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Journal articles on the topic 'Pécule'
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Novkirishka-Stoyanova, Malina. "Le pécule romain et l’origine de la responsabilite limitée en droit romain." Studia Universitatis Babeş-Bolyai Iurisprudentia 65, no. 4 (March 16, 2021): 672–725. http://dx.doi.org/10.24193/subbiur.65(2020).4.20.
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The study is a part of one deeper study on the Roman Law about the slaves and personae alieni iuris presented in its evolution. The accent is mainly on the emergence of the limited liability of the pater familias/ dominus in the case of contracts with pecuniary property. It is a study for the place of the actio de peculio among the other actiones adjectitiae qualitatis, the notion of the merx pexuliaris and the concessio particulii.
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Bénézech, Michel, and Jean-René Bernadet. "L’argent des aliénés : pécule et monnaie de nécessité à l’hôpital psychiatrique autonome de Cadillac." Annales Médico-psychologiques, revue psychiatrique 170, no. 8 (October 2012): 596–600. http://dx.doi.org/10.1016/j.amp.2012.08.004.
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Py, Michel. "Un pécule d’oboles de Marseille du milieu du Ve siècle avant notre ère sur l’oppidum du Marduel à Saint-Bonnet-du-Gard." Revue numismatique 6, no. 174 (2017): 119–40. http://dx.doi.org/10.3406/numi.2017.3353.
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Guihard, Pierre-Marie, Cécile Allinne, and Éric Broine. "La fouille du trésor monétaire de Saint-Germain-de-Varreville (Manche) : stratigraphie d’un pécule de 14 528 nummi (première moitié du ive siècle)." Annales de Normandie 63e année, no. 1 (2013): 3. http://dx.doi.org/10.3917/annor.631.0003.
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Charbonneau, Alexandre. "Jean-Pierre Le Crom et Marc Boninchi (dir.), La chicotte et le pécule. Les travailleurs à l’épreuve du droit colonial français (XIXe-XXe siècles)." Revue de droit comparé du travail et de la sécurité sociale, no. 2 (May 31, 2022): 168–71. http://dx.doi.org/10.4000/rdctss.3858.
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Lachaud, Stéphanie. "Approche socio-économique du petit peuple des vignes en Sauternais aux XVIIe et XVIIIe siècles." Annales du Midi : revue archéologique, historique et philologique de la France méridionale 129, no. 298 (2017): 231–53. http://dx.doi.org/10.3406/anami.2017.8879.
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Petit vignoble du sud-ouest du royaume de France, le Sauternais connaît une population rurale assez abondante aux XVIIe et XVIIIe siècles, majoritairement composée de vignerons, de journaliers ou manouvriers. Cette société rurale largement organisée autour de la production viticole est en mutation aux XVII e et XVIII e siècles, car le vignoble s’oriente vers une production de plus grande qualité et vers les exportations sous l’impulsion des grands propriétaires. Mais quelle est la place de ces modestes travailleurs de la terre dans un vignoble largement tenu par des élites, nobiliaires ou bordelaises ? Cette place a-t-elle notablement évolué en lien avec la transformation progressive des perspectives économiques ? La réalité économique que recouvrent ces dénominations de manouvriers et de journaliers est complexe et modeste à la fois, dans une société rurale où la pluriactivité et la polyculture restent bien présentes. Le cadre de vie de ces petites gens de la terre confirme cette précarité économique car il se caractérise par une plus grande simplicité que chez les laboureurs, chez certains artisans (notamment les tonneliers) ou chez les marchands : une voire deux pièces à vivre, une absence d’intimité, un mobilier réduit au minimum. Les sources permettent aussi d’envisager les questions d’endogamie et surtout d’homogamie sociales, mais aussi celle des mobilités : il apparaît alors que les trajectoires d’ascension sociale des petites gens restent difficiles à retracer car elles sont rares. Les mobilités observées sont souvent géographiques et temporaires, avec notamment des emplois de domestiques à Bordeaux ou des emplois saisonniers (même s’ils sont peu nombreux en raison du calendrier viticole) pour se constituer un petit pécule en vue du mariage. Ces modestes travailleurs de la terre sont un rouage essentiel mais peu connu de la formation d’un vignoble de qualité en Bordelais.
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Lacroix, Annick. "Jean-Pierre Le Crom et Marc Boninchi (dir.), La chicotte et le pécule. Les travailleurs à l’épreuve du droit colonial français ( xix e - xx e siècles) , Rennes, Presses universitaire de Rennes, « Histoire », 2021, 332 p." Le Mouvement Social N° 282, no. 1 (September 8, 2023): 150–53. http://dx.doi.org/10.3917/lms1.282.0150.
