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1
Shelukhin, V. V. "Bingham Viscoplastic as a Limit of Non-Newtonian Fluids." Journal of Mathematical Fluid Mechanics 4, no. 2 (2002): 109–27. http://dx.doi.org/10.1007/s00021-002-8538-7.
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Bhargava, R., H. S. Takhar, S. Rawat, Tasveer A. Bég, and O. Anwar Bég. "Finite Element Solutions for Non-Newtonian Pulsatile Flow in a Non-Darcian Porous Medium Conduit." Nonlinear Analysis: Modelling and Control 12, no. 3 (2007): 317–27. http://dx.doi.org/10.15388/na.2007.12.3.14690.
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The present analysis is motivated by the need to elucidate with more accuracy and sophistication the hydrodynamics of non-Newtonian flow via a channel containing a porous material under pulsating pressure gradient. A one-dimensional transient rheological model for pulsating flow through a Darcy-Forcheimmer porous channel is used. A modified Casson non-Newtonian constitutive model is employed for the transport fluid with a drag force formulation for the porous body force effects. The model is transformed and solved using a finite element numerical technique. Rheological effects are examined using a β parameter which vanishes in the limit (Newtonian flow). Velocity profiles are plotted for studying the influence of Reynolds number, Darcy number, Forchheimer number and the β (non-Newtonian) parameter. The channel considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. The model finds applications in industrial filtration systems, pumping of polymeric fluids etc.
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Kuhn, J. R. "Non-newtonian forces and the observed solar oscillation spectrum." Symposium - International Astronomical Union 123 (1988): 119. http://dx.doi.org/10.1017/s0074180900157882.
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Motivated by recent interest in the possibility of a long range gravitation-like force we have considered the effects a deviation from the Newtonian force law would have on the solar normal mode spectrum. Observations of low order and degree modes provide the most interesting limits to possible new physics. The constraint from solar oscillation observations is distinct from other planetary data in that it provides an integral bound on force law deviations on spatial scales between roughly 2×104 km and planetary scales. This limit is −0.02 ≤ δG/G ≤ 0.3 and is presently limited by systematic differences between the low-l observations and uncertainty in the solar model.
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COLOSQUI, CARLOS E., and VICTOR YAKHOT. "LATTICE BOLTZMANN SIMULATION OF A NON-NEWTONIAN OSCILLATING FLOW IN A HIGH-FREQUENCY LIMIT." International Journal of Modern Physics C 18, no. 04 (2007): 473–82. http://dx.doi.org/10.1142/s012918310701070x.
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The Lattice Boltzmann simulation of a flow generated by an oscillating plate is conducted in a wide range of frequency variation 0 < ωτ < ∞. The theoretically predicted transition from the viscoelastic (ωτ ≪ 1) Newtonian behavior to purely elastic non-Newtonian regime (ωτ ≫ 1) has been demonstrated. The relation of the derived solutions to microfluidics (high-frequency micro-resonators) is shown on an example of a "plane oscillator".
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Briscese, Fabio, and Francesco Calogero. "Isochronous solutions of Einstein’s equations and their Newtonian limit." International Journal of Geometric Methods in Modern Physics 15, no. 06 (2018): 1850101. http://dx.doi.org/10.1142/s0219887818501013.
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It has been recently demonstrated that it is possible to construct isochronous cosmologies, extending to general relativity a result valid for non-relativistic Hamiltonian systems. In this paper, we review these findings and we discuss the Newtonian limit of these isochronous spacetimes, showing that it reproduces the analogous findings in the context of non-relativistic dynamics.
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COLOSQUI, CARLOS E., and VICTOR YAKHOT. "ERRATUM: "LATTICE BOLTZMANN SIMULATION OF A NON-NEWTONIAN OSCILLATING FLOW IN A HIGH-FREQUENCY LIMIT"." International Journal of Modern Physics C 18, no. 05 (2007): 917. http://dx.doi.org/10.1142/s012918310701125x.
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The Lattice Boltzmann simulation of a flow generated by an oscillating plate is conducted in a wide range of frequency variation 0< ωτ < ∞. The theoretically predicted transition from the viscoelastic (ωτ ≪ 1) Newtonian behavior to purely elastic non-Newtonian regime (ωτ ≫ 1) has been demonstrated. The relation of the derived solutions to microfluidics (high-frequency micro-resonators) is shown on an example of a "plane oscillator".
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Underhill, Patrick T., Amir H. Hirsa, and Juan M. Lopez. "Modelling steady shear flows of Newtonian liquids with non-Newtonian interfaces." Journal of Fluid Mechanics 814 (January 31, 2017): 5–23. http://dx.doi.org/10.1017/jfm.2017.25.
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In countless biological and technological processes, the flow of Newtonian liquids with a non-Newtonian interface is a common occurrence, such as in monomolecular films in ‘solid’ phases atop of aqueous bulk fluid. There is a lack of models that can predict the flow under conditions different from those used to measure the rheological response of the interface. Here, we present a model which describes interfacial hydrodynamics, including two-way coupling to a bulk Newtonian fluid described by the Navier–Stokes equations, that allows for shear-thinning response of the interface. The model includes a constitutive equation for the interface under steady shear that takes the Newtonian functional form but where the surface shear viscosity is generalized to be a function of the local shear rate. In the limit of a highly viscous interface, the interfacial hydrodynamics is decoupled from the bulk flow and the model can be solved analytically. This provides not only insight into the flow but also a means to validate the numerical technique for solving the two-way coupled problem. The numerical results of the coupled problem shed new light on existing experimental results on steadily sheared monolayers of dipalmitoylphosphatidylcholine (DPPC), the primary constituent of lung surfactant and the bilayers of mammalian cell walls. For low packing density DPPC monolayers, a Newtonian shear-independent surface shear viscosity model can reproduce the interfacial flows, but at high packing density, the shear-thinning properties of the new model presented here are needed.
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BERGENHOLTZ, J., J. F. BRADY, and M. VICIC. "The non-Newtonian rheology of dilute colloidal suspensions." Journal of Fluid Mechanics 456 (April 9, 2002): 239–75. http://dx.doi.org/10.1017/s0022112001007583.
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The non-Newtonian rheology is calculated numerically to second order in the volume fraction in steady simple shear flows for Brownian hard spheres in the presence of hydrodynamic and excluded volume interactions. Previous analytical and numerical results for the low-shear structure and rheology are confirmed, demonstrating that the viscosity shear thins proportional to Pe2, where Pe is the dimensionless shear rate or Péclet number, owing to the decreasing contribution of Brownian forces to the viscosity. In the large Pe limit, remnants of Brownian diffusion balance convection in a boundary-layer in the compressive region of the flow. In consequence, the viscosity shear thickens when this boundary-layer coincides with the near-contact lubrication regime of the hydrodynamic interaction. Wakes are formed at large Pe in the extensional zone downstream from the reference particle, leading to broken symmetry in the pair correlation function. As a result of this asymmetry and that in the boundary-layer, finite normal stress differences are obtained as well as positive departures in the generalized osmotic pressure from its equilibrium value. The first normal stress difference changes from positive to negative values as Pe is increased when the hard-sphere limit is approached. This unusual effect is caused by the hydrodynamic lubrication forces that maintain particles in close proximity well into the extensional quadrant of the flow. The study demonstrates that many of the non-Newtonian effects observed in concentrated suspensions by experiments and by Stokesian dynamics simulations are present also in dilute suspensions.
