Articles de revues : « Non-simple fluid »

1

Zatloukal, Martin. « A simple phenomenological non-Newtonian fluid model ». Journal of Non-Newtonian Fluid Mechanics 165, n^o 11-12 (juin 2010) : 592–95. http://dx.doi.org/10.1016/j.jnnfm.2010.02.019.

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Teja, Amyn S., et Tongfan Sun. « A simple non-classical equation of state for fluids and fluid mixtures ». Fluid Phase Equilibria 161, n^o 1 (juillet 1999) : 63–76. http://dx.doi.org/10.1016/s0378-3812(99)00161-2.

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ZHOU, SHIQI. « EXTENDING SIMPLE WEIGHTED DENSITY APPROXIMATION FOR HARD SPHERE FLUID TO LENNARD–JONES FLUID (I) : TEST ». International Journal of Modern Physics B 19, n^o 32 (30 décembre 2005) : 4701–21. http://dx.doi.org/10.1142/s0217979205033078.

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A theoretical formalism which can be combined with any hard sphere density functional approximations (DFA) to construct DFA for non-hard sphere fluids with a hard or soft core subjected to diverse external potentials is proposed. To show validity and power of the present formalism, we employ a simple weighted density approximation as an illustrating example. It is found that the resultant DFA for Lennard–Jones fluid under influences of diverse extenal potentials is in generally satisfactory agreement with corresponding simulational results even though the co-existence bulk fluid in the particle reservoir with which the non-uniform fluid under consideration is connected, is situated at "dangerous" regions. The significance of the present formalism lies in that it can be combined with any other hard sphere DFAs to construct DFAs for any non-hard sphere fluids with a hard or soft core.

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Fujitani, Youhei. « A Simple Formulation of Non-Equilibrium Thermodynamics of a Polarizable Fluid ». Journal of the Physical Society of Japan 70, n^o 6 (15 juin 2001) : 1556–64. http://dx.doi.org/10.1143/jpsj.70.1556.

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Payam, A. F., W. Trewby et K. Voïtchovsky. « Simultaneous viscosity and density measurement of small volumes of liquids using a vibrating microcantilever ». Analyst 142, n^o 9 (2017) : 1492–98. http://dx.doi.org/10.1039/c6an02674e.

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An analytical model is derived to calculate the viscosity and density of small volumes of fluid from the resonance frequencies of an immersed microcantilever. Its accuracy is verified on simple and non-Newtonian fluids.

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Dai, F., et M. M. Khonsari. « A Theory of Hydrodynamic Lubrication Involving the Mixture of Two Fluids ». Journal of Applied Mechanics 61, n^o 3 (1 septembre 1994) : 634–41. http://dx.doi.org/10.1115/1.2901507.

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Based on the principles of continuum mechanics, we drive the governing equations for the hydrodynamic lubrication involving the mixture of two incompressible fluids. The governing equations are general in the sense that they can be applied to the mixture of any simple non-Newtonian fluid with a Newtonian fluid. A mixture thus formed is considered to be nonhomogeneous and non-Newtonian. In the theoretical development, the interaction between the constituents is taken into consideration. It is shown that a number of currently available models are special cases of the theory presented in this paper. As an example, results are presented for journal bearing performance lubricated with a mixture of a power-law fluid mixed with Newtonian oil.

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Lenci, Alessandro, et Luca Chiapponi. « An Experimental Setup to Investigate Non-Newtonian Fluid Flow in Variable Aperture Channels ». Water 12, n^o 5 (1 mai 2020) : 1284. http://dx.doi.org/10.3390/w12051284.

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Non-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.

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SASAKI, Kazuhiko, et Kazuhiko KASAI. « MACROSCOPIC AND SIMPLE NON-LINEAR MODELING OF VISCOUS FLUID MATERIAL UNDER LARGER STRAINS ». Journal of Structural and Construction Engineering (Transactions of AIJ) 78, n^o 685 (2013) : 607–15. http://dx.doi.org/10.3130/aijs.78.607.

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Sekimoto, Ken. « An exact non-stationary solution of simple shear flow in a Bingham fluid ». Journal of Non-Newtonian Fluid Mechanics 39, n^o 1 (janvier 1991) : 107–13. http://dx.doi.org/10.1016/0377-0257(91)80006-6.

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McKinney, Michella M., et Andrew Parkinson. « A simple, non-chromatographic procedure to purify immunoglobulins from serum and ascites fluid ». Journal of Immunological Methods 96, n^o 2 (février 1987) : 271–78. http://dx.doi.org/10.1016/0022-1759(87)90324-3.

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Dostalík, Mark, Josef Málek, Vít Průša et Endre Süli. « A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids ». Fluids 5, n^o 3 (11 août 2020) : 133. http://dx.doi.org/10.3390/fluids5030133.

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We revisit some classical models for dilute polymeric fluids, and we show that thermodynamically consistent models for non-isothermal flows of these fluids can be derived in a very elementary manner. Our approach is based on the identification of energy storage mechanisms and entropy production mechanisms in the fluid of interest, which, in turn, leads to explicit formulae for the Cauchy stress tensor and for all of the fluxes involved. Having identified these mechanisms and derived the governing equations, we document the potential use of the thermodynamic basis of the model in a rudimentary stability analysis. In particular, we focus on finite amplitude (nonlinear) stability of a stationary spatially homogeneous state in a thermodynamically isolated system.

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Tamburrini, Stefania, Letizia Consoli, Marco Garrone, Giuseppe Sfuncia, Marina Lugarà, Maria Gabriella Coppola, Miryam Piccirillo et al. « The “Black Pattern”, a Simplified Ultrasound Approach to Non-Traumatic Abdominal Emergencies ». Tomography 8, n^o 2 (15 mars 2022) : 798–814. http://dx.doi.org/10.3390/tomography8020066.