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Simon, Bence, Anita Benes, Szilvia Joháczi, and Ferenc Barna. "New excavation of the Roman Age settlement at Budapest dist. XVII, Péceli út (15127) site." Dissertationes Archaeologicae 3, no. 7 (October 16, 2020): 273–80. http://dx.doi.org/10.17204/dissarch.2019.273.
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In autumn 2019 the staff of the Institute of Archaeological Sciences conducted a rescue excavation in the suburbs of Budapest, on the territory of Pécel. Based on the long research history of the investigated site (Budapest dist. XVII, Péceli út) a settlement of the Imperial Period was expected. The excavation confirmed the expectations and two buildings, several ditches, an outdoor oven and numerous refuse pits were unearthed from the 3rd–4th century AD. The features contained many Samian ware fragments, which shed light on the Roman-Barbarian trade relations during the middle Imperial Period.
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Dion, Robert, and Frances Fortier. "Péculat biographique et enchevêtrement générique." Protée 31, no. 1 (June 10, 2004): 51–64. http://dx.doi.org/10.7202/008501ar.
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Résumé Cette étude examine les divers phénomènes de transposition qui se trouvent au principe de l’ouvrage de Thomas De Quincey intitulé Les Derniers Jours d’Emmanuel Kant (1827). La première partie révèle la singularité essentielle de ce texte qui a longtemps été attribué à De Quincey lui-même alors qu’il n’était, de fait, que la reprise intégrale, en traduction, d’Immanuel Kant in seinen letzten Lebensjahren (1804), œuvre du secrétaire de Kant, Wasianski. Ce matériau biographique se voit transposé par l’ajout d’un appareil de notes qui vient gauchir le statut proprement factuel du texte et lui donner une tonalité ironique ; les diverses traductions françaises du texte de De Quincey viendront d’ailleurs encore épaissir le palimpseste. La seconde partie de l’étude met en lumière, à partir de traits textuels majeurs (brouillage énonciatif, télescopage des temps, etc.), toute une série de transpositions proprement génériques qui interfèrent avec les genres mineurs, en vogue à l’époque, du recueil d’anecdotes, des mémoires et du tombeau. En fin de compte, Les Derniers Jours d’Emmanuel Kant apparaissent comme le détournement délibéré, sur les plans diégétique, discursif et axiologique, des traits prototypiques de la biographie.
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Visudmedanukul, Punlop, and Masashi Kamon. "Graphically Determined Column Péclet Number." Journal of Geotechnical and Geoenvironmental Engineering 133, no. 2 (February 2007): 227–30. http://dx.doi.org/10.1061/(asce)1090-0241(2007)133:2(227).
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Fournier, Clarisse, Marc Michard, and Françoise Bataille. "Heat Transfer in a Laminar Channel Flow Generated by Injection Through Porous Walls." Journal of Fluids Engineering 129, no. 8 (March 18, 2007): 1048–57. http://dx.doi.org/10.1115/1.2746908.
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Steady state similarity solutions are computed to determine the temperature profiles in a laminar channel flow driven by uniform fluid injection at one or two porous walls. The temperature boundary conditions are non-symmetric. The numerical solution of the governing equations permit to analyze the influence of the governing parameters, the Reynolds and Péclet numbers. For both geometries, we deduce a scaling law for the boundary layer thickness as a function of the Péclet number. We also compare the numerical solutions with asymptotic expansions in the limit of large Péclet numbers. Finally, for non-symmetric injection, we derive from the computed temperature profile a relationship between the Nusselt and Péclet numbers.
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Lohöfer, Georg. "On the relation between Nusselt and Péclet number in high Péclet number convective heat transfer." International Journal of Thermal Sciences 109 (November 2016): 201–5. http://dx.doi.org/10.1016/j.ijthermalsci.2016.06.006.
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DURMUS, A., I. BOZTOSUN, and F. YASUK. "COMPARATIVE STUDY OF THE MULTIQUADRIC AND THIN-PLATE SPLINE RADIAL BASIS FUNCTIONS FOR THE TRANSIENT-CONVECTIVE DIFFUSION PROBLEMS." International Journal of Modern Physics C 17, no. 08 (August 2006): 1151–69. http://dx.doi.org/10.1142/s0129183106009783.
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The numerical solutions of the unsteady transient-convective diffusion problems are investigated by using multiquadric (MQ) and thin-plate spline (TPS) radial basis functions (RBFs) based on mesh-free collocation methods with global basis functions. The results of radial basis functions are compared with the mesh-dependent boundary element and finite difference methods as well as the analytical solution for high Péclet numbers. It is reported that for low Péclet numbers, MQ-RBF provides excellent agreement, while for high Péclet numbers, TPS-RBF is better than MQ-RBF.