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Sac-Épée, J. M., and K. Taous. "On a wide class of nonlinear models for non-Newtonian fluids with mixed boundary conditions in thin domains." Asymptotic Analysis 44, no. 1-2 (2005): 151–71. https://doi.org/10.3233/asy-2005-706.
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The behaviour of Newtonian and non-Newtonian flows through a thin three-dimensional domain are widely studied in the literature. Usually, authors deal with special models related to particular concrete fluids. In this work, our aim is to present a general model, governing the behaviour of a large class of Newtonian and non-Newtonian fluids. Moreover, we deal with mixed boundary conditions, which are not often studied in the literature related to flows in thin domains. We consider a nonlinear model of a flow in a thin three-dimensional domain, and we study its behaviour when the thickness in one direction tends to zero. At the limit, we obtain a quasilinear two-dimensional problem for the pressure, a nonlinear Reynolds's law for the velocity and a nonlinear Darcy's law for the averaged velocity. Finally, we check that our results hold for a large class of non-Newtonian fluids by producing concrete examples.
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Fröhlich, Jürg, Tai-Peng Tsai, and Horng-Tzer Yau. "On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation." Communications in Mathematical Physics 225, no. 2 (2002): 223–74. http://dx.doi.org/10.1007/s002200100579.
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Cadoni, Mariano, and Marcello Casula. "General models of Einstein gravity with a non-Newtonian weak-field limit." General Relativity and Gravitation 42, no. 1 (2009): 103–12. http://dx.doi.org/10.1007/s10714-009-0820-z.
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Niedermaier, Max. "Nonstandard Action of Diffeomorphisms and Gravity’s Anti-Newtonian Limit." Symmetry 12, no. 5 (2020): 752. http://dx.doi.org/10.3390/sym12050752.
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A tensor calculus adapted to the Anti-Newtonian limit of Einstein gravity is developed. The limit is defined in terms of a global conformal rescaling of the spatial metric. This enhances spacelike distances compared to timelike ones and in the limit effectively squeezes the lightcones to lines. Conventional tensors admit an analogous Anti-Newtonian limit, which however transforms according to a non-standard realization of the spacetime Diffeomorphism group. In addition to the type of the tensor the transformation law depends on, a set of integer-valued weights is needed to ensure the existence of a nontrivial limit. Examples are limiting counterparts of the metric, Einstein, and Riemann tensors. An adapted purely temporal notion of parallel transport is presented. By introducing a generalized Ehresmann connection and an associated orthonormal frame compatible with an invertible Carroll metric, the weight-dependent transformation laws can be mapped into a universal one that can be read off from the index structure. Utilizing this ‘decoupling map’ and a realization of the generalized Ehresmann connection in terms of scalar field, the limiting gravity theory can be endowed with an intrinsic Levi–Civita type notion of spatio-temporal parallel transport.
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Jeyasountharan, Anoshanth, and Francesco Del Giudice. "Viscoelastic Particle Encapsulation Using a Hyaluronic Acid Solution in a T-Junction Microfluidic Device." Micromachines 14, no. 3 (2023): 563. http://dx.doi.org/10.3390/mi14030563.
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The encapsulation of particles and cells in droplets is highly relevant in biomedical engineering as well as in material science. So far, however, the majority of the studies in this area have focused on the encapsulation of particles or cells suspended in Newtonian liquids. We here studied the particle encapsulation phenomenon in a T-junction microfluidic device, using a non-Newtonian viscoelastic hyaluronic acid solution in phosphate buffer saline as suspending liquid for the particles. We first studied the non-Newtonian droplet formation mechanism, finding that the data for the normalised droplet length scaled as the Newtonian ones. We then performed viscoelastic encapsulation experiments, where we exploited the fact that particles self-assembled in equally-spaced structures before approaching the encapsulation area, to then identify some experimental conditions for which the single encapsulation efficiency was larger than the stochastic limit predicted by the Poisson statistics.
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Achour, Lila, Mathieu Specklin, Miguel Asuaje, Smaine Kouidri, and Idir Belaidi. "Energy loss analysis of volute centrifugal pump handling non-Newtonian emulsions through entropy production theory." Mechanics & Industry 25 (2024): 13. http://dx.doi.org/10.1051/meca/2024009.
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Flow losses in centrifugal pumps handling non-Newtonian fluids are of great importance for design optimization, performance prediction, and energy savings. Traditional methods are very limited in determining energy losses due to the complex rheological behavior of such fluids. This study aims to investigate the hydraulic losses and performance degradation mechanism of centrifugal volute pumps handling non-Newtonian emulsions using the entropy production method, focusing on the influence of emulsion type on the loss mechanism. The influence of pump size on fluid’s non-Newtonian behavior and energy loss in a centrifugal pump is also investigated by comparing the entropy distribution in two geometrically similar pumps operating with different emulsions exhibiting shear-thinning behavior. The flow field and entropy production are predicted by computational fluid dynamics (CFD) based on the Reynolds-averaged Navier-Stokes (RANS) equations coupled with the k-epsilon turbulence model. The latter is used to acquire the dissipative entropic components of the flow. The results showed that for a non-Newtonian fluid, energy loss occurs primarily in the impeller, regardless of pump size and flow rate. In addition, the shear-thinning behavior of concentrated emulsions significantly affects hydraulic losses, especially in small-size pumps. Most importantly, small-size pumps generate relatively the highest entropy loss over the entire flow range and the entropy loss increases with the lower limit of the non-Newtonian plateau. This approach showed that the predominance of losses in centrifugal volute pumps operating with non-Newtonian fluids depends on the pump size. Thus, indicating that the hydrodynamic characteristics of two geometrically similar pumps do not scale when the liquid has non-Newtonian rheology.
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Mai, La-Su, Hai-Liang Li, and Pierangelo Marcati. "Non-relativistic limit analysis of the Chandrasekhar–Thorne relativistic Euler equations with physical vacuum." Mathematical Models and Methods in Applied Sciences 29, no. 03 (2019): 531–79. http://dx.doi.org/10.1142/s0218202519500155.
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Our results provide a first step to make the formal analysis rigorous in terms of [Formula: see text] proposed by Chandrasekhar [S. Chandrasekhar, The post-Newtonian equations of hydrodynamics in general relativity, Astrophys. J. 142 (1965) 1488–1512; S. Chandrasekhar, post-Newtonian equations of hydrodynamics and the stability of gaseous masses in general relativity, Phys. Rev. Lett. 14 (1965) 241–244], motivated by the methods of Einstein, Infeld and Hoffmann, see Thorne [K. S. Thorne, The general-relativistic theory of stellar structure and dynamics, in Proc. Int. School of Physics “Enrico Fermi,” Course XXXV, at Varenna, Italy, July 12–24, 1965, ed. L. Gratton (Academic Press, 1966), pp. 166–280]. We consider the non-relativistic limit for the local smooth solutions to the free boundary value problem of the cylindrically symmetric relativistic Euler equations when the mass energy density includes the vacuum states at the free boundary. For large enough (rescaled) speed of light [Formula: see text] and suitably small time [Formula: see text] we obtain uniform, with respect to [Formula: see text] “a priori” estimates for the local smooth solutions. Moreover, the smooth solutions of the cylindrically symmetric relativistic Euler equations converge to the solutions of the classical compressible Euler equation at the rate of order [Formula: see text].