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Background: A key issue in abdominal US is the assessment of fluid, which is usually anechoic, thus appearing “black”. Our approach focuses on searching for fluid in non-traumatic patients, providing a new, simplified method for point-of-care US (POCUS). Objective: Fluid assessment is based on a three-step analysis that we can thus summarize. 1. Look for black where it should not be. This means searching for effusions or collections. 2. Check if black is too much. This means evaluating anatomical landmarks where fluid should normally be present but may be abnormally abundant. 3. Look for black that is not clearly black. This means evaluating fluid aspects, whether wholly anechoic or not (suggesting heterogeneous or corpusculated fluid). Discussion: Using this simple method focused on US fluid presence and appearance should help clinicians to make a timely diagnosis. Although our simplified, systematic algorithm of POCUS may identify abnormalities; this usually entails a second-level imaging. An accurate knowledge of the physio–pathological and anatomical ultrasound bases remains essential in applying this algorithm. Conclusion: The black pattern approach in non -traumatic emergencies may be applied to a broad spectrum of abnormalities. It may represent a valuable aid for emergency physicians, especially if inexperienced, involved in a variety of non-traumatic scenarios. It may also be a simple and effective teaching aid for US beginners.

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Ayub, Syahrial, Hikmawati Hikmawati, Ni Nyoman Sri Putu Verawati et Muhammad Zuhdi. « PENGEMBANGAN KIT FLUIDA ALTERNATIF YANG BERASAL DARI SAMPAH ANORGANIK UNTUK PEMBELAJARAN FISIKA ». ORBITA : Jurnal Kajian, Inovasi dan Aplikasi Pendidikan Fisika 5, n^o 2 (28 novembre 2019) : 59. http://dx.doi.org/10.31764/orbita.v5i2.1185.

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ABSTRAKPenelitian ini bertujuan mengembangkan kit fluida alternatif pada pembelajaran fisika. Kit fluida alternatif ini dibuat dengan memanfaatkan sampah anorganik yang sudah tidak digunakan. Sampah anorganik adalah sampah yang dihasilkan dari bahan-bahan non-hayati, baik berupa produk sintetik maupun hasil proses teknologi pengolahan bahan tambang atau sumber daya alam dan tidak dapat diuraikan oleh alam, seperti botol plastik, tas plastik, kaleng dan lain-lain. Alat-alat yang terdapat pada kit fluida alternatif adalah alat peraga kapal selam sederhana, alat peraga aliran air, alat peraga pompa air tekanan udara, alat peraga barometer botol, alat peraga roket tekanan udara, dan alat peraga helikopter sederhana. Alat-alat peraga ini disusun dalam satu kotak dan mudah dibawa (portable). Kotak inilah yang disebut dengan kit fluida alternatif. Kit fluida ini diterapkan pada pembelajaran IPA (Fisika) di SD Negeri 6 Mataram. Respon peserta didik terhadap pembelajaran dengan integrasi kit fluida alternatif adalah 78 % menyatakan sangat setuju dan hanya 22 % yang menyatakan setuju dan tidak ada yang memilih tidak setuju. Berdasarkan data ini, disimpulkan bahwa pembelajaran IPA (fisika) di SD Negeri 6 Mataram dengan integrasi kit fluida alternatif mendapat respon baik dari peserta didik. Kata kunci: Kit Fluida Alternatif; Sampah Anorganik; Pembelajaran Fisika ABSTRACTThis research aims to develop alternative fluid kits in learning physics. This alternative fluid kit is made using inorganic waste that is not used. Inorganic waste is waste generated from non-biological materials, either in the form of synthetic products or the results of the processing technology of mining materials or natural resources and cannot be broken down by nature, such as plastic bottles, plastic bags, cans and others. The tools contained in the alternative fluid kit are simple submarine props, water flow props, air pressure water pump props, bottle barometer props, air pressure rocket props, and simple helicopter props. These props are arranged in one box and are easy and portable. This box is called the alternative fluid kit. This fluid kit is applied to learning science (physics) in SD Negeri 6 Mataram. Learners' responses to learning with the integration of alternative fluid kits is 78% stating strongly agree and only 22% who agree and no one chooses to disagree. Based on this data, it was concluded that learning science (physics) at SD Negeri 6 Mataram with the integration of alternative fluid kits received good responses from students. Keywords: Alternative Fluid Kits; Inorganic Waste; Physics Learning

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Hegaj, Efim, et Evgeny Borzenko. « Numerical Simulation of the Steady-State Herschel-Bulkley Fluid Flow in a Channel with Sudden Expansion ». Key Engineering Materials 743 (juillet 2017) : 474–79. http://dx.doi.org/10.4028/www.scientific.net/kem.743.474.

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In this paper, the steady-state flow of non-Newtonian fluid in a planar channel with sudden expansion is investigated. The rheological behavior of this media is described by the Herschel-Bulkley model. To determine both steady-state velocity and pressure fields, a numerical algorithm based on the relaxation method and SIMPLE procedure is used.The mathematical problem statement includes three non-dimensional parameters: the Reynolds number, the Bingham number (non-dimensional viscoplasticity parameter), and the power-law index. The results of numerical simulation are obtained in a range of the Reynolds number 1 ≤ Re ≤ 40, Bingham number 0 ≤ Se ≤ 2, and power-law index 0.4 ≤k ≤ 2 (for shear thinning, Newtonian, and shear thickening fluids).The distribution of the main fluid flow characteristics and localization of the two-dimensional region in an expansion zone is presented. The impact of main parameters of the problem on a dead zone distribution in the fluid flow is shown.

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Rana, Mehwish, Nazish Shahid et Azhar Ali Zafar. « Effects of Side Walls on the Motion Induced by an Infinite Plate that Applies Shear Stresses to an Oldroyd-B Fluid ». Zeitschrift für Naturforschung A 68, n^o 12 (1 décembre 2013) : 725–34. http://dx.doi.org/10.5560/zna.2013-0052.

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Unsteady motions of Oldroyd-B fluids between two parallel walls perpendicular to a plate that applies two types of shears to the fluid are studied using integral transforms. Exact solutions are obtained both for velocity and non-trivial shear stresses. They are presented in simple forms as sums of steady-state and transient solutions and can easily be particularized to give the similar solutions for Maxwell, second-grade and Newtonian fluids. Known solutions for the motion over an infinite plate, applying the same shears to the fluid, are recovered as limiting cases of general solutions. Finally, the influence of side walls on the fluid motion, the distance between walls for which their presence can be neglected, and the required time to reach the steady-state are graphically determined.