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App, J. F. F., and K. Yoshioka. "Impact of Reservoir Permeability on Flowing Sandface Temperatures: Dimensionless Analysis." SPE Journal 18, no. 04 (April 17, 2013): 685–94. http://dx.doi.org/10.2118/146951-pa.
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Summary Layer flow contributions are increasingly being quantified through the analysis of measured sandface flowing temperatures. It is commonly known that the maximum temperature change is affected by the magnitude of the drawdown and the Joule-Thomson expansion coefficient of the fluid. Another parameter that strongly impacts layer sandface flowing temperatures is the layer permeability. Aside from determining the drawdown, the layer permeability also affects the ratio of heat transfer by convection to conduction within a reservoir. The impact of permeability can be represented by the Péclet number, which is a dimensionless quantity representing the ratio of heat transfer by convection to conduction. The Péclet number is directly proportional to reservoir permeability. Through dimensionless analysis, it will be shown that for a given drawdown (based on a dimensionless Joule-Thomson expansion coefficient JTD) the temperature change diminishes at low Péclet numbers and increases at high Péclet numbers. This implies that for low-permeability reservoirs such as shale gas or tight oil, the temperature changes will be minimal (less than 0.1ºF) despite the large drawdowns in many instances. Dimensionless analysis is performed for both steady-state and transient thermal models. Results from multilayer transient simulations illustrate the ability to identify contrasting permeability layers on the basis of the Péclet number effect.
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SHORT, MARK, and DAVID A. KESSLER. "Asymptotic and numerical study of variable-density premixed flame propagation in a narrow channel." Journal of Fluid Mechanics 638 (September 29, 2009): 305–37. http://dx.doi.org/10.1017/s0022112009990966.
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The influence of thermal expansion on the dynamics of thick to moderately thick premixed flames (flame thickness less than or comparable to the channel height) for a variable-density flow in a narrow, rectangular channel is explored. The study is conducted within the framework of the zero-Mach-number, variable-density Navier–Stokes equations. Both adiabatic and non-adiabatic channel walls are considered. A small Péclet number asymptotic solution is developed for steady, variable-density flame propagation in the narrow channel. The dynamics of channel flames are also examined numerically for O(1) Péclet numbers in configurations which include flame propagation in a semi-closed channel from the closed to the open end of the channel, flame propagation in a semi-closed channel towards the closed end of the channel and flame propagation in an open channel in which a Poiseuille flow (flame assisting or flame opposing) is imposed at the channel inlet. Comparisons of the finite-Péclet-number dynamics are made with the behaviour of the small-Péclet-number solutions. We also compare how thermal expansion modifies the flow dynamics from those determined by a constant-density model. The small-Péclet-number variable-density solution for a flame propagating in a circular pipe is given in the Appendix.
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Lucking Bigué, Jean-Philippe, François Charron, and Jean-Sébastien Plante. "Squeeze-strengthening of magnetorheological fluids (part 1): Effect of geometry and fluid composition." Journal of Intelligent Material Systems and Structures 29, no. 1 (May 3, 2017): 62–71. http://dx.doi.org/10.1177/1045389x17705214.
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Recent research has shown that magnetorheological fluid can undergo squeeze-strengthening when flow conditions promote filtration. While a Péclet number has been used to predict filtration in non-magnetic two-phase fluids submitted to slow compression, the approach has yet to be adapted to magnetorheological fluid behavior in order to predict the conditions leading to squeeze-strengthening behavior of magnetorheological fluid. In this article, a Péclet number is derived and adapted to the Bingham rheological model. This Péclet number is then compared to the experimental occurrence of squeeze-strengthening behavior obtained from several squeeze geometries and magnetorheological fluid compositions submitted to pure-squeeze conditions. Results show that the Péclet number well predicts the occurrence of squeeze-strengthening behavior in high-concentration magnetorheological fluid made from various particle sizes and using various squeeze geometries. Moreover, it is shown that squeeze-strengthening occurrence is increased when using annulus geometries or by increasing average particle radius. While lowering concentration increases filtration, tested conditions only led to squeeze-strengthening behavior after concentration had increased close to packing limit. Altogether, results suggest that the Péclet number derived in this study can be used to predict the occurrence of squeeze-strengthening for various magnetorheological fluids and squeeze geometries using the well-known rheological properties of magnetorheological fluids.
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BONN, JAMES, and RICHARD M. McLAUGHLIN. "Sensitive enhanced diffusivities for flows with fluctuating mean winds: a two-parameter study." Journal of Fluid Mechanics 445 (October 16, 2001): 345–75. http://dx.doi.org/10.1017/s002211200100564x.