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Kun, Emma, Zoltán Keresztes, Saurya Das, and László Á. Gergely. "Dark Matter as a Non-Relativistic Bose–Einstein Condensate with Massive Gravitons." Symmetry 10, no. 10 (2018): 520. http://dx.doi.org/10.3390/sym10100520.
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We confront a non-relativistic Bose–Einstein Condensate (BEC) model of light bosons interacting gravitationally either through a Newtonian or a Yukawa potential with the observed rotational curves of 12 dwarf galaxies. The baryonic component is modeled as an axisymmetric exponential disk and its characteristics are derived from the surface luminosity profile of the galaxies. The purely baryonic fit is unsatisfactory, hence a dark matter component is clearly needed. The rotational curves of five galaxies could be explained with high confidence level by the BEC model. For these galaxies, we derive: (i) upper limits for the allowed graviton mass; and (ii) constraints on a velocity-type and a density-type quantity characterizing the BEC, both being expressed in terms of the BEC particle mass, scattering length and chemical potential. The upper limit for the graviton mass is of the order of 10 - 26 eV/c2, three orders of magnitude stronger than the limit derived from recent gravitational wave detections.
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Anguiano, María, Matthieu Bonnivard, and Francisco J. Suárez-Grau. "Carreau law for non-newtonian fluid flow through a thin porous media." Quarterly Journal of Mechanics and Applied Mathematics 75, no. 1 (2022): 1–27. http://dx.doi.org/10.1093/qjmam/hbac004.
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Summary We consider the flow of generalized Newtonian fluid through a thin porous media. The media under consideration is a bounded perforated three dimensional domain confined between two parallel plates, where the distance between the plates is described by a small parameter $\varepsilon$. The perforation consists in an array of solid cylinders, which connect the plates in perpendicular direction, with diameter of size $\varepsilon$ and distributed periodically with period $\varepsilon$. The flow is described by the three dimensional incompressible stationary Stokes system with a nonlinear viscosity following the Carreau law. We study the limit when the thickness tends to zero and prove that the averaged velocity satisfies a nonlinear two-dimensional homogenized law of Carreau type. We illustrate our homogenization result by numerical simulations showing the influence of the Carreau law on the behavior of the limit system, in the case where the flow is driven by a constant pressure gradient and for different geometries of perforations.
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Harikumar, E., Leela Ganesh Chandra Lakkaraju, and Vishnu Rajagopal. "Emergence of maximal acceleration from non-commutativity of spacetime." Modern Physics Letters A 36, no. 10 (2021): 2150069. http://dx.doi.org/10.1142/s0217732321500693.
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In this paper, we show that the causally connected four-dimensional line element of the [Formula: see text]-deformed Minkowski spacetime induces an upper cut-off on the proper acceleration and derive this maximal acceleration, valid up to first order in the deformation parameter. We find a contribution to maximal acceleration which is independent of [Formula: see text] and thus signals effect of the non-commutativity alone. We also construct the [Formula: see text]-deformed geodesic equation and obtain its [Formula: see text]-deformed Newtonian limit, valid up to first order in deformation parameter. Using this, we constrain non-commutative parameters present in the expression for maximal acceleration. We analyze different limits of the maximal acceleration and also discuss its implication to maximal temperature. We also obtain a bound on the deformation parameter.
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Buckholz, R. H. "On The Role of a Non-Newtonian Fluid in Short Bearing Theory." Journal of Tribology 107, no. 1 (1985): 68–74. http://dx.doi.org/10.1115/1.3261004.
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The importance of rheological properties of lubricants has arisen from the realization that non-Newtonian fluid effects are manifested over a broad range of lubrication applications. In this paper a theoretical investigation of short journal bearings performance characteristics for non-Newtonian power-law lubricants is given. A modified form of the Reynolds’ equation for hydrodynamic lubrication is studied in the asymptotic limit of small slenderness ratio (i.e., bearing length to diameter, L/D = λ→0). Fluid film pressure distributions in short bearings of arbitrary azimuthal length are studied using matched asymptotic expansions in the slenderness ratio. The merit of the short bearing approach used in solving a modified Reynolds’ equation by the method of matched asymptotic expansions is emphasized. Fluid film pressure distributions are determined without recourse to numerical solutions to a modified Reynolds’ equation. Power-law rheological exponents less than and equal to one are considered; power-law fluids exhibit reduced load capacities relative to the Newtonian fluid. The cavitation boundary shape is determined from Reynolds’ free surface condition; and the boundary shape is shown to be independent of the bearing eccentricity ratio.
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Arif, Mohammad, Saurabh Kango, and Dinesh Kumar Shukla. "Effect of slip boundary condition and non-newtonian rheology of lubricants on the dynamic characteristics of finite hydrodynamic journal bearing." Surface Topography: Metrology and Properties 10, no. 1 (2022): 015002. http://dx.doi.org/10.1088/2051-672x/ac4403.
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Abstract In the present study, the influence of various slip zone locations on the dynamic stability of finite hydrodynamic journal bearing lubricated with non-Newtonian and Newtonian lubricants has been investigated. Linearized equation of motion with free vibration of rigid rotor has been used to find the optimum location of the slip region with maximum stability margin limit. It has been observed that bearing with interface of slip and no-slip region near the upstream side of minimum film-thickness location is effective in improving the direct and cross stiffness coefficient, critical mass parameter, and critical whirling speed. The magnitude of dynamic performance parameters with slip effect is highly dependent on the rheology of lubricant. Shear-thinning lubricants combined with slip boundary condition shows higher dynamic stability as compared to the Newtonian lubricants under the conventional boundary condition. For all considered rheology of lubricants, the dynamic stability of bearing with slip effect is improving by increasing the eccentricity ratio.
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Cadoni, M. "Letter: An Einstein-Like Theory of Gravity with a Non-Newtonian Weak-Field Limit." General Relativity and Gravitation 36, no. 12 (2004): 2681–88. http://dx.doi.org/10.1023/b:gerg.0000048982.05514.18.
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Conry, T. F., S. Wang, and C. Cusano. "A Reynolds-Eyring Equation for Elastohydrodynamic Lubrication in Line Contacts." Journal of Tribology 109, no. 4 (1987): 648–54. http://dx.doi.org/10.1115/1.3261526.
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A new Reynolds equation, based on the Eyring theory of non-Newtonian flow, is derived for flow in one dimension. It is shown that this new equation reduces to the traditional Reynolds equation as the Eyring model approaches the Newtonian model in the limit. Numerical solutions are presented for a selected oil at two different temperatures. The central film thickness decreases with increasing dimensionless viscosity parameter and slide/roll ratios. A transition zone is noted through which the ratio of minimum to central film thickness passes as the pressure distribution goes from near Hertzian to a distribution that appreciably deviates from Hertzian.
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Rousset, F., S. Millet, V. Botton, and H. Ben Hadid. "Temporal Stability of Carreau Fluid Flow Down an Incline." Journal of Fluids Engineering 129, no. 7 (2007): 913–20. http://dx.doi.org/10.1115/1.2742737.
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This paper deals with the temporal stability of a Carreau fluid flow down an inclined plane. As a first step, a weakly non-Newtonian behavior is considered in the limit of very long waves. It is found that the critical Reynolds number is lower for shear-thinning fluids than for Newtonian fluids, while the celerity is larger. In a second step, the general case is studied numerically. Particular attention is paid to small angles of inclination for which either surface or shear modes can arise. It is shown that shear dependency can change the nature of instability.