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Luo, Zheng Yuan, et Bo Feng Bai. « Dynamics of capsules enclosing viscoelastic fluid in simple shear flow ». Journal of Fluid Mechanics 840 (14 février 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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Švec, Oldřich, et Jan Skoček. « Simple Navier’s slip boundary condition for the non-Newtonian Lattice Boltzmann fluid dynamics solver ». Journal of Non-Newtonian Fluid Mechanics 199 (septembre 2013) : 61–69. http://dx.doi.org/10.1016/j.jnnfm.2013.06.003.

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Zhuo, Jingxuan, Ricardo Cortez et Robert Dillon. « Lagrangian Mesh Model with Regridding for Planar Poiseuille Flow ». Communications in Computational Physics 22, n^o 1 (3 mai 2017) : 112–32. http://dx.doi.org/10.4208/cicp.oa-2016-0109.

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AbstractMany biological settings involve complex fluids that have non-Newtonian mechanical responses that arise from suspended microstructures. In contrast, Newtonian fluids are liquids or mixtures of a simple molecular structure that exhibit a linear relationship between the shear stress and the rate of deformation. In modeling complex fluids, the extra stress from the non-Newtonian contribution must be included in the governing equations.In this study we compare Lagrangian mesh and Oldroyd-B formulations of fluid-structure interaction in an immersed boundary framework. The start-up phase of planar Poiseuille flow between two parallel plates is used as a test case for the fluid models. For Newtonian and Oldroyd-B fluids there exist analytical solutions which are used in the comparison of simulation and theoretical results. The Lagrangian mesh results are compared with Oldroyd-B using comparable parameters. A regridding algorithm is introduced for the Lagrangian mesh model. We show that the Lagrangian mesh model simulations with regridding produce results in close agreement with the Oldfoyd-B model.

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BOMBELLI, LUCA. « PERFECT FLUID PERTURBATIONS OF ROBERTSON-WALKER SPACETIMES ». International Journal of Modern Physics D 03, n^o 01 (mars 1994) : 153–56. http://dx.doi.org/10.1142/s0218271894000174.

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I report on recent work on perturbations of Robertson-Walker spacetimes using the Bardeen-Stewart variables to describe metric perturbations. The gauge freedom available in the formalism is larger than that arising purely from spacetime diffeomorphisms. The associated non-uniqueness and non-locality problems have a simple solution, but the extra gauge freedom must be taken into account to obtain deterministic linearized field equations. The linearized Einstein equation decouples into scalar, vector and tensor sectors; I write down and comment on the equations one obtains using as matter an isentropic perfect fluid.

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Stankov, M. N., A. P. Jovanovic, V. Lj Markovic et S. N. Stamenkovic. « Two-dimensional fluid modeling of DC glow discharge in argon at low pressure ». Facta universitatis - series : Physics, Chemistry and Technology 13, n^o 3 (2015) : 153–62. http://dx.doi.org/10.2298/fupct1503153s.

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The modeling of DC glow discharge in argon at the pressure p = 1.5 Torr and inter-electrode distance d = 1 cm was performed for different voltages and glow currents. For the first time, argon glow discharge is modeled using a two-dimensional (2D) fluid model with non-local ionization. A detailed numerical procedure for 2D fluid modeling is given. The 2D profiles of particle number densities and electric potential obtained from the fluid model with non-local ionization and the simple fluid model are presented and compared.

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Fetecau, Corina, Mehwish Rana, Niat Nigar et Constantin Fetecau. « First Exact Solutions for Flows of Rate Type Fluids in a Circular Duct that Applies a Constant Couple to the Fluid ». Zeitschrift für Naturforschung A 69, n^o 5-6 (1 juin 2014) : 232–38. http://dx.doi.org/10.5560/zna.2014-0022.

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Rotational flow of an Oldroyd-B fluid induced by an infinite circular cylinder that applies a constant couple to the fluid is studied by means of integral transforms. Such a problem is not solved in the existing literature for rate type fluids and the present solutions are based on a simple but important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easy be reduced to the similar solutions corresponding to Maxwell, second-grade, and Newtonian fluids performing the same motion. Finally, the influence of material parameters on the velocity and shear stress distributions is graphically underlined.

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Tripathi, M. K., K. C. Sahu, G. Karapetsas, K. Sefiane et O. K. Matar. « Non-isothermal bubble rise : non-monotonic dependence of surface tension on temperature ». Journal of Fluid Mechanics 763 (10 décembre 2014) : 82–108. http://dx.doi.org/10.1017/jfm.2014.659.

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AbstractWe study the motion of a bubble driven by buoyancy and thermocapillarity in a tube with a non-uniformly heated walls, containing a so-called ‘self-rewetting fluid’; the surface tension of the latter exhibits a parabolic dependence on temperature, with a well-defined minimum. In the Stokes flow limit, we derive the conditions under which a spherical bubble can come to rest in a self-rewetting fluid whose temperature varies linearly in the vertical direction, and demonstrate that this is possible for both positive and negative temperature gradients. This is in contrast to the case of simple fluids whose surface tension decreases linearly with temperature, for which bubble motion is arrested only for negative temperature gradients. In the case of self-rewetting fluids, we propose an analytical expression for the position of bubble arrestment as a function of other dimensionless numbers. We also perform direct numerical simulation of axisymmetric bubble motion in a fluid whose temperature increases linearly with vertical distance from the bottom of the tube; this is done for a range of Bond and Galileo numbers, as well as for various parameters that govern the functional dependence of surface tension on temperature. We demonstrate that bubble motion can be reversed and then arrested only in self-rewetting fluids, and not in linear fluids, for sufficiently small Bond numbers. We also demonstrate that considerable bubble elongation is possible under significant wall confinement, and for strongly self-rewetting fluids and large Bond numbers. The mechanisms underlying the phenomena observed are elucidated by considering how the surface tension dependence on temperature affects the thermocapillary stresses in the flow.