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Enhanced diffusion coefficients arising from the theory of periodic homogenized averaging for a passive scalar diffusing in the presence of a large-scale, fluctuating mean wind superimposed upon a small-scale, steady flow with non-trivial topology are studied. The purpose of the study is to assess how the extreme sensitivity of enhanced diffusion coefficients to small variations in large-scale flow parameters previously exhibited for steady flows in two spatial dimensions is modified by either the presence of temporal fluctuation, or the consideration of fully three-dimensional steady flow. We observe the various mixing parameters (Péclet, Strouhal and periodic Péclet numbers) and related non-dimensionalizations. We document non-monotonic Péclet number dependence in the enhanced diffusivities, and address how this behaviour is camouflaged with certain non-dimensional groups. For asymptotically large Strouhal number at fixed, bounded Péclet number, we establish that rapid wind fluctuations do not modify the steady theory, whereas for asymptotically small Strouhal number the enhanced diffusion coefficients are shown to be represented as an average over the steady geometry. The more difficult case of large Péclet number is considered numerically through the use of a conjugate gradient algorithm. We consider Péclet-number-dependent Strouhal numbers, S = QPe−(1+γ), and present numerical evidence documenting critical values of γ which distinguish the enhanced diffusivities as arising simply from steady theory (γ < −1) for which fluctuation provides no averaging, fully unsteady theory (γ ∈ (−1, 0)) with closure coefficients plagued by non-monotonic Péclet number dependence, and averaged steady theory (γ > 0). The transitional case with γ = 0 is examined in detail. Steady averaging is observed to agree well with the full simulations in this case for Q [les ] 1, but fails for larger Q. For non-sheared flow, with Q [les ] 1, weak temporal fluctuation in a large-scale wind is shown to reduce the sensitivity arising from the steady flow geometry; however, the degree of this reduction is itself strongly dependent upon the details of the imposed fluctuation. For more intense temporal fluctuation, strongly aligned orthogonal to the steady wind, time variation averages the sensitive scaling existing in the steady geometry, and the present study observes a Pe1 scaling behaviour in the enhanced diffusion coefficients at moderately large Péclet number. Finally, we conclude with the numerical documentation of sensitive scaling behaviour (similar to the two-dimensional steady case) in fully three dimensional ABC flow.
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BALMFORTH, NEIL J., and YUAN-NAN YOUNG. "Stratified Kolmogorov flow." Journal of Fluid Mechanics 450 (January 9, 2002): 131–67. http://dx.doi.org/10.1017/s0022111002006371.
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In this study we investigate the Kolmogorov flow (a shear flow with a sinusoidal velocity profile) in a weakly stratified, two-dimensional fluid. We derive amplitude equations for this system in the neighbourhood of the initial bifurcation to instability for both low and high Péclet numbers (strong and weak thermal diffusion, respectively). We solve amplitude equations numerically and find that, for low Péclet number, the stratification halts the cascade of energy from small to large scales at an intermediate wavenumber. For high Péclet number, we discover diffusively spreading, thermal boundary layers in which the stratification temporarily impedes, but does not saturate, the growth of the instability; the instability eventually mixes the temperature inside the boundary layers, so releasing itself from the stabilizing stratification there, and thereby grows more quickly. We solve the governing fluid equations numerically to compare with the asymptotic results, and to extend the exploration well beyond onset. We find that the arrest of the inverse cascade by stratification is a robust feature of the system, occurring at higher Reynolds, Richards and Péclet numbers – the flow patterns are invariably smaller than the domain size. At higher Péclet number, though the system creates slender regions in which the temperature gradient is concentrated within a more homogeneous background, there are no signs of the horizontally mixed layers separated by diffusive interfaces familiar from doubly diffusive systems.
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MIKELIĆ, ANDRO, and C. J. VAN DUIJN. "RIGOROUS DERIVATION OF A HYPERBOLIC MODEL FOR TAYLOR DISPERSION." Mathematical Models and Methods in Applied Sciences 21, no. 05 (May 2011): 1095–120. http://dx.doi.org/10.1142/s0218202510005264.
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In this paper, we upscale the classical convection-diffusion equation in a narrow slit. We suppose that the transport parameters are such that we are in Taylor's regime, i.e. we deal with dominant Péclet numbers. In contrast to the classical work of Taylor, we undertake a rigorous derivation of the upscaled hyperbolic dispersion equation. Hyperbolic effective models were proposed by several authors and our goal is to confirm rigorously the effective equations derived by Balakotaiah et al. in recent years using a formal Lyapounov–Schmidt reduction. Our analysis uses the Laplace transform in time and an anisotropic singular perturbation technique, the small characteristic parameter ε being the ratio between the thickness and the longitudinal observation length. The Péclet number is written as Cε-α, with α < 2. Hyperbolic effective model corresponds to a high Péclet number close to the threshold value when Taylor's regime turns to turbulent mixing and we characterize it by assuming 4/3 < α < 2. We prove that the difference between the dimensionless physical concentration and the effective concentration, calculated using the hyperbolic upscaled model, divided by ε2-α (the local Péclet number) converges strongly to zero in L2-norm. For Péclet numbers considered in this paper, the hyperbolic dispersion equation turns out to give a better approximation than the classical parabolic Taylor model.
