the current, \u3b1, (ii) the geometry of the channel, parameterized by \u3b2 and (iii) the exponent n of the rheological equation. It is found that for a critical value \u3b1c = n/(n + 1), F2 is independent on the shape of the channel; for \u3b1 \u3b1c. Upon comparing results with free-surface viscous flow in open channels, it is found that: (i) the same expression for \u3b1c holds; (ii) the exponent F2 increases or decreases monotonically with \u3b2, while for the triangular section (\u3b2 = 1) in open channels, a maximum or minimum value of F2 is attained for \u3b1 \u3b1c, respectively

Gravity-driven flow of non-Newtonian fluids in heterogeneous porous media: a theoretical and experimental analysis

A theoretical and experimental analysis of non-Newtonian gravity-driven flow in porous media with spatially variable properties is presented. The motivation for our study is the rheological complexity exhibited by several environmental contaminants (wastewater sludge, oil pollutants, waste produced by the minerals and coal industries) and remediation agents (suspensions employed to enhance the efficiency of in-situ remediation). Natural porous media are inherently heterogeneous, and this heterogeneity influences the extent and shape of the porous domain invaded by the contaminant or remediation agent. To grasp the combined effect of rheology and spatial heterogeneity, we consider: a) the release of a thin current of non-Newtonian power-law fluid into a 2-D, semi-infinite and saturated porous medium above a horizontal bed; b) perfectly stratified media, with permeability and porosity varying along the direction transverse (vertical) or parallel (horizontal) to the flow direction. This continuous variation of spatial properties is described by two additional parameters. In order to represent several possible spreading scenarios, we consider: i) instantaneous injection with constant mass; ii) continuous injection with time-variable mass; iii) instantaneous release of a mound of fluid, which can drain freely out of the formation at the origin (dipole flow). Under these assumptions, scalings for current length and thickness are derived in self similar form. An analysis of the conditions on model parameters required to avoid an unphysical or asymptotically invalid result is presented. Theoretical results are validated against multiple sets of experiments, conducted for different combinations of spreading scenarios and types of stratification. Two basic setups are employed for the experiments: I) direct flow simulation in an artificial porous medium constructed superimposing layers of glass beads of different diameter; II) a Hele-Shaw (HS) analogue made of two parallel plates set at an angle. The HS analogy is extended to power-law fluid flow in porous media with variable properties parallel or transverse to the flow direction. Comparison with experimental results show that the proposed models capture the propagation of the current front and the current profile at intermediate and late time

Gravity-Driven Flow of non-Newtonian Fluids in Heterogeneous Porous Media: a Theoretical and Experimental Analysis

A theoretical and experimental analysis of non-Newtonian gravity-driven flow in porous media with spatially variable properties is presented. The motivation for our study is the rheological complexity exhibited by several environmental contaminants (wastewater sludge, oil pollutants, waste produced by the minerals and coal industries) and remediation agents (suspensions employed to enhance the efficiency of in-situ remediation). Natural porous media are inherently heterogeneous, and this heterogeneity influences the extent and shape of the porous domain invaded by the contaminant or remediation agent. To grasp the combined effect of rheology and spatial heterogeneity, we consider: a) the release of a thin current of non-Newtonian power-law fluid into a 2-D, semi-infinite and saturated porous medium above a horizontal bed; b) perfectly stratified media, with permeability and porosity varying along the direction transverse (vertical) or parallel (horizontal) to the flow direction. This continuous variation of spatial properties is described by two additional parameters. In order to represent several possible spreading scenarios, we consider: i) instantaneous injection with constant mass; ii) continuous injection with time-variable mass; iii) instantaneous release of a mound of fluid, which can drain freely out of the formation at the origin (dipole flow). Under these assumptions, scalings for current length and thickness are derived in self similar form. An analysis of the conditions on model parameters required to avoid an unphysical or asymptotically invalid result is presented. Theoretical results are validated against multiple sets of experiments, conducted for different combinations of spreading scenarios and types of stratification. Two basic setups are employed for the experiments: I) direct flow simulation in an artificial porous medium constructed superimposing layers of glass beads of different diameter; II) a Hele-Shaw (HS) analogue made of two parallel plates set at an angle. The HS analogy is extended to power-law fluid flow in porous media with variable properties parallel or transverse to the flow direction. Comparison with experimental results show that the proposed models capture the propagation of the current front and the current profile at intermediate and late time