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Spencer, Timothy J., Ian Halliday et Chris M. Care. « A local lattice Boltzmann method for multiple immiscible fluids and dense suspensions of drops ». Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences 369, n^o 1944 (13 juin 2011) : 2255–63. http://dx.doi.org/10.1098/rsta.2011.0029.

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The lattice Boltzmann method (LBM) for computational fluid dynamics benefits from a simple, explicit, completely local computational algorithm making it highly efficient. We extend LBM to recover hydrodynamics of multi-component immiscible fluids, while retaining a completely local, explicit and simple algorithm. Hence, no computationally expensive lattice gradients, interaction potentials or curvatures, that use information from neighbouring lattice sites, need to be calculated, which makes the method highly scalable and suitable for high performance parallel computing. The method is analytical and is shown to recover correct continuum hydrodynamic equations of motion and interfacial boundary conditions. This LBM may be further extended to situations containing a high number (O(100)) of individually immiscible drops. We make comparisons of the emergent non-Newtonian behaviour with a power-law fluid model. We anticipate our method will have a range applications in engineering, industrial and biological sciences.

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Hou, J. S., M. H. Holmes, W. M. Lai et V. C. Mow. « Boundary Conditions at the Cartilage-Synovial Fluid Interface for Joint Lubrication and Theoretical Verifications ». Journal of Biomechanical Engineering 111, n^o 1 (1 février 1989) : 78–87. http://dx.doi.org/10.1115/1.3168343.

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The objective of this study is to establish and verify the set of boundary conditions at the interface between a biphasic mixture (articular cartilage) and a Newtonian or non-Newtonian fluid (synovial fluid) such that a set of well-posed mathematical problems may be formulated to investigate joint lubrication problems. A “pseudo-no-slip” kinematic boundary condition is proposed based upon the principle that the conditions at the interface between mixtures or mixtures and fluids must reduce to those boundary conditions in single phase continuum mechanics. From this proposed kinematic boundary condition, and balances of mass, momentum and energy, the boundary conditions at the interface between a biphasic mixture and a Newtonian or non-Newtonian fluid are mathematically derived. Based upon these general results, the appropriate boundary conditions needed in modeling the cartilage-synovial fluid-cartilage lubrication problem are deduced. For two simple cases where a Newtonian viscous fluid is forced to flow (with imposed Couette or Poiseuille flow conditions) over a porous-permeable biphasic material of relatively low permeability, the well known empirical Taylor slip condition may be derived using matched asymptotic analysis of the boundary layer at the interface.

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Evans, D. J., et P. T. Cummings. « Non-equilibrium molecular dynamics algorithm for the calculation of thermal diffusion in simple fluid mixtures ». Molecular Physics 72, n^o 4 (mars 1991) : 893–98. http://dx.doi.org/10.1080/00268979100100621.

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Czerwiński, Andrzej, et Jan Łuczko. « Non-planar vibrations of slightly curved pipes conveying fluid in simple and combination parametric resonances ». Journal of Sound and Vibration 413 (janvier 2018) : 270–90. http://dx.doi.org/10.1016/j.jsv.2017.10.026.

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Bourgin, Patrick, et Joseph-Marc Francois. « A Simple Approach to Evaluate Non-Newtonian Viscosity Effects in a Lubricating System ». Journal of Tribology 109, n^o 1 (1 janvier 1987) : 177–82. http://dx.doi.org/10.1115/1.3261314.

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The working characteristics of a finite width slider bearing lubricated by a non-Newtonian fluid are computed. The analysis proposed here allows its performances to be evaluated by means of a pocket calculator. For that purpose, a computer code based on a finite element method is used. The program runs for different values of pertinent kinematical, geometrical and rheological parameters. The corresponding results are fitted by means of adequate analytical formulas, which are very easy to handle. The accuracy of these empirical formulas is investigated in several typical cases. The agreement with the numerical solution is proven to be satisfactory.

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Gagnon, D. A., et P. E. Arratia. « The cost of swimming in generalized Newtonian fluids : experiments with C. elegans ». Journal of Fluid Mechanics 800 (14 juillet 2016) : 753–65. http://dx.doi.org/10.1017/jfm.2016.420.

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Numerous natural processes are contingent on microorganisms’ ability to swim through fluids with non-Newtonian rheology. Here, we use the model organism Caenorhabditis elegans and tracking methods to experimentally investigate the dynamics of undulatory swimming in shear-thinning fluids. Theory and simulation have proposed that the cost of swimming, or mechanical power, should be lower in a shear-thinning fluid compared to a Newtonian fluid of the same zero-shear viscosity. We aim to provide an experimental investigation into the cost of swimming in a shear-thinning fluid from (i) an estimate of the mechanical power of the swimmer and (ii) the viscous dissipation rate of the flow field, which should yield equivalent results for a self-propelled low Reynolds number swimmer. We find the cost of swimming in shear-thinning fluids is less than or equal to the cost of swimming in Newtonian fluids of the same zero-shear viscosity; furthermore, the cost of swimming in shear-thinning fluids scales with a fluid’s effective viscosity and can be predicted using fluid rheology and simple swimming kinematics. Our results agree reasonably well with previous theoretical predictions and provide a framework for understanding the cost of swimming in generalized Newtonian fluids.

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Samad, Abdus, A. Husain, M. Zunaid et A. Samad. « Newtonian and Non-Newtonian Pulsatile Flows through an Artery with Stenosis ». Journal of Engineering Research [TJER] 14, n^o 2 (30 juin 2017) : 191. http://dx.doi.org/10.24200/tjer.vol14iss2pp191-205.