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Salimi, Hamidreza, and Johannes Bruining. "Upscaling in Partially Fractured Oil Reservoirs Using Homogenization." SPE Journal 16, no. 02 (November 24, 2010): 273–93. http://dx.doi.org/10.2118/125559-pa.
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Summary Flow modeling in fractured reservoirs is largely confined to the so-called sugar-cube model. Here, we consider a situation where matrix blocks are connected to neighboring blocks so that part of the global flow occurs only in the matrix domain. We call this a partially fractured reservoir (PFR). As opposed to the sugar-cube model, global flow in the matrix blocks plays an important role in the PFR when the interconnections between the matrix blocks are sufficiently large. We apply homogenization to derive an upscaled model for PFRs that combines dual-porosity and dual-permeability concepts simultaneously. We formulate a well-posed fully implicit 3D upscaled numerical model and investigate oil-recovery mechanisms for different dimensionless characteristic numbers. As we found previously for the sugar-cube model, the Péclet number, defined here as the ratio of the capillary diffusion time in the matrix to the residence time of the fluids in the fracture, plays a crucial role. The gravity number and specific fracture/matrix-interface area play a secondary role. For low Péclet numbers and high gravity numbers, the results are sensitive to gravity and water-injection rates, but relatively insensitive to the specific fracture/matrix-interface area, matrix-block size, and reservoir geometry (i.e., sugar cube vs. PFR). At low Péclet numbers and high gravity numbers, ECLIPSE simulations using the Barenblatt or Warren and Root (BWR) approach give poor predictions and overestimate the oil recovery, but, at short injection times, show good agreement with the solution of the PFR model at intermediate Péclet numbers. At high Péclet numbers, the results are relatively insensitive to gravity, but sensitive to the other conditions mentioned. In particular, when the specific fracture/matrix-interface area is large, it enhances the imbibition and, consequently, leads to a higher oil production. If this specific interface area is small, it leads to a considerable retardation of the imbibition process, which leads to an earlier water breakthrough and lower oil recovery. The BWR (commercial simulator) simulations and the sugar-cube model result in inaccurate predictions of the oil-production rate at high Péclet numbers. This can be inferred from the discrepancy with respect to the PFR model for which we assert that it accurately predicts the oil recovery. We conclude that, at low Péclet numbers and large gravity numbers, it is advantageous to increase the water-injection rate to improve the net present value. However, at high Péclet numbers, increasing the flow rate may lead to uneconomical water cuts.
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Chang, Yu Chen, and Huan J. Keh. "Thermophoresis at small but finite Péclet numbers." Aerosol Science and Technology 52, no. 9 (August 15, 2018): 1028–36. http://dx.doi.org/10.1080/02786826.2018.1498588.
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Raynal, Florence, and Romain Volk. "Diffusiophoresis, Batchelor scale and effective Péclet numbers." Journal of Fluid Mechanics 876 (August 8, 2019): 818–29. http://dx.doi.org/10.1017/jfm.2019.589.
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We study the joint mixing of colloids and salt released together in a stagnation point or in a globally chaotic flow. In the presence of salt inhomogeneities, the mixing time is strongly modified depending on the sign of the diffusiophoretic coefficient $D_{dp}$. Mixing is delayed when $D_{dp}>0$ (salt-attracting configuration), or faster when $D_{dp}<0$ (salt-repelling configuration). In both configurations, as for molecular diffusion alone, large scales are barely affected in the dilating direction while the Batchelor scale for the colloids, $\ell _{c,diff}$, is strongly modified by diffusiophoresis. We propose here to measure a global effect of diffusiophoresis in the mixing process through an effective Péclet number built on this modified Batchelor scale. Whilst this small scale is obtained analytically for the stagnation point, in the case of chaotic advection, we derive it using the equation of gradients of concentration, following Raynal & Gence (Intl J. Heat Mass Transfer, vol. 40 (14), 1997, pp. 3267–3273). Comparing to numerical simulations, we show that the mixing time can be predicted by using the same function as in absence of salt, but as a function of the effective Péclet numbers computed for each configuration. The approach is shown to be valid when the ratio $D_{dp}^{2}/D_{s}D_{c}\gg 1$, where $D_{c}$ and $D_{s}$ are the diffusivities of the colloids and salt.
