Determination of the Effective Viscosity of Non-newtonian Fluids Flowing Through Porous Media

When non-Newtonian fluids flow through porous media, the topology of the pore space leads to a broad range of flow velocities and shear rates. Consequently, the local viscosity of the fluid also varies in space with a non-linear dependence on the Darcy velocity. Therefore, an effective viscosity μeff is usually used to describe the flow at the Darcy scale. For most non-Newtonian flows the rheology of the fluid can be described by a (non linear) function of the shear rate. Current approaches estimate the effective viscosity by first calculating an effective shear rate mainly by adopting a power-law model for the rheology and including an empirical correction factor. In a second step this averaged shear rate is used together with the real rheology of the fluid to calculate μeff. In this work, we derive a semi-analytical expression for the local viscosity profile using a Carreau type fluid, which is a more broadly applicable model than the power-law model. By solving the flow equations in a circular cross section of a capillary we are able to calculate the average viscous resistance 〈μ〉 directly as a spatial average of the local viscosity. This approach circumvents the use of classical capillary bundle models and allows to upscale the viscosity distribution in a pore with a mean pore size to the Darcy scale. Different from commonly used capillary bundle models, the presented approach does neither require tortuosity nor permeability as input parameters. Consequently, our model only uses the characteristic length scale of the porous media and does not require empirical coefficients. The comparison of the proposed model with flow cell experiments conducted in a packed bed of monodisperse spherical beads shows, that our approach performs well by only using the physical rheology of the fluid, the porosity and the estimated mean pore size, without the need to determine an effective shear rate. The good agreement of our model with flow experiments and existing models suggests that the mean viscosity 〈μ〉 is a good estimate for the effective Darcy viscosity μeff providing physical insight into upscaling of non-Newtonian flows in porous media

Violation of local realism with freedom of choice

Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's theorem is based on the assumptions of realism, locality, and the freedom to choose between measurement settings. In experimental tests, "loopholes" arise which allow observed violations to still be explained by local realistic theories. Violating Bell's inequality while simultaneously closing all such loopholes is one of the most significant still open challenges in fundamental physics today. In this paper, we present an experiment that violates Bell's inequality while simultaneously closing the locality loophole and addressing the freedom-of-choice loophole, also closing the latter within a reasonable set of assumptions. We also explain that the locality and freedom-of-choice loopholes can be closed only within non-determinism, i.e. in the context of stochastic local realism.Comment: 12 pages, 3 figures, 2 tables, published online before print: http://www.pnas.org/content/early/2010/10/29/1002780107.abstrac

Determination of the Effective Viscosity of Non-newtonian Fluids Flowing Through Porous Media

When non-Newtonian fluids flow through porous media, the topology of the pore space leads to a broad range of flow velocities and shear rates. Consequently, the local viscosity of the fluid also varies in space with a non-linear dependence on the Darcy velocity. Therefore, an effective viscosity μeff is usually used to describe the flow at the Darcy scale. For most non-Newtonian flows the rheology of the fluid can be described by a (non linear) function of the shear rate. Current approaches estimate the effective viscosity by first calculating an effective shear rate mainly by adopting a power-law model for the rheology and including an empirical correction factor. In a second step this averaged shear rate is used together with the real rheology of the fluid to calculate μeff. In this work, we derive a semi-analytical expression for the local viscosity profile using a Carreau type fluid, which is a more broadly applicable model than the power-law model. By solving the flow equations in a circular cross section of a capillary we are able to calculate the average viscous resistance ⟨μ⟩ directly as a spatial average of the local viscosity. This approach circumvents the use of classical capillary bundle models and allows to upscale the viscosity distribution in a pore with a mean pore size to the Darcy scale. Different from commonly used capillary bundle models, the presented approach does neither require tortuosity nor permeability as input parameters. Consequently, our model only uses the characteristic length scale of the porous media and does not require empirical coefficients. The comparison of the proposed model with flow cell experiments conducted in a packed bed of monodisperse spherical beads shows, that our approach performs well by only using the physical rheology of the fluid, the porosity and the estimated mean pore size, without the need to determine an effective shear rate. The good agreement of our model with flow experiments and existing models suggests that the mean viscosity ⟨μ⟩ is a good estimate for the effective Darcy viscosity μeff providing physical insight into upscaling of non-Newtonian flows in porous media

Mapping the local viscosity of non-Newtonian fluids flowing through disordered porous structures

Flow of non-Newtonian fluids through topologically complex structures is ubiquitous in most biological, industrial and environmental settings. The interplay between local hydrodynamics and the fluid’s constitutive law determines the distribution of flow paths. Consequently the spatial heterogeneity of the viscous resistance controls mass and solute transport from the micron to the meter scale. Examples range from oil recovery and groundwater engineering to drug delivery, filters and catalysts. Here we present a new methodology to map the spatial variation of the local viscosity of a non-Newtonian fluid flowing through a complex pore geometry. We use high resolution image velocimetry to determine local shear rates. Knowing the local shear rate in combination with a separate measurement of the fluid’s constitutive law allows to quantitatively map the local viscosity at the pore scale. Our experimental results—which closely match with three-dimensional numerical simulations—demonstrate that the exponential decay of the longitudinal velocity distributions, previously observed for Newtonian fluids, is a function of the spatial heterogeneity of the local viscosity. This work sheds light on the relationship between hydraulic properties and the viscosity at the pore scale, which is of fundamental importance for predicting transport properties, mixing, and chemical reactions in many porous systems.ISSN:2045-232

Development of predator defences in fishes

A variety of development characteristics, morphological, behavioural, and experiential, contribute to the extreme vulnerability of young fishes to predation. The influence of these characteristics is complicated by the fact that the larval period is one of substantial and rapid change. Yet survival is the ultimate goal;-it is only by reaching maturity that individual fish have the opportunity to reproduce. With such high stakes it is not surprising that predator defences are of major importance during all phases of life. Developmental constraints may limit the defensive options for young fishes. Avoidance behaviours, which reduce the likelihood of encountering a predator or of being attacked by it, are particulaly evident in the youngest stages. Here size, coloration and dispersal are used to help elude the predator's attention. As fishes grow and acquire greater morphological and behavioural sophistication, there is more scope for predator evasion when avoidance fails. Older fishes are increasingly able to respond to external stimuli and can detect and react to predators or join conspecifics in common defence (schooling). Behavioural development is not simply a consequence of growth and the concomitant physical alterations of the body; it is also mediated by experience that comes through interaction with the physical and biotic environment. Predispositions to respond to experience may be a product of evolutionary history. Although mortality rates decline markedly with development and maturity, changes in size or behaviour can render fishes vulnerable to new suites of predators. Effective predator avoidance can compromise other activities, such as foraging, and individuals may be forced to reconcile conflicting demands. Developmental niche shifts that occur, for example, when certain size classes take refuge in less profitable feeding habitats, represent one such trade-off. Niche shifts may also be mediated by the influence of the programme for morphological development on sensory or behavioural capabilities. In addition to all of these developmental consderations, natural variations in environmental conditions - such as temperature, photoperiod, predator density and variety, and presence of alternative prey - represent additional challenges to predator defences during the rite of passage from birth to reproduction.</p