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The current study presents three-dimensional modeling and analysis of blood flow through artery stenosis under several variants of pulsatile flow to mimic the atherosclerosis artery disease. The study considered Newtonian and non-Newtonian blood flow models and solved the three-dimensional laminar and unsteady Navier-Stokes (NS) equations for different inlet velocity profiles. The Carreau Yasuda model was used for hemodynamics modeling of fluid viscosity. A comparative analysis was carried out for Newtonian and non-Newtonian fluid models under several simple pulsatile, equivalent pulsatile and physiological velocity profiles. The non-Newtonian fluid exhibited a higher centerline velocity. Wall shear stresses, shear strain rates, velocity fields, and vortex distribution for Newtonian and non-Newtonian fluid flows show significant differences. A higher wall shear was noticed near the stenosis. The vortex formed near the stenosis shifts to upstream and downstream of the stenosis with the change of velocity pulse. The velocity profile deflates more for non-Newtonian flows than the Newtonian flows.

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Fetecau, Constantin, Tahir Mushtaq Qureshi, Abdul Rauf et Dumitru Vieru. « On the Modified Stokes Second Problem for Maxwell Fluids with Linear Dependence of Viscosity on the Pressure ». Symmetry 14, n^o 2 (24 janvier 2022) : 219. http://dx.doi.org/10.3390/sym14020219.

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The modified Stokes second problem for incompressible upper-convected Maxwell (UCM) fluids with linear dependence of viscosity on the pressure is analytically and numerically investigated. The fluid motion, between infinite horizontal parallel plates, is generated by the lower wall, which oscillates in its plane. The movement region of the fluid is symmetric with respect to the median plane, but its motion is asymmetric due to the boundary conditions. Closed-form expressions are found for the steady-state components of start-up solutions for non-dimensional velocity and the corresponding non-trivial shear and normal stresses. Similar solutions for the simple Couette flow are obtained as limiting cases of the solutions corresponding to the motion due to cosine oscillations of the wall. For validation, it is graphically proved that the start-up solutions (numerical solutions) converge to their steady-state components. Solutions for motions of ordinary incompressible UCM fluids performing the same motions are obtained as special cases of present results using asymptotic approximations of standard Bessel functions. The time needed to reach the permanent or steady state is also determined. This time is higher for motions of ordinary fluids, compared with motions of liquids with pressure-dependent viscosity. The impact of physical parameters on the fluid motion and the spatial–temporal distribution of start-up solutions are graphically investigated and discussed. Ordinary fluids move slower than fluids with pressure-dependent viscosity.

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Walicka, A., P. Jurczak et J. Falicki. « Curvilinear Squeeze Film Bearing Lubricated with a Dehaven Fluid or with Similar Fluids ». International Journal of Applied Mechanics and Engineering 22, n^o 3 (1 août 2017) : 697–715. http://dx.doi.org/10.1515/ijame-2017-0044.

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AbstractIn the paper, the model of a DeHaven fluid and some other models of non-Newtonian fluids, in which the shear strain rates are known functions of the powers of shear stresses, are considered. It was demonstrated that these models for small values of material constants can be presented in a form similar to the form of a DeHaven fluid. This common form, called a unified model of the DeHaven fluid, was used to consider a curvilinear squeeze film bearing. The equations of motion of the unified model, given in a specific coordinate system are used to derive the Reynolds equation. The solution to the Reynolds equation is obtained by a method of successive approximations. As a result one obtains formulae expressing the pressure distribution and load-carrying capacity. The numerical examples of flows of the unified DeHaven fluid in gaps of two simple squeeze film bearings are presented.

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Kuwahara, T., H. Yamaguchi et F. De Vuyst. « Flow regime discrimination technique for gas—liquid two-phase flow in magnetic fluid ». Proceedings of the Institution of Mechanical Engineers, Part C : Journal of Mechanical Engineering Science 222, n^o 6 (1 juin 2008) : 935–44. http://dx.doi.org/10.1243/09544062jmes491.

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This paper describes a new discrimination technique of flow regime (flow pattern) for gas—liquid two-phase flow in magnetic fluid. The proposed technique can identify the flow regime with simple devices by exploiting the wave patterns of signals obtained by electromagnetic induction. This utilization achieves a mechanically non-contact measuring method for objective fluids. In this study, verification experiments for practical measurement were conducted in upward gas—liquid two-phase flow. The results of the experiments have verified that the proposed measuring technique is useful as a method for flow regime discrimination.

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Dupuy, Hélène. « Non-linear description of massive neutrinos in the framework of large-scale structure formation ». Proceedings of the International Astronomical Union 11, S308 (juin 2014) : 121–24. http://dx.doi.org/10.1017/s174392131600973x.

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AbstractThere is now no doubt that neutrinos are massive particles fully involved in the non-linear growth of the large-scale structure of the universe. A problem is that they are particularly difficult to include in cosmological models because the equations describing their behavior in the non-linear regime are cumbersome and difficult to handle. In this manuscript I present a new method allowing to deal with massive neutrinos in a very simple way, based on basic conservation laws. This method is still valid in the non-linear regime. The key idea is to describe neutrinos as a collection of single-flow fluids instead of seeing them as a single hot multi-flow fluid. In this framework, the time evolution of neutrinos is encoded in fluid equations describing macroscopic fields, just as what is done for cold dark matter. Although valid up to shell-crossing only, this approach is a further step towards a fully non-linear treatment of the dynamical evolution of neutrinos in the framework of large-scale structure growth.

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Dirks, Jan-Henning. « Physical principles of fluid-mediated insect attachment - Shouldn’t insects slip ? » Beilstein Journal of Nanotechnology 5 (28 juillet 2014) : 1160–66. http://dx.doi.org/10.3762/bjnano.5.127.

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Insects use either hairy or smooth adhesive pads to safely adhere to various kinds of surfaces. Although the two types of adhesive pads are morphologically different, they both form contact with the substrate via a thin layer of adhesive fluid. To model adhesion and friction forces generated by insect footpads often a simple “wet adhesion” model is used, in which two flat undeformable substrates are separated by a continuous layer of fluid. This review summarizes the key physical and tribological principles that determine the adhesion and friction in such a model. Interestingly, such a simple wet-adhesion model falls short in explaining several features of insect adhesion. For example, it cannot predict the observed high static friction forces of the insects, which enable them to cling to vertical smooth substrates without sliding. When taking a closer look at the “classic” attachment model, one can see that it is based on several simplifications, such as rigid surfaces or continuous layers of Newtonian fluids. Recent experiments show that these assumptions are not valid in many cases of insect adhesion. Future tribological models for insect adhesion thus need to incorporate deformable adhesive pads, non-Newtonian properties of the adhesive fluid and/or partially “dry” or solid-like contact between the pad and the substrate.