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Lister, John R. "On penetrative convection at low Péclet number." Journal of Fluid Mechanics 292 (June 10, 1995): 229–48. http://dx.doi.org/10.1017/s0022112095001509.
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A new theoretical model is developed for the growth of a convecting fluid layer at the base of a stable, thermally stratified layer when heated from below. The imposed convective heat flux is taken to be comparable to the heat flux conducted down the background gradient so that diffusion ahead of the interface between the convecting and stable layers makes a significant contribution to the interfacial heat flux and to the rate of rise of the interface. Closure of the diffusion problem in the stable region requires the interfacial heat flux to be specified, and it is argued that this is determined by the ability of convective eddies to mix warmed fluid below the interface downwards. The interfacial velocity, which may be positive or negative, is then determined by the joint requirements of continuity of heat flux and temperature. A similarity solution is derived for the case of an initially linear temperature gradient and uniform heating. Solutions are also given for a heat flux that undergoes a step change and for a heat flux determined from a four-thirds power law with a fixed base temperature. Numerical calculations show that the predictions of the model are in good agreement with previously reported experimental measurements. Similar calculations are applicable to a wide range of geophysical problems in which the tendency for diffusive restratification is comparable to that for mixed-layer deepening by entrainment.
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Michelin, Sébastien, and Eric Lauga. "Phoretic self-propulsion at finite Péclet numbers." Journal of Fluid Mechanics 747 (April 23, 2014): 572–604. http://dx.doi.org/10.1017/jfm.2014.158.
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AbstractPhoretic self-propulsion is a unique example of force- and torque-free motion on small scales. The classical framework describing the flow field around a particle swimming by self-diffusiophoresis neglects the advection of the solute field by the flow and assumes that the chemical interaction layer is thin compared to the particle size. In this paper we quantify and characterize the effect of solute advection on the phoretic swimming of a sphere. We first rigorously derive the regime of validity of the thin-interaction-layer assumption at finite values of the Péclet number (${Pe}$). Under this assumption, we solve computationally the flow around Janus phoretic particles and examine the impact of solute advection on propulsion and the flow created by the particle. We demonstrate that although advection always leads to a decrease of the swimming speed and flow stresslet at high values of the Péclet number, an increase can be obtained at intermediate values of ${Pe}$. This possible enhancement of swimming depends critically on the nature of the chemical interactions between the solute and the surface. We then derive an asymptotic analysis of the problem at small ${Pe}$ which allows us to rationalize our computational results. Our computational and theoretical analysis is accompanied by a parallel study of the influence of reactive effects at the surface of the particle (Damköhler number) on swimming.
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Pradhan, R. K., S. Shrestha, and D. B. Gurung. "Mathematical modeling of mixed-traffic in urban areas." Mathematical Modeling and Computing 9, no. 2 (2022): 226–40. http://dx.doi.org/10.23939/mmc2022.02.226.
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Transportation is the means of mobility. Due to the growth in the population, rising traffic on road, delay in the movement of vehicles and traffic chaos could be observed in urban areas. Traffic congestion causes many social and economic problems. Because of the convenience and the quickness, motor-bikes gradually become the main travel mode of urban cities. In this paper, we extend the Lighthill–Whitham–Richards (LWR) traffic flow model equation into the mixed-traffic flow of two entities: car and motor-bike in a unidirectional single-lane road segment. The flow of cars is modeled by the advection equation and the flow of motor-bikes is modeled by the advection-diffusion equation. The model equations for cars and motor-bikes are coupled based on total traffic density on the road section, and they are non-dimensionalized to introduce a non-dimensional number widely known as Péclet number. Explicit finite difference schemes satisfying the CFL conditions are employed to solve the model equations numerically to compute the densities of cars and motor-bikes. The simulation of densities over various time instants is studied and presented graphically. Finally, the average densities of cars and motor-bikes on the road section are calculated for various values of Péclet numbers and mixed-traffic behavior are discussed. It is observed that the mixed-traffic behavior of cars and motor-bikes depends upon the Péclet number. The densities of motor-bikes and cars in the mixed-traffic flow approach the equilibrium state earlier in time for smaller values of Péclet number whereas densities take longer time to approach the equilibrium for the greater values of Péclet number.
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Wells, Andrew J., Claudia Cenedese, J. Thomas Farrar, and Christopher J. Zappa. "Variations in Ocean Surface Temperature due to Near-Surface Flow: Straining the Cool Skin Layer." Journal of Physical Oceanography 39, no. 11 (November 1, 2009): 2685–710. http://dx.doi.org/10.1175/2009jpo3980.1.