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CARRASCO-TEJA, M., and I. A. FRIGAARD. "Non-Newtonian fluid displacements in horizontal narrow eccentric annuli: effects of slow motion of the inner cylinder." Journal of Fluid Mechanics 653 (June 2, 2010): 137–73. http://dx.doi.org/10.1017/s0022112010000212.
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We study non-Newtonian fluid displacements in horizontal narrow eccentric annuli in the situation where the inner cylinder is moving. This represents a practically important extension of the model analysed by Carrasco-Teja et al. (J. Fluid Mech., vol. 605, 2008, pp. 293–327). When motion of the inner cylinder is included, the Hele-Shaw model closure becomes significantly more complex and extremely costly to compute, except for Newtonian fluids. In the first part of the paper we address the model derivation and closure relations. The second part of the paper considers the limit of large buoyancy number, in which the interface elongates along the annulus. We derive a lubrication-style model for this situation, showing that the leading-order interface is symmetric. Rotation of the inner cylinder only affects the length of the leading-order interface, and this occurs only for non-Newtonian fluids via shear-thinning effects. At first order, casing rotation manifests in an asymmetrical ‘shift’ of the interface in the direction of the rotation. We also derive conditions on the eccentricity, fluid rheology and inner cylinder velocity, under which we are able to find steady travelling wave displacement solutions.
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Chakrabarty, Sankha Subhra, Luisa Ostorero, Arianna Gallo, Stefano Ebagezio, and Antonaldo Diaferio. "Probing modified Newtonian dynamics with hypervelocity stars." Astronomy & Astrophysics 657 (January 2022): A115. http://dx.doi.org/10.1051/0004-6361/202141136.
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We show that measuring the velocity components of hypervelocity stars (HVSs) can discriminate between modified Newtonian dynamics (MOND) and Newtonian gravity. Hypervelocity stars are ejected from the Galactic center on radial trajectories with a null tangential velocity component in the reference frame of the Galaxy. They acquire tangential components due to the nonspherical components of the Galactic gravitational potential. Axisymmetric potentials only affect the latitudinal components, vθ, and non-null azimuthal components, vϕ, originate from non-axisymmetric matter distributions. For HVSs with sufficiently high ejection speed, the azimuthal velocity components are proportionate to the deviation of the gravitational potential from axial symmetry. The ejection velocity threshold is ∼750 km s−1 for 4 M⊙ stars and increases with decreasing HVS mass. We determine the upper limit of vϕ as a function of the galactocentric distance for these high-speed HVSs if MOND, in its quasi-linear formulation QUMOND, is the correct theory of gravity and either the triaxial Galactic bulge or a nonspherical hot gaseous halo is the primary source of the azimuthal component, vϕ. In Newtonian gravity, the HVSs within 60 kpc of the Galactic center may easily have vϕ values higher than the QUMOND upper limit if the dark matter halo is triaxial or if the dark matter halo and the baryonic components are axisymmetric but their two axes of symmetry are misaligned. Therefore, even a limited sample of high-speed HVSs could in principle allow us to distinguish between the QUMOND scenario and the dark matter model. This test is currently limited by (i) the lack of a proper procedure to assess whether a star originates from the Galactic center and thus is indeed an HVS in the model one wishes to constrain; and (ii) the large uncertainties on the galactocentric azimuthal velocity components, which should be reduced by at least a factor of ∼10 to make this test conclusive. A proper procedure to assess the HVS nature of the observed stars and astrometric measurements with microarcsecond precision would make this test feasible.
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Panasenko, Grigory, Konstantin Pileckas, and Bogdan Vernescu. "Steady state non-Newtonian flow with strain rate dependent viscosity in domains with cylindrical outlets to infinity." Nonlinear Analysis: Modelling and Control 26, no. 6 (2021): 1166–99. http://dx.doi.org/10.15388/namc.2021.26.24600.
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The paper deals with a stationary non-Newtonian flow of a viscous fluid in unbounded domains with cylindrical outlets to infinity. The viscosity is assumed to be smoothly dependent on the gradient of the velocity. Applying the generalized Banach fixed point theorem, we prove the existence, uniqueness and high order regularity of solutions stabilizing in the outlets to the prescribed quasi-Poiseuille flows. Varying the limit quasi-Poiseuille flows, we prove the stability of the solution.
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Zvyagin, V. G., and V. P. Orlov. "THE PROBLEM OF THE FLOW OF ONE TYPE OF NON-NEWTONIAN FLUID THROUGH THE BOUNDARY OF A MULTI-CONNECTED DOMAIN." Доклады Российской академии наук. Математика, информатика, процессы управления 510, no. 1 (2023): 33–38. http://dx.doi.org/10.31857/s2686954323600064.
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In this paper, the existence of a weak solution of the initial boundary value problem for the equations of motion of a viscoelastic non-newtonian fluid in a multi-connected domain with memory along the trajectories of a non-smooth velocity field and an inhomogeneous boundary condition. The study assumes the approximation of the original problem by Galerkin-type approximations followed by a passage to the limit based on a priori estimates. The theory of regular Lagrangian flows is used to study the behavior of trajectories of a non-smooth velocity field.
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ANGUIANO, MARÍA. "Homogenization of a non-stationary non-Newtonian flow in a porous medium containing a thin fissure." European Journal of Applied Mathematics 30, no. 2 (2018): 248–77. http://dx.doi.org/10.1017/s0956792518000049.
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We consider a non-stationary incompressible non-Newtonian Stokes system in a porous medium with characteristic size of the pores ϵ and containing a thin fissure of width ηϵ. The viscosity is supposed to obey the power law with flow index$\frac{5}{3}\leq q\leq 2$. The limit when size of the pores tends to zero gives the homogenized behaviour of the flow. We obtain three different models depending on the magnitude ηϵwith respect to ϵ: if ηϵ≪$\varepsilon^{q\over 2q-1}$the homogenized fluid flow is governed by a time-dependent non-linear Darcy law, while if ηϵ≫$\varepsilon^{q\over 2q-1}$is governed by a time-dependent non-linear Reynolds problem. In the critical case, ηϵ≈$\varepsilon^{q\over 2q-1}$, the flow is described by a time-dependent non-linear Darcy law coupled with a time-dependent non-linear Reynolds problem.
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Fang, Li, and Zhenhua Guo. "Zero dissipation limit to rarefaction wave with vacuum for a one-dimensional compressible non-Newtonian fluid." Communications on Pure & Applied Analysis 16, no. 1 (2017): 209–42. http://dx.doi.org/10.3934/cpaa.2017010.
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Guo, Zhenhua, Yifan Su, and Jinjing Liu. "The existence and limit behavior of the shock layer for 1D stationary compressible non-Newtonian fluids." Communications in Mathematical Sciences 21, no. 1 (2023): 239–53. http://dx.doi.org/10.4310/cms.2023.v21.n1.a11.
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Banik, Indranil, and Pavel Kroupa. "Solar System limits on gravitational dipoles." Monthly Notices of the Royal Astronomical Society 495, no. 4 (2020): 3974–80. http://dx.doi.org/10.1093/mnras/staa1447.