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Ren, Zhongfu, Fanzhi Kong, Yongxiang Kang et Haiyan Kong. « Thermal and hydrodynamic performance analysis of charged jet in electrospinning ». International Journal of Numerical Methods for Heat & ; Fluid Flow 24, n^o 6 (29 juillet 2014) : 1260–67. http://dx.doi.org/10.1108/hff-01-2013-0028.

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Purpose – The purpose of this paper is to theoretically investigate the thermal and hydrodynamic performance of the flow pattern of fluid in the charged jet. The flow pattern includes laminar flow in which all fluid layers move at different accelerated speeds, and shear forces between the fluid layers give rise to friction forces. This is a favorable condition for the parallel arrangement of the branches on polymer molecules. Design/methodology/approach – The dynamic mechanism of the flow pattern is conducted through analyzing the forces acting on the charged jet. The differential equation obtained in the analyzing process has the solution designating the laminar flow pattern of the fluid in the charged jet. Findings – The fluid in the charged jet flows in laminar pattern, which is favorable to the parallel arrangement of the branches on polymer molecules. Research limitations/implications – Although the flow pattern is conveyed by means of the simple condition of uniformly accelerated motion, it has the similar effect on the arrangement of the polymer molecules in general conditions, such as non-Newtonian fluids and non-uniformly accelerated motions. Originality/value – The laminar flow introduced by this paper to the charged jet implies anisotropic properties of the electrospun nanofibers.

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Bojko, Marian, Sylva Drábková, Josef Veselý et Rostislav Zapletal. « Numerical modelling of a non-Newtonian fluid in the twin-screw pump ». EPJ Web of Conferences 269 (2022) : 01005. http://dx.doi.org/10.1051/epjconf/202226901005.

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Twin screw pump is a positive displacement pump, which is widely used in numerous type of foodstuff applications. Numerical CFD analysis presented in this paper focuses on the investigation of the influence of the clearances and the non-Newtonian behaviour of the fluid. The pump operates at low rotational speed and low inlet pressure. As the first step 3D CFD simulation of twin-screw pump non-rotating segment has been carried out using static mesh without rotation. Various empirical equations have been applied to represent the viscosity relations for non-Newtonian fluid in simple shear. The results are compared for two different values of clearances and various approaches to non-Newtonian fluid description. The obtained results showed the effect of both tested parameters. The physical experiment is under preparation to validate the calculation results.

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Vu, Truong V., Vinh T. Nguyen, Phan H. Nguyen, Nang X. Ho, Binh D. Pham, Hoe D. Nguyen et Hung V. Vu. « Dynamics of a contracting fluid compound filament with a variable density ratio ». Science and Technology Development Journal 24, n^o 2 (10 mai 2021) : first. http://dx.doi.org/10.32508/stdj.v24i2.2515.

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Introduction: Compound fluid filaments appear in many applications, e.g., drug delivery and processing or microfluidic systems. This paper focuses on the numerical simulation of an incompressible, immiscible, and Newtonian fluid for the contraction process of a fluid compound filament by solving the Navier-Stokes equations. The front-tracking method is used to solve this problem, which uses connected segments (Lagrangian grid) that move on a fixed grid (Eulerian grid) to represent the interface between the liquids. Methods: The interface points are advected by the velocity interpolated from those of the fixed grid using the area weighting function. The coordinates of the interface points are used to construct the indicators specifying the different fluids and compute the interfacial tension force. Results: The simulation results show that under the effects of the interfacial tension, the capsuleshaped filament can transform into a spherical compound droplet (i.e., non-breakup) or can break up into smaller spherical compound and simple droplets (i.e., breakup). When the density ratio of the outer to middle fluids increases, the filament changes from non-breakup to breakup upon contraction. Conclusion: Increasing the density ratio enhances the breakup of the compound filament during contraction. The breakup is also promoted by increasing the initial length of the filament.

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Shi, Y., et G. H. Tang. « Lattice Boltzmann Simulation of Droplet Formation in Non-Newtonian Fluids ». Communications in Computational Physics 17, n^o 4 (avril 2015) : 1056–72. http://dx.doi.org/10.4208/cicp.2014.m333.

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AbstractNewtonian and non-Newtonian dispersed phase droplet formation in non-Newtonian continuous phase in T-junction and cross junction microchannels are investigated by the immiscible lattice BGK model. The effects of the non-Newtonian fluid power-law exponent, viscosity and interfacial tension on the generation of the droplet are studied. The final droplet size, droplet generation frequency, and detachment point of the droplet change with the power-law exponent. The results reveal that it is necessary to take into account the non-Newtonian rheology instead of simple Newtonian fluid assumption in numerical simulations. The present analysis also demonstrates that the lattice Boltzmann method is of potential to investigate the non-Newtonian droplet generation in multiphase flow.

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Shaukin, Shilpi, Satosh U. Kafle et Mrinalini Singh. « Spectrum of Exfoliative Cytology at Birat Medical College and Teaching Hospital ». Birat Journal of Health Sciences 4, n^o 2 (4 septembre 2019) : 734–37. http://dx.doi.org/10.3126/bjhs.v4i2.25456.

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Introduction: Exfoliative cytological study of body fluids is easy, simple, rapid, cost effective and patient compliant investigation that helps in characterizing the disease into their varying subtypes. These presumptive and sometimes definitive diagnoses are in most cases the cornerstone which helps in staging and prognosis of the patient Objective: To determine the spectrum of malignant and non-malignant lesions in exfoliative cytology Methodology: This was a quantitative retrospective cross sectional study conducted at Birat Medical College Teaching Hospital from 24th December 2014 to 24th December 2018. All the exfoliative samples received at the lab were accepted in our study. Results: Of the 300 samples received, the maximum number were those of sputum followed by pleural fluid and ascitic fluid. Peritoneal fluid, Cerebrospinal fluid, synovial fluid, fluid from suspected abscess and breast fluid were also received. Malignancy was found in 1.67% of the samples studies. Conclusion: A study of different cytomorphological features of exfoliative cytology samples will help in establishing the role of cytology as an important diagnostic tool in improving the effectiveness of diagnosis , treatment & prognosis of the patient in the medical field.