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Abstract The aqueous thermal boundary layer near to the ocean surface, or skin layer, has thickness O(1 mm) and plays an important role in controlling the exchange of heat between the atmosphere and the ocean. Theoretical arguments and experimental measurements are used to investigate the dynamics of the skin layer under the influence of an upwelling flow, which is imposed in addition to free convection below a cooled water surface. Previous theories of straining flow in the skin layer are considered and a simple extension of a surface straining model is posed to describe the combination of turbulence and an upwelling flow. An additional theory is also proposed, conceptually based on the buoyancy-driven instability of a laminar straining flow cooled from above. In all three theories considered two distinct regimes are observed for different values of the Péclet number, which characterizes the ratio of advection to diffusion within the skin layer. For large Péclet numbers, the upwelling flow dominates and increases the free surface temperature, or skin temperature, to follow the scaling expected for a laminar straining flow. For small Péclet numbers, it is shown that any flow that is steady or varies over long time scales produces only a small change in skin temperature by direct straining of the skin layer. Experimental measurements demonstrate that a strong upwelling flow increases the skin temperature and suggest that the mean change in skin temperature with Péclet number is consistent with the theoretical trends for large Péclet number flow. However, all of the models considered consistently underpredict the measured skin temperature, both with and without an upwelling flow, possibly a result of surfactant effects not included in the models.
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Salimi, Hamidreza, and Johannes Bruining. "The Influence of Heterogeneity, Wetting, and Viscosity Ratio on Oil Recovery From Vertically Fractured Reservoirs." SPE Journal 16, no. 02 (December 23, 2010): 411–28. http://dx.doi.org/10.2118/140152-pa.
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Summary We use upscaling through homogenization to predict oil recovery from fractured reservoirs consisting of matrix columns, also called vertically fractured reservoirs (VFRs), for a variety of conditions. The upscaled VFR model overcomes limitations of the dual-porosity model, including the use of a shape factor. The purpose of this paper is to investigate three main physical aspects of multiphase flow in fractured reservoirs: reservoir wettability, viscosity ratio, and heterogeneity in rock/fluid properties. The main characteristic that determines reservoir behavior is the Péclet number that expresses the ratio of the average imbibition time divided by the residence time of the fluids in the fractures. The second characteristic dimensionless number is the gravity number. Upscaled VFR simulations, aimed at studying the mentioned features, add new insights. First, we discuss the results at low Péclet numbers. For only small gravity numbers, the effect of contact angle, delay time for the nonequilibrium capillary effect, the heterogeneity of the matrix-column size, and the matrix permeability can be ignored without appreciable loss of accuracy. The ultimate oil recovery for mixed-wet VFRs is approximately equal to the Amott index, and the oil production does not depend on the absolute value of the phase viscosity but on viscosity ratio. However, large gravity numbers enhance underriding, aggravated by large contact angles, longer delay times, and higher viscosity ratios. Layering can lead to an improvement or deterioration, depending on the fracture aperture and permeability distribution. At low Péclet numbers, the fractured reservoir behaves very similarly to a conventional reservoir and depends largely on the viscosity ratio and the gravity number. At high Péclet numbers, after water breakthrough, the oil recovery appears to be proportional to the cosine of the contact angle and inversely proportional to the sum of the oil and water viscosity. In addition, the mixed-wetting effect is more pronounced; there are significant influences of delay time (nonequilibrium effects), matrix permeability, matrix-column size, and the column-size distribution on oil recovery. At low gravity numbers and an effective length/thickness ratio larger than 10, the oil recovery is independent of the vertical-fracture-aperture distribution. For the same amount of injected water, the recovery at low Péclet numbers is larger than the recovery at high Péclet numbers.
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Forster, Michael A. "The importance of conduction versus convection in heat pulse sap flow methods." Tree Physiology 40, no. 5 (February 6, 2020): 683–94. http://dx.doi.org/10.1093/treephys/tpaa009.