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ABSTRACT The gravitational dipole theory of Hadjukovic (2010) is based on the hypothesis that antimatter has a negative gravitational mass and thus falls upwards on the Earth. Astrophysically, the model is similar to but more fundamental than Modified Newtonian Dynamics (MOND), with the Newtonian gravity $g_{_\mathrm{ N}}$ towards an isolated point mass boosted by the factor $\nu = 1 + \left(\alpha /x \right) \tanh \left(\sqrt{x}/\alpha \right)$, where $x \equiv g_{_\mathrm{ N}}/a_{_0}$ and $a_{_0} = 1.2 \times 10^{-10}$ m s−2 is the MOND acceleration constant. We show that α must lie in the range 0.4–1 to acceptably fit galaxy rotation curves. In the Solar System, this interpolating function implies an extra Sunwards acceleration of ${\alpha a_{_0}}$. This would cause Saturn to deviate from Newtonian expectations by 7000(α/0.4) km over 15 yr, starting from known initial position and velocity on a near-circular orbit. We demonstrate that this prediction should not be significantly altered by the postulated dipole haloes of other planets due to the rather small region in which each planet’s gravity dominates over that of the Sun. The orbit of Saturn should similarly be little affected by a possible ninth planet in the outer Solar System and by the Galactic gravity causing a non-spherical distribution of gravitational dipoles several kAU from the Sun. Radio tracking of the Cassini spacecraft orbiting Saturn yields a 5σ upper limit of 160 m on deviations from its conventionally calculated trajectory. These measurements imply a much more stringent upper limit on α than the minimum required for consistency with rotation curve data. Therefore, no value of α can simultaneously match all available constraints, falsifying the gravitational dipole theory in its current form at extremely high significance.
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Taghavi, S. M. "A two-layer model for buoyant displacement flows in a channel with wall slip." Journal of Fluid Mechanics 852 (August 10, 2018): 602–40. http://dx.doi.org/10.1017/jfm.2018.555.
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We study theoretically buoyant displacement flows of two generalized Newtonian fluids in a two-dimensional (2-D) channel with wall slip. We assume that a pseudo-interface separates two miscible (immiscible) fluids at the limit of negligible molecular diffusion (negligible surface tension). A heavy fluid displaces a light fluid at near-horizontal channel inclinations, implying that a stratified flow assumption is relevant. We develop a classical lubrication approximation model as a semi-analytical framework that includes a number of dimensionless parameters, such as a buoyancy number, the viscosity ratio, the non-Newtonian properties and the upper and lower wall slip coefficients. For specified interface heights and slopes, the reduced model can furnish the flux and velocity functions in displacing and displaced phases. We numerically solve the interface kinematic condition for four different wall slip cases: no slip (Case I), slip at the lower wall (Case II), slip at the upper wall (Case III) and slip at both walls (Case IV). The solutions for these cases deliver the interface propagation in time, for which leading and trailing displacement front heights, shapes and speeds and several key displacement features, such as front characteristic spreading lengths and short time behaviours, can be directly predicted by simplified analyses. The results reveal in detail how the presence of a channel wall slip may significantly affect the overall displacement flow and the interface evolution characteristics, for both Newtonian and non-Newtonian fluids. Regarding the latter, our analysis quantifies in particular the appearance and removal of static residual wall layers of the displaced phase, versus the wall slip cases.
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El‐Khatib, F. H., and E. R. Damiano. "Linear and nonlinear analyses of pulsatile blood flow in a cylindrical tube." Biorheology: The Official Journal of the International Society of Biorheology 40, no. 5 (2003): 503–22. http://dx.doi.org/10.1177/0006355x2003040005003.
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A non‐Newtonian shear‐thinning constitutive relation is proposed to study pulsatile flow of whole blood in a cylindrical tube. The constitutive relation, which satisfies the principle of material frame indifference, is derived from viscometric data obtained from whole blood over a range of hematocrits. Assuming axisymmetric flow in a rigid cylindrical tube of constant diameter, a second‐order, nonlinear partial differential equation governing the axial velocity component is obtained. Imposing a periodic pressure gradient, the governing equation was solved numerically using finite difference methods over a range of Stokes values and hematocrits. For a forcing frequency of 1 Hz, results are presented over tube diameters ranging between 0.1 and 2 cm and over hematocrits ranging between 10 and 80%. For a given hematocrit, velocity profiles predicted for the non‐Newtonian model under sinusoidal forcing reveal attenuated volume flow rate and enhanced vorticity transport over the tube cross‐section relative to a Newtonian fluid having a viscosity corresponding to the high shear‐rate limit. For moderate to high Stokes numbers, consistent with flow in large arteries, our results revealed a viscosity distribution that was nearly time invariant. An analytic solution was obtained for a fluid having arbitrarily prescribed radially varying, temporally invariant viscosity and density distributions under arbitrary periodic pressure forcing. Close agreement was observed between our numerical and analytical results when the imposed viscosity distribution was chosen to approximate the time‐averaged viscosity distribution predicted by the shear‐thinning non‐Newtonian model. For $\mathit{St}\gtrsim 100$ , the disparity between our results and those of a Newtonian fluid of constant viscosity grows with a decreasing ratio of the DC to AC components of the pressure‐gradient amplitude below 50%. In particular, for any purely oscillatory pressure‐gradient (vanishing DC component), the Womersley solution is a particularly poor predictor of the amplitude and phase of wall shear rate for over half of the flow cycle. Under such circumstances, the analytical models presented here provide a simple and accurate means of estimating instantaneous wall shear rate, knowing only the pressure gradient and hematocrit.
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Laborie, Benoît, Florence Rouyer, Dan E. Angelescu, and Elise Lorenceau. "Yield-stress fluid deposition in circular channels." Journal of Fluid Mechanics 818 (April 6, 2017): 838–51. http://dx.doi.org/10.1017/jfm.2017.161.
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Since the pioneering works of Taylor and Bretherton, the thickness $h$ of the film deposited behind a long bubble invading a Newtonian fluid is known to increase with the capillary number power $2/3$ ($h\sim RCa^{2/3}$), where $R$ is the radius of the circular tube and $Ca$ is the capillary number, comparing the viscous and capillary effects. This law, known as Bretherton’s law, is valid only in the limit of $Ca<0.01$ and negligible inertia and gravity. We revisit this classical problem when the fluid is a yield-stress fluid (YSF) exhibiting both a yield stress and a shear-thinning behaviour. First, we provide quantitative measurement of the thickness of the deposited layer for Carbopol, a Herschel–Bulkley fluid, in the limit where the yield stress is of a similar order of magnitude to the capillary pressure and for $0.1<Ca<1$. To understand our observations, we use scaling arguments to extend the analytical expression of Bretherton’s law to YSFs in circular tubes. In the limit of $Ca<0.1$, our scaling law, in which the adjustable parameters are set using previous results concerning non-Newtonian fluids, successfully retrieves several features of the literature. First, it shows that (i) the thickness deposited behind a Bingham YSF (exhibiting a yield stress only) is larger than for a Newtonian fluid and (ii) the deposited layer increases with the amplitude of the yield stress. This is in quantitative agreement with previous numerical results concerning Bingham fluids. It also agrees with results concerning pure shear-thinning fluids in the absence of yield stress: the shear-thinning behaviour of the fluid reduces the deposited thickness as previously observed. Last, in the limit of vanishing velocity, our scaling law predicts that the thickness of the deposited YSF converges towards a finite value, which presumably depends on the microstructure of the YSF, in agreement with previous research on the topic performed in different geometries. For $0.1<Ca<1$, the scaling law fails to describe the data. In this limit, nonlinear effects must be taken into account.