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Maharjan, Sushana, Sabin Ranabhat, Mamata Tiwari, Anita Bhandari, Bidur Prasad Osti et Puja Neopane. « Exfoliative cytology analysis from different sites of the body ». Journal of Chitwan Medical College 7, n^o 2 (30 juin 2017) : 33–39. http://dx.doi.org/10.3126/jcmc.v7i2.23674.

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Background: Cytological study of body fluids a non-invasive, simple procedure, relatively inexpensive, and helps in faster reporting that has high population acceptance. The present study aims to determine the proportion of malignant and non malignant lesions. Methods: A total of 1129 specimens of exfoliative cytology were examined during the period over five years from year January 2011 to December 2016 at Department of Pathology at Chitwan Medical College Teaching Hospital, Nepal. The fluid received was centrifuged at 3000 revolutions per minute for five minutes. Smears were made from the sediment. Two to three slides were air dried and stained with Giemsa stain. One slide was immediately fixed in 95% alcohol and stained with Papanicolaou (Pap) stain for cytological evaluation. Results: Pleural fluid was most common specimen (49.3%) with peritoneal fluid (32%), pericardial fluid (1%), BAL (7.8%), CSF (4%), sputum (3.4%), synovial fluid (2%) and urine (0.5%) specimens. Male to female ratio was 1.33:1. Maximum cases belonged to age group of 50-69 years. Only (5.8%) 67 cases were neoplastic. The maximum cases of malignant neoplasm were detected in pericardial fluid and pleural fluid, each 21 (1.8%) cases, and 20 (1.7%) cases BAL. Malignant effusions were detected in 46 (4%) cases. Maximum malignant cases were adenocarcinoma (71.6%), followed by squamous cell carcinoma (20.8%). Conclusion: Exfoliative cytology should be suggested in all cases of effusion and suspected malignancies which helps in reaching at a particular diagnosis and aids in further management.

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Mikielewicz, Dariusz, et Jarosław Mikielewicz. « Criteria for selection of working fluid in low-temperature ORC ». Chemical and Process Engineering 37, n^o 3 (1 septembre 2016) : 429–40. http://dx.doi.org/10.1515/cpe-2016-0035.

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Abstract The economics of an ORC system is strictly linked to thermodynamic properties of the working fluid. A bad choice of working fluid could lead to a less efficient and expensive plant/generation unit. Some selection criteria have been put forward by various authors, incorporating thermodynamic properties, provided in literature but these do not have a general character. In the paper a simple analysis has been carried out which resulted in development of thermodynamic criteria for selection of an appropriate working fluid for subcritical and supercritical cycles. The postulated criteria are expressed in terms of non-dimensional numbers, which are characteristic for different fluids. The efficiency of the cycle is in a close relation to these numbers. The criteria are suitable for initial fluid selection. Such criteria should be used with other ones related to environmental impact, economy, system size, etc. Examples of such criteria have been also presented which may be helpful in rating of heat exchangers, which takes into account both heat transfer and flow resistance of the working fluid.

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Hartkamp, Remco, B. D. Todd et Stefan Luding. « A constitutive framework for the non-Newtonian pressure tensor of a simple fluid under planar flows ». Journal of Chemical Physics 138, n^o 24 (28 juin 2013) : 244508. http://dx.doi.org/10.1063/1.4810746.

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MENDONÇA, J. T., A. SERBETO et S. ALI. « Effective charge of photons and plasmons ». Journal of Plasma Physics 76, n^o 3-4 (8 janvier 2010) : 287–92. http://dx.doi.org/10.1017/s002237780999047x.

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AbstractWe review the concept of photon effective charge in a plasma, and extend it to the case of longitudinal photons or plasmons. A simple electrostatic fluid model is considered in a non-magnetized and non-relativistic plasma. The contribution of the ions to the plasmon charge is also considered.

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Chandan, Dr Rajesh h., Dr Sumana Pawar et Dr Purushotham Redd. « Analysis of diagnostic value of cytological smear method versus cell block method in body fluids with clinical and biochemical correlation : study of 150 cases ». Tropical Journal of Pathology and Microbiology 7, n^o 1 (20 février 2021) : 9–16. http://dx.doi.org/10.17511/jopm.2021.i01.02.

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Background: Aspiration of serous cavities is a simple and relatively non-invasive technique toachieve diagnosis. Cytological evaluation of body cavity fluid is diagnostically challenging. Especiallyin malignant effusions, helps in staging, prognosis and management of the patients. Aims: Toassess the utility and sensitivity of cell block method over conventional smear technique incytodiagnosis of the serous effusions. And to assess the utility and sensitivity of cytologicalevaluation of body fluids with biochemical and clinical correlation. Methods: A total of 150 fluidspecimens were examined for conventional cytological smear (CS) and cell block method (CB). Outof 150 fluids, 96 were pleural fluid, 48 were ascitic fluid, 04 fluid from pouch of Douglas and 01 wasfrom synovial fluid. Results: In this study, the utility of the CB method in the cytodiagnosis ofmalignant effusions was found to be highly significant as compared to the CS method. The additionalyield of malignancy was 12% more as was obtained by the CB method. Conclusion: For the finalcytodiagnosis of body fluid, there is statistically significant difference between the two techniques. Inother words, CB is superior to CS method. It gives more information about the architecturalarrangement and the likely source of primary. More important is that diagnostic material in cellblocks is available for special studies for Immunohistochemistry which can further supplement ourknowledge about the primary source of metastasis.

