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An experimental setup to investigate non-Newtonian fluid flow in variable aperture channels
Full text linkNon-Newtonian fluid flow in porous and fractured media is of considerable technical and environmental interest. Here, the flow of a non-Newtonian fluid in a variable aperture fracture is studied theoretically, experimentally and numerically. We consider a shear-thinning power-law fluid with flow behavior index n. The natural logarithm of the fracture aperture is a two-dimensional, spatially homogeneous and correlated Gaussian random field. An experimental device has been conceived and realized to allow the validation of the theory, and several tests are conducted with Newtonian and shear-thinning fluids and different combinations of parameters to validate the model. For Newtonian fluids, experimental results match quite well the theoretical predictions, mostly with a slight overestimation. For non-Newtonian fluids, the discrepancy between experiments and theory is larger, with an underestimation of the experimental flow rate. We bear in mind the high shear-rates involved in the experiments, covering a large range where simple models seldom are effective in reproducing the process, and possible interferences like slip at the wall. For all test conditions, the comparison between analytical and numerical model is fairly good
A Channel Model for Bi-viscous Fluid Flow in Fractures
No full textIn the last decade, the interest towards fluids characterized by a complex rheology has increased in the scientific community. Physicochemical, rheological and fluid mechanical approaches are adopted to characterize the peculiarities of non-Newtonian fluids. These fluids show remarkable properties that can be exploited to improve remediation techniques or optimize industrial operations. While the existence of actual yield stress is still debated, the presence of a plug or pseudo-plug zone is frequent in emulsions, soft glassy materials, jammed non-colloidal suspensions or colloidal gels. Even if simple yield stress models are often faulted because of their acknowledged deficiencies, they allow to study important phenomena without introducing excessive complexity. In this study, the randomness describing the aperture field of a natural rock fracture is coupled with a bi-viscous fluid rheology of parameter ε, representing the viscosity ratio; the cases ε= 0 and ε→ 1 represent the Bingham and Newtonian behaviour, respectively. The conceptual model proposed describes the flow of such fluids through a fracture with aperture variable along a single direction, the aperture being constant along the other. The aperture variation is modelled via a generic probability distribution function of assigned mean and variance. Two limit flow cases are considered: (1) parallel arrangement (PA), representing the case of maximum conductance, with the fluid flowing in the direction of channels of constant aperture; and (2) series arrangement (SA), the case of minimum conductance, with flow directed orthogonally to the constant aperture side of the fracture. Results are illustrated for log normal and gamma aperture distributions. The influence of aperture variability and applied pressure gradient on flow rate is investigated for both arrangements. The pressure gradient affects in a nonlinear fashion the flow rate, with a marked increase around a threshold value for both PA and SA. The channel flow rate exhibits a direct dependency upon aperture variability for PA, an inverse one for SA. The shape of the distribution has an impact on model responses: for the PA, the influence is significant but limited to an intermediate threshold range of pressure gradients, while results for the SA are affected in the whole range of pressure gradient. An example application in dimensional form is included
Collocation in the Mind: Investigating Collocational Priming in Second Language Speakers of Italian
No full textCollocational priming is a priming effect induced by collocationally related words; it has been taken to explain the cognitive reality of collocation. Collocational priming has largely been observed in first language (L1) speakers, whereas work on the representation of collocation in a second language (L2) is still limited. In the present study, we sought to investigate this phenomenon in L1 and L2 speakers of Italian. We used a lexical decision task to explore collocational priming in verb–noun and noun–adjective collocations differing in frequency and collocational strength. Both L1 and L2 speakers were found sensitive to the frequency of collocations. Importantly, exposure to L2 Italian was found to play a role. The results suggest that collocational priming occurs both in L1 and L2 speakers, and that the mechanisms associated with collocation processing and representation in L1 and L2 speakers may be comparable
Shear-thinning fluid flow in variable-aperture channels
Full text linkNon-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
Drainage of power-law fluids from fractured or porous finite domains
No full textWe develop a sharp-interface model that captures the coupled effect of spatial heterogeneity and fluid rheology on one-dimensional Newtonian and non-Newtonian buoyancy-driven flow spreading in fractured and porous media over a horizontal impermeable bed. We study the flow in three different geometries: (i) a constant uniform aperture, (ii) an aperture variable along the vertical axis, i.e. perpendicular to the direction of propagation and (iii) an aperture variable along the horizontal axis, i.e. parallel to the direction of propagation. The non-Newtonian rheology is described by the power-law equation of rheological index n and the aperture variation in both directions by a positive number r. The self-similar solutions of the flow obtained at late times allow the transformation of the nonlinear PDEs governing the spreading into nonlinear ODEs. The current shape is affected by the interplay between the rheological index and the spatial variability of the aperture. The residual liquid mass that remains in the fracture at any given time is computed from the current profiles, obtaining a negative power-law behavior in the time of exponent dependent on n and r. In addition, sensitivity analysis is performed to highlight the impact of the model parameters on the current profile and residual mass. The dimensionless analysis outcomes are compared to two real examples of flow within a uniform and a wedge-shaped aperture along the flow direction. The numerical results of the examples confirm that the proposed model can successfully capture the propagation of the gravity current, its profile, and drainage flow rate
Iterativity vs. habituality (and gnomic imperfectivity)
Full text linkfrom the introduction: Habituality, as commonly conceived, presupposes a more or less regular iteration
of an event, such that the resulting habit is regarded as a characterizing property of a
given referent. The notion of habituality is thus strictly related to iterativity, although
it should not be confused with it. In this paper we aim at defining the respective
features of habituality and iterativity and at placing them both in the framework of the
broader notion of “verbal pluractionality” on the one side, and of “gnomic
imperfectivity” on the other side
Effective Forchheimer Coefficient for Layered Porous Media
Full text linkInertial flow in porous media, governed by the Forchheimer equation, is affected by domain heterogeneity at the field scale. We propose a method to derive formulae of the effective Forchheimer coefficient with application to a perfectly stratified medium. Consider uniform flow under a constant pressure gradient Delta P/L in a layered permeability field with a given probability distribution. The local Forchheimer coefficient beta is related to the local permeability k via the relation beta = a/k(c), where a > 0 being a constant and c is an element of [0, 2]. Under ergodicity, an effective value of beta is derived for flow (i) perpendicular and (ii) parallel to layers. Expressions for effective Forchheimer coefficient, beta(e), generalize previous formulations for discrete permeability variations. Closed-form beta(e) expressions are derived for flow perpendicular to layers and under two limit cases, F << 1 and F >> 1, for flow parallel to layering, with F a Forchheimer number depending on the pressure gradient. For F of order unity, beta(e) is obtained numerically: when realistic values of Delta P/L and a are adopted, beta(e) approaches the results valid for the high Forchheimer approximation. Further, beta(e) increases with heterogeneity, with values always larger than those it would take if the beta - k relationship was applied to the mean permeability; it increases (decreases) with increasing (decreasing) exponent c for flow perpendicular (parallel) to layers. beta(e) is also moderately sensitive to the permeability distribution, and is larger for the gamma than for the lognormal distribution
Monte Carlo approach to assessing the influence of aperture variability on non-Newtonian fracture flow
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