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Comiti, J., N. E. Sabiri, and A. Montillet. "Experimental characterization of flow regimes in various porous media — III: limit of Darcy's or creeping flow regime for Newtonian and purely viscous non-Newtonian fluids." Chemical Engineering Science 55, no. 15 (2000): 3057–61. http://dx.doi.org/10.1016/s0009-2509(99)00556-4.
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Wójtowicz, Ryszard, Katarzyna Kocewiak, and Andrey A. Lipin. "IDENTIFICATION OF RHEOLOGICAL PROPERTIES OF POLY(ETHYLENE OXIDE) – WATER SOLUTIONS." IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII KHIMIYA KHIMICHESKAYA TEKHNOLOGIYA 63, no. 9 (2020): 82–87. http://dx.doi.org/10.6060/ivkkt.20206309.6236.
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In the paper results of investigations of rheological properties for selected PEO-water solutions are presented. On the basis of measurements, carried out with use of rotational viscosimeter values of shear stresses were determined in the relatively wide range of shear rates. Rheological curves were described by the Ostwald de Waele model (or so-called power-law). The model coefficients such as the fluid consistency coefficient k and the flow behavior index n were determined using Levenberg−Marquardt algorithm for nonlinear estimation. The influence of temperature on properties and behavior examined non-Newtonian fluids was also determined. Results were processed in the curve shift parameter at. Experiments shown a significant effect of poly(ethylene oxide) concentration cPEO on rheological properties of examined solutions. For the lowest concentration (cPEO=1.2%) solutions exhibited properties similar to Newtonian fluids with values of n close to 1. With increasing of PEO concentration in water (cPEO=2.4-4.8%), solutions exhibited properties as non - Newtonian fluids, pseudoplastic, without yield limit. In these cases values of n were below unity and for the highest concentration (cPEO=4.8%) belonged to the range of n=0.5694-0.7536, depending on the temperature. Results of investigations can be used during numerical simulations, design and optimization of industrial equipment, working with fluids of this kind, including mixing vessels, columns or heat exchangers.
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YALÇIN, Numan, and Sinem KAYMAK. "On Bigeometric Laplace Integral Transform." Journal of the Institute of Science and Technology 13, no. 3 (2023): 2042–56. http://dx.doi.org/10.21597/jist.1283580.
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The purpose of this study is to mention the Laplace integral transform in bigeometric analysis, which is one of the non-Newtonian analysis by using the fundamental definitions and theorems of the Laplace integral transform, which is one of the integral transform methods of classical analysis. First of all, the concept of exponential arithmetic, which forms the basis of non Newtonian analysis, is given. As in classical analysis, definitions of the concepts of bigeometric limit, bigeometric continuity, bigeometric derivative and bigeometric integral are given in bigeometric analysis. Here, the definition of the bigeometric Laplace integral transform in bigeometric analysis is given. Then, some basic concepts and theorems of the bigeometric Laplace integral transform are given. For this purpose, the definitions of the concepts of bigeometric derivative and bigeometric indefinite integral and bigeometric definite integral in bigeometric analysis and the properties of these concepts are used. In addition, the properties of the bigeometric Laplace integral transform are investigated. Finally, solutions of bigeometric linear differential equations are investigated with the help of the bigeometric Laplace integral transform.
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Jiménez, Javier. "Hyperviscous vortices." Journal of Fluid Mechanics 279 (November 25, 1994): 169–76. http://dx.doi.org/10.1017/s0022112094003861.
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The structure of diffusing planar and axisymmetric vortices of the hyperviscous Navier-Stokes equations is studied for different orders of the dissipative operator. It is found that, except for the classical Newtonian case, the vorticity decays at large distances by means of oscillatory tails, containing circulation of alternating signs. This oscillation becomes stronger for large hyperviscosity orders, and the limit of infinite order is studied. It is argued that these solutions would become unstable for large enough Reynolds numbers, and may contribute non-trivial spurious dynamics to flow simulations using hyperviscosity.
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ALI, N., M. SAJID, Z. ABBAS, and O. ANWAR BÉG. "SWIMMING DYNAMICS OF A MICRO-ORGANISM IN A COUPLE STRESS FLUID: A RHEOLOGICAL MODEL OF EMBRYOLOGICAL HYDRODYNAMIC PROPULSION." Journal of Mechanics in Medicine and Biology 17, no. 03 (2017): 1750054. http://dx.doi.org/10.1142/s0219519417500543.
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Mathematical simulations of embryological fluid dynamics are fundamental to improving clinical understanding of the intricate mechanisms underlying sperm locomotion. The strongly rheological nature of reproductive fluids has been established for a number of decades. Complimentary to clinical studies, mathematical models of reproductive hydrodynamics provide a deeper understanding of the intricate mechanisms involved in spermatozoa locomotion which can be of immense benefit in clarifying fertilization processes. Although numerous non-Newtonian studies of spermatozoa swimming dynamics in non-Newtonian media have been communicated, very few have addressed the micro-structural characteristics of embryological media. This family of micro-continuum models include Eringen’s micro-stretch theory, Eringen’s microfluid and micropolar constructs and V. K. Stokes’ couple stress fluid model, all developed in the 1960s. In the present paper we implement the last of these models to examine the problem of micro-organism (spermatozoa) swimming at low Reynolds number in a homogenous embryological fluid medium with couple stress effects. The micro-organism is modeled as with Taylor’s classical approach, as an infinite flexible sheet on whose surface waves of lateral displacement are propagated. The swimming speed of the sheet and rate of work done by it are determined as function of the parameters of orbit and the couple stress fluid parameter ([Formula: see text]). The perturbation solutions are validated with a Nakamura finite difference algorithm. The perturbation solutions reveal that the normal beat pattern is effective for both couple stress and Newtonian fluids only when the amplitude of stretching wave is small. The swimming speed is observed to decrease with couple stress fluid parameter tending to its Newtonian limit as alpha tends to infinity. However the rate of work done by the sheet decreases with [Formula: see text] and approaches asymptotically to its Newtonian value. The present solutions also provide a good benchmark for more advanced numerical simulations of micro-organism swimming in couple-stress rheological biofluids.
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Bergé, Joel, Martin Pernot-Borràs, Jean-Philippe Uzan, et al. "MICROSCOPE’s constraint on a short-range fifth force." Classical and Quantum Gravity 39, no. 20 (2022): 204010. http://dx.doi.org/10.1088/1361-6382/abe142.
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Abstract The MICROSCOPE experiment was designed to test the weak equivalence principle in space, by comparing the low-frequency dynamics of cylindrical ‘free-falling’ test masses controlled by electrostatic forces. We use data taken during technical sessions aimed at estimating the electrostatic stiffness of MICROSCOPE’s sensors to constrain a short-range Yukawa deviation from Newtonian gravity. We take advantage of the fact that in the limit of small displacements, the gravitational interaction (both Newtonian and Yukawa-like) between nested cylinders is linear, and thus simply characterised by a stiffness. By measuring the total stiffness of the forces acting on a test mass as it moves, and comparing it with the theoretical electrostatic stiffness (expected to dominate), it is a priori possible to infer constraints on the Yukawa potential parameters. However, we find that measurement uncertainties are dominated by the gold wires used to control the electric charge of the test masses, though their related stiffness is indeed smaller than the expected electrostatic stiffness. Moreover, we find a non-zero unaccounted for stiffness that depends on the instrument’s electric configuration, hinting at the presence of patch-field effects. Added to significant uncertainties on the electrostatic model, they only allow for poor constraints on the Yukawa potential. This is not surprising, as MICROSCOPE was not designed for this measurement, but this analysis is the first step to new experimental searches for non-Newtonian gravity in space.