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Wu, Ge Ping, Ping Lu et Jun Wang. « Non-Uniform Heating Condition Effects in Microchannels of the MTPV Systems ». Applied Mechanics and Materials 437 (octobre 2013) : 120–23. http://dx.doi.org/10.4028/www.scientific.net/amm.437.120.

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Heat transfer and fluid flow in the microchannel cooling passages of plane cell type MTPV systems are numerically investigated. The Finite Volume method is adopted for the governing equations discretization; The SIMPLE method is applied to deal with the linkage between pressure and velocities. The microscale effects, such as surface roughness and viscous dissipation are taken into account. Influence of non-uniform heating condition on the flow and heat transfer characteristics of the microchannel cooling passage was discussed. The computer simulations were validated by the experiment data. Numerical results confirm that the effects of non-uniform heating condition on fluid flow and heat transfer in microchannels could not be neglected.

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Dirks, Jan-Henning, et Walter Federle. « Mechanisms of fluid production in smooth adhesive pads of insects ». Journal of The Royal Society Interface 8, n^o 60 (5 janvier 2011) : 952–60. http://dx.doi.org/10.1098/rsif.2010.0575.

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Insect adhesion is mediated by thin fluid films secreted into the contact zone. As the amount of fluid affects adhesive forces, a control of secretion appears probable. Here, we quantify for the first time the rate of fluid secretion in adhesive pads of cockroaches and stick insects. The volume of footprints deposited during consecutive press-downs decreased exponentially and approached a non-zero steady state, demonstrating the presence of a storage volume. We estimated its size and the influx rate into it from a simple compartmental model. Influx was independent of step frequency. Fluid-depleted pads recovered maximal footprint volumes within 15 min. Pads in stationary contact accumulated fluid along the perimeter of the contact zone. The initial fluid build-up slowed down, suggesting that flow is driven by negative Laplace pressure. Freely climbing stick insects left hardly any traceable footprints, suggesting that they save secretion by minimizing contact area or by recovering fluid during detachment. However, even the highest fluid production rates observed incur only small biosynthesis costs, representing less than 1 per cent of the resting metabolic rate. Our results show that fluid secretion in insect wet adhesive systems relies on simple physical principles, allowing for passive control of fluid volume within the contact zone.

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Evans, C. R., et K. L. Johnson. « The Rheological Properties of Elastohydrodynamic Lubricants ». Proceedings of the Institution of Mechanical Engineers, Part C : Journal of Mechanical Engineering Science 200, n^o 5 (septembre 1986) : 303–12. http://dx.doi.org/10.1243/pime_proc_1986_200_134_02.

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The methods of measuring the rheological properties of EHD lubricants are reviewed, but for pressures in excess of 1.0 GPa there is currently no simple alternative to the disc machine. A technique has been developed which enables disc machine traction tests to be carried out at constant mean film temperature. Isothermal tests provide further evidence for the existence of a limiting shear stress τc at which the fluid shears in the manner of a plastic solid. At stresses below this limit the experimental data are found to be in very good accord with the non-linear Maxwell rheological model based on the Eyring theory of fluid flow proposed by Johnson and Tevaarwerk and by Hirst and Moore. The model incorporates three fluid properties: shear modulus G, viscosity τ and Eyring stress τ0. Disc machine measurements of τ, τ0 and the limiting shear stress τc for three fluids—a mineral oil HVI 650, a synthetic polyphenyl ether 5P4E and a traction fluid Santotrac 50—are presented for a range of pressures (0.6–2.5 GPa) and temperatures (40–120°C).

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Xu, Chang-Lian, et Yu-Zhong Wang. « Novel dual superlyophobic materials in water–oil systems : under oil magneto-fluid transportation and oil–water separation ». Journal of Materials Chemistry A 6, n^o 7 (2018) : 2935–41. http://dx.doi.org/10.1039/c7ta10739k.

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Moslemi, Mehdi, et Kourosh Javaherdeh. « Viscous Dissipation Effect in the Free Convection of Non-Newtonian Fluid with Heat Generation or Absorption Effect on the Vertical Wavy Surface ». Journal of Applied Mathematics 2021 (11 octobre 2021) : 1–14. http://dx.doi.org/10.1155/2021/7567981.

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The present article analyzes the effect of viscous dissipations on natural convection heat transfer. The power law model for non-Newtonian fluid with heat generation or absorption effect along a sinusoidal wavy surface with isothermal boundary condition is investigated. A simple coordinate transform is employed to map the wavy surface into a flat surface, and also, the fully implicit finite difference method is incorporated for the numerical solution. The findings of this study can help better understand the effect of parameters such as the Brinkman number, heat generation/absorption, wave amplitude magnitude, and generalized Prandtl number on convective heat transfer in dilatant and pseudoplastic non-Newtonian. Results show that as the Brinkman number increases, the amount of heat transfer decreases. This is physically justifiable considering that the fluid becomes warmer due to the viscous dissipation, decreasing its temperature difference with the constant temperature surface. Also, the effect of the power law viscosity index is surveyed. It is demonstrated that the magnitude of the local Nusselt number in the plane leading edge has the smallest quantity for pseudoplastic fluids compared to dilatant Newtonian fluids. Additionally, as the distance from the plane leading edge increases, the heat transfer declines.

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Nohel, John A., Robert L. Pego et Athanasios E. Tzavaras. « Stability of discontinuous steady states in shearing motions of a non-Newtonian fluid ». Proceedings of the Royal Society of Edinburgh : Section A Mathematics 115, n^o 1-2 (1990) : 39–59. http://dx.doi.org/10.1017/s0308210500024550.

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SynopsisWe study the nonlinear stability of discontinuous steady states of a model initial-boundary value problem in one space dimension for incompressible, isothermal shear flow of a non-Newtonian fluid driven by a constant pressure gradient. The non-Newtonian contribution to the shear stress is assumed to satisfy a simple differential constitutive law. The key feature is a non-monotone relation between the total steady shear stress and shear strain-rate that results in steady states having, in general, discontinuities in the strain rate. We show that every solution tends to a steady state as t → ∞, and we identify steady states that are stable.

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