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BRADY, JOHN F., and JEFFREY F. MORRIS. "Microstructure of strongly sheared suspensions and its impact on rheology and diffusion." Journal of Fluid Mechanics 348 (October 10, 1997): 103–39. http://dx.doi.org/10.1017/s0022112097006320.
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The effects of Brownian motion alone and in combination with an interparticle force of hard-sphere type upon the particle configuration in a strongly sheared suspension are analysed. In the limit Pe→∞ under the influence of hydrodynamic interactions alone, the pair-distribution function of a dilute suspension of spheres has symmetry properties that yield a Newtonian constitutive behaviour and a zero self-diffusivity. Here, Pe=γ˛a2/2D is the Péclet number with γ˛ the shear rate, a the particle radius, and D the diffusivity of an isolated particle. Brownian diffusion at large Pe gives rise to an O(aPe−1) thin boundary layer at contact in which the effects of Brownian diffusion and advection balance, and the pair-distribution function is asymmetric within the boundary layer with a contact value of O(Pe0.78) in pure-straining motion; non-Newtonian effects, which scale as the product of the contact value and the O(a3Pe−1) layer volume, vanish as Pe−0.22 as Pe→∞.
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D. Stepanov, A. "Statistical Method for Tracing Hydraulic Fracture Front Without Evaluation of the Normal." International Journal of Engineering & Technology 7, no. 4.26 (2018): 274. http://dx.doi.org/10.14419/ijet.v7i4.26.27936.
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In numerical simulation of hydraulic fracture propagation, tangent component of the fluid velocity generally considered to be neglected near the crack front. Then Reynolds transport theorem yields that the limit of the particle velocity coincides with the vector of the front propagation speed. We use this fact in combination with the Poiseuille-type equation, which implies that the particle velocity is always collinear to pressure gradient. We show that this specific feature of the hydraulic fracture problem may serve to simplify tracing the front propagation. The latter may be traced without explicit evaluation of the normal to the front, which is needed in conventional applications of the theory of propagating interfaces. Numerical experiments confirm that, despite huge errors in pressure and even greater errors in its gradient, the propagation speed, statistically averaged over a distance of a mesh size, is found quite accurate. We conclude that suggested method may simplify numerical simulation of hydraulic fractures driven by Newtonian and non-Newtonian fluids.
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ALAM, MEHEBOOB, and STEFAN LUDING. "Rheology of bidisperse granular mixtures via event-driven simulations." Journal of Fluid Mechanics 476 (February 10, 2003): 69–103. http://dx.doi.org/10.1017/s002211200200263x.
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The bulk rheology of bidisperse mixtures of granular materials is examined under homogeneous shear flow conditions using the event-driven simulation method. The granular material is modelled as a system of smooth inelastic disks, interacting via the hard-core potential. In order to understand the effect of size and mass disparities, two cases were examined separately, namely, a mixture of different sized particles with particles having either the same mass or the same material density. The relevant macroscopic quantities are the pressure, the shear viscosity, the granular energy (fluctuating kinetic energy) and the first normal stress difference.Numerical results for pressure, viscosity and granular energy are compared with a kinetic-theory constitutive model with excellent agreement in the low dissipation limit even at large size disparities. Systematic quantitative deviations occur for stronger dissipations. Mixtures with equal-mass particles show a stronger shear resistance than an equivalent monodisperse system; in contrast, however, mixtures with equal-density particles show a reduced shear resistance. The granular energies of the two species are unequal, implying that the equi-partition principle assumed in most of the constitutive models does not hold. Inelasticity is responsible for the onset of energy non-equipartition, but mass disparity significantly enhances its magnitude. This lack of energy equipartition can lead to interesting non-monotonic variations of the pressure, viscosity and granular energy with the mass ratio if the size ratio is held fixed, while the model predictions (with the equipartition assumption) suggest a monotonic behaviour in the same limit. In general, the granular fluid is non-Newtonian with a measurable first normal stress difference (which is positive if the stress is defined in the compressive sense), and the effect of bidispersity is to increase the normal stress difference, thus enhancing the non-Newtonian character of the fluid.
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Buckholz, R. H., and B. Hwang. "The Accuracy of Short Bearing Theory for Newtonian Lubricants." Journal of Tribology 108, no. 1 (1986): 73–79. http://dx.doi.org/10.1115/1.3261147.
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The accuracy of the short bearing approximation is analyzed in this discussion. The results apply to Newtonian lubricants, and they can also be extended to non-Newtonian power-law lubricants. Reynolds’ lubrication equation is first solved by applying a regular perturbation expansion in pressure to the π film journal bearing; after this, a matched asymptotic expansion is applied to linear slider bearings. Approximate solutions are then compared with numerical solutions, to estimate the accuracy of the short bearing approximation. Finally, the accuracy of fluid film pressures predicted via short bearing theory is shown to depend upon three factors: the bearing aspect ratio, eccentricity ratio, and the partial-arc extent. Ocvirk’s short bearing series approximation—for finite bearing aspect ratio—is shown to become singular in the limit as the eccentricity ratio approaches unity. The one term π film Ocvirk solution is shown to be a nonconservative approximation to the journal bearing load capacity. A method to extend the accuracy of the short bearing approximation for partial-arcs and slider bearings is then presented.
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Luo, Zheng Yuan, and Bo Feng Bai. "Dynamics of capsules enclosing viscoelastic fluid in simple shear flow." Journal of Fluid Mechanics 840 (February 14, 2018): 656–87. http://dx.doi.org/10.1017/jfm.2018.88.
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Previous studies on capsule dynamics in shear flow have dealt with Newtonian fluids, while the effect of fluid viscoelasticity remains an unresolved fundamental question. In this paper, we report a numerical investigation of the dynamics of capsules enclosing a viscoelastic fluid and which are freely suspended in a Newtonian fluid under simple shear. Systematic simulations are performed at small but non-zero Reynolds numbers (i.e. $Re=0.1$) using a three-dimensional front-tracking finite-difference model, in which the fluid viscoelasticity is introduced via the Oldroyd-B constitutive equation. We demonstrate that the internal fluid viscoelasticity presents significant effects on the deformation behaviour of initially spherical capsules, including transient evolution and equilibrium values of their deformation and orientation. Particularly, the capsule deformation decreases slightly with the Deborah number De increasing from 0 to $O(1)$. In contrast, with De increasing within high levels, i.e. $O(1{-}100)$, the capsule deformation increases continuously and eventually approaches the Newtonian limit having a viscosity the same as the Newtonian part of the viscoelastic capsule. By analysing the viscous stress, pressure and viscoelastic stress acting on the capsule membrane, we reveal that the mechanism underlying the effects of the internal fluid viscoelasticity on the capsule deformation is the alterations in the distribution of the viscoelastic stress at low De and its magnitude at high De, respectively. Furthermore, we find some new features in the dynamics of initially non-spherical capsules induced by the internal fluid viscoelasticity. Particularly, the transition from tumbling to swinging of oblate capsules can be triggered at very high viscosity ratios by increasing De alone. Besides, the critical viscosity ratio for the tumbling-to-swinging transition is remarkably enlarged with De increasing at relatively high levels, i.e. $O(1{-}100)$, while it shows little change at low De, i.e. below $O(1)$.
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Plaut, Emmanuel, Nicolas Roland, and Chérif Nouar. "Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology." Journal of Fluid Mechanics 818 (April 5, 2017): 595–622. http://dx.doi.org/10.1017/jfm.2017.149.
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In order to model the transition to turbulence in pipe flow of non-Newtonian fluids, the influence of a strongly shear-thinning rheology on the travelling waves with a threefold rotational symmetry of Faisst & Eckhardt (Phys. Rev. Lett., vol. 91, 2003, 224502) and Wedin & Kerswell (J. Fluid Mech., vol. 508, 2004, pp. 333–371) is analysed. The rheological model is Carreau’s law. Besides the shear-thinning index $n_{C}$, the dimensionless characteristic time $\unicode[STIX]{x1D706}$ of the fluid is considered as the main non-Newtonian control parameter. If $\unicode[STIX]{x1D706}=0$, the fluid is Newtonian. In the relevant limit $\unicode[STIX]{x1D706}\rightarrow +\infty$, the fluid approaches a power-law behaviour. The laminar base flows are first characterized. To compute the nonlinear waves, a Petrov–Galerkin code is used, with continuation methods, starting from the Newtonian case. The axial wavenumber is optimized and the critical waves appearing at minimal values of the Reynolds number $\mathit{Re}_{w}$ based on the mean velocity and wall viscosity are characterized. As $\unicode[STIX]{x1D706}$ increases, these correspond to a constant value of the Reynolds number based on the mean velocity and viscosity. This viscosity, close to the one of the laminar flow, can be estimated analytically. Therefore the experimentally relevant critical Reynolds number $\mathit{Re}_{wc}$ can also be estimated analytically. This Reynolds number may be viewed as a lower estimate of the Reynolds number for the transition to developed turbulence. This demonstrates a quantified stabilizing effect of the shear-thinning rheology. Finally, the increase of the pressure gradient in waves, as compared to the one in the laminar flow with the same mass flux, is calculated, and a kind of ‘drag reduction effect’ is found.
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Pevere, A., G. Guibaud, E. van Hullebusch, P. Lens, and M. Baudu. "Effect of inoculum and sludge concentration on viscosity evolution of anaerobic granular sludges." Water Science and Technology 52, no. 1-2 (2005): 509–14. http://dx.doi.org/10.2166/wst.2005.0560.
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The rheological behaviour of granular sludges (diameter 20–315 μm) originating from different anaerobic reactors was carried out using rotation tests. The sieved granular sludges suspensions display a non-Newtonian rheological behaviour and the limit viscosity was therefore used as a rheological parameter. The values obtained, which depend on the shear rate used, were strongly influenced by the total suspended solids (TSS) content of granular sludge and an exponential relation was found between the TSS and the rheological parameter limit viscosity. The increase of viscosity as a function of TSS content of the granular sludge as well as the increase of granule size underlines the importance of the interaction between granules in the evolution of this rheological parameter. Significant differences in granular sludge limit viscosity were found for granular sludge of different origins. All measurements performed with 10 g.l−1 TSS granular sludge indicate the ability of the chosen rheological parameter to describe different granular sludge quality.
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Alba, K., S. M. Taghavi, and I. A. Frigaard. "A weighted residual method for two-layer non-Newtonian channel flows: steady-state results and their stability." Journal of Fluid Mechanics 731 (August 28, 2013): 509–44. http://dx.doi.org/10.1017/jfm.2013.381.
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AbstractWe study buoyant displacement flows in a plane channel with two fluids in the long-wavelength limit in a stratified configuration. Weak inertial effects are accounted for by developing a weighted residual method. This gives a first-order approximation to the interface height and flux functions in each layer. As the fluids are shear-thinning and have a yield stress, to retain a formulation that can be resolved analytically requires the development of a system of special functions for the weight functions and various integrals related to the base flow. For displacement flows, the addition of inertia can either slightly increase or decrease the speed of the leading displacement front, which governs the displacement efficiency. A more subtle effect is that a wider range of interface heights are stretched between advancing fronts than without inertia. We study stability of these systems via both a linear temporal analysis and a numerical spatiotemporal method. To start with, the Orr–Sommerfeld equations are first derived for two generalized non-Newtonian fluids satisfying the Herschel–Bulkley model, and analytical expressions for growth rate and wave speed are obtained for the long-wavelength limit. The predictions of linear analysis based on the weighted residual method shows excellent agreement with the Orr–Sommerfeld approach. For displacement flows in unstable parameter ranges we do observe growth of interfacial waves that saturate nonlinearly and disperse. The observed waves have similar characteristics to those observed experimentally in pipe flow displacements. Although the focus in this study is on displacement flows, the formulation laid out can be easily used for similar two-layer flows, e.g. co-extrusion flows.
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Haghani, Zahra, and Tiberiu Harko. "Effects of Quantum Metric Fluctuations on the Cosmological Evolution in Friedmann-Lemaitre-Robertson-Walker Geometries." Physics 3, no. 3 (2021): 689–714. http://dx.doi.org/10.3390/physics3030042.
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In this paper, the effects of the quantum metric fluctuations on the background cosmological dynamics of the universe are considered. To describe the quantum effects, the metric is assumed to be given by the sum of a classical component and a fluctuating component of quantum origin . At the classical level, the Einstein gravitational field equations are equivalent to a modified gravity theory, containing a non-minimal coupling between matter and geometry. The gravitational dynamics is determined by the expectation value of the fluctuating quantum correction term, which can be expressed in terms of an arbitrary tensor Kμν. To fix the functional form of the fluctuation tensor, the Newtonian limit of the theory is considered, from which the generalized Poisson equation is derived. The compatibility of the Newtonian limit with the Solar System tests allows us to fix the form of Kμν. Using these observationally consistent forms of Kμν, the generalized Friedmann equations are obtained in the presence of quantum fluctuations of the metric for the case of a flat homogeneous and isotropic geometry. The corresponding cosmological models are analyzed using both analytical and numerical method. One finds that a large variety of cosmological models can be formulated. Depending on the numerical values of the model parameters, both accelerating and decelerating behaviors can be obtained. The obtained results are compared with the standard ΛCDM (Λ Cold Dark Matter) model.
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Re, Federico, and Oliver F. Piattella. "Non-Zero Coriolis Field in Ehlers’ Frame Theory." Galaxies 13, no. 2 (2025): 38. https://doi.org/10.3390/galaxies13020038.
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Ehlers’ Frame Theory is a class of geometric theories parameterized by λ:=1/c2 and identical to the General Theory of Relativity for λ≠0. The limit λ→0 does not recover Newtonian gravity, as one might expect, but yields the so-called Newton–Cartan theory of gravity, which is characterized by a second gravitational field ω, called the Coriolis field. Such a field encodes at a non-relativistic level the dragging feature of general spacetimes, as we show explicitly for the case of the (η,H) geometries. Taking advantage of the Coriolis field, we apply Ehlers’ theory to an axially symmetric distribution of matter, mimicking, for example, a disc galaxy, and show how its dynamics might reproduce a flattish rotation curve. In the same setting, we further exploit the formal simplicity of Ehlers’ formalism in addressing non-stationary cases, which are remarkably difficult to treat with the General Theory of Relativity. We show that the time derivative of the Coriolis field gives rise to a tangential acceleration which allows for studying a possible formation in time of the rotation curve’s flattish feature.