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Abstract Heat pulse methods are a popular approach for estimating sap flow and transpiration. Yet, many methods are unable to resolve the entire heat velocity measurement range observable in plants. Specifically, the Heat Ratio (HRM) and Tmax heat pulse methods can only resolve slow and fast velocities, respectively. The Dual Method Approach (DMA) combines optimal data from HRM and Tmax to output the entire range of heat velocity. However, the transition between slow and fast methods in the DMA currently does not have a theoretical solution. A re-consideration of the conduction/convection equation demonstrated that the HRM equation is equivalent to the Péclet equation which is the ratio of conduction to convection. This study tested the hypothesis that the transition between slow and fast methods occurs when conduction/convection, or the Péclet number, equals one, and the DMA would be improved via the inclusion of this transition value. Sap flux density was estimated via the HRM, Tmax and DMA methods and compared with gravimetric sap flux density measured via a water pressure system on 113 stems from 15 woody angiosperm species. When the Péclet number ≤ 1, the HRM yielded accurate results and the Tmax was out of range. When the Péclet number > 1, the HRM reached a maximum heat velocity at approximately 15 cm hr −1 and was no longer accurate, whereas the Tmax yielded accurate results. The DMA was able to output accurate data for the entire measurement range observed in this study. The linear regression analysis with gravimetric sap flux showed an r2 of 0.541 for HRM, 0.879 for Tmax and 0.940 for DMA. With the inclusion of the Péclet equation, the DMA resolved the entire heat velocity measurement range observed across 15 taxonomically diverse woody species. Consequently, the HRM and Tmax are redundant sap flow methods and have been superseded by the DMA.
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Zhang, Lianzhong, Chenbing Zhang, Wen Liu, and Yizhi Ren. "Sedimentation of charged particles at large péclet number." China Particuology 2, no. 6 (December 2004): 253–55. http://dx.doi.org/10.1016/s1672-2515(07)60069-4.
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Plaschko, P. "High Péclet number heat exchange between cocurrent streams." Archive of Applied Mechanics 70, no. 8-9 (October 2000): 597–611. http://dx.doi.org/10.1007/s004190000085.
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Schnitzer, O., I. Frankel, and E. Yariv. "Shear-induced Electrokinetic Lift at Large Péclet Numbers." Mathematical Modelling of Natural Phenomena 7, no. 4 (2012): 64–81. http://dx.doi.org/10.1051/mmnp/20127406.
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Shetty, Priya. "Bernard Pécoul: championing the cause of neglected diseases." Lancet 376, no. 9742 (August 2010): 677. http://dx.doi.org/10.1016/s0140-6736(10)61324-4.
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Chapman, S. J., J. M. H. Lawry, and J. R. Ockendon. "Ray Theory for High-Péclet-Number Convection-Diffusion." SIAM Journal on Applied Mathematics 60, no. 1 (January 1999): 121–35. http://dx.doi.org/10.1137/s0036139998344088.
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Pfeifer, Kent B., W. Graham Yelton, and Dayle R. Kerr. "Two-Dimensional Péclet Numbers for Peak Quality Scoring." IEEE Sensors Journal 11, no. 9 (September 2011): 2108–10. http://dx.doi.org/10.1109/jsen.2011.2112345.
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Molho, P., A. J. Simon, and A. Libchaber. "Péclet number and crystal growth in a channel." Physical Review A 42, no. 2 (July 1, 1990): 904–10. http://dx.doi.org/10.1103/physreva.42.904.
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Loisy, Aurore, Aurore Naso, and Peter D. M. Spelt. "The effective diffusivity of ordered and freely evolving bubbly suspensions." Journal of Fluid Mechanics 840 (February 9, 2018): 215–37. http://dx.doi.org/10.1017/jfm.2018.84.
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We investigate the dispersion of a passive scalar such as the concentration of a chemical species, or temperature, in homogeneous bubbly suspensions, by determining an effective diffusivity tensor. Defining the longitudinal and transverse components of this tensor with respect to the direction of averaged bubble rise velocity in a zero mixture velocity frame of reference, we focus on the convective contribution thereof, this being expected to be dominant in commonly encountered bubbly flows. We first extend the theory of Kochet al.(J. Fluid Mech., vol. 200, 1989, pp. 173–188) (which is for dispersion in fixed beds of solid particles under Stokes flow) to account for weak inertial effects in the case of ordered suspensions. In the limits of low and of high Péclet number, including the inertial effect of the flow does not affect the scaling of the effective diffusivity with respect to the Péclet number. These results are confirmed by direct numerical simulations performed in different flow regimes, for spherical or very deformed bubbles and from vanishingly small to moderate values of the Reynolds number. Scalar transport in arrays of freely rising bubbles is considered by us subsequently, using numerical simulations. In this case, the dispersion is found to be convectively enhanced at low Péclet number, like in ordered arrays. At high Péclet number, the Taylor dispersion scaling obtained for ordered configurations is replaced by one characterizing a purely mechanical dispersion, as in random media, even if the level of disorder is very low.
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Koch, Donald L., and John F. Brady. "Dispersion in fixed beds." Journal of Fluid Mechanics 154 (May 1985): 399–427. http://dx.doi.org/10.1017/s0022112085001598.
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A macroscopic equation of mass conservation is obtained by ensemble-averaging the basic conservation laws in a porous medium. In the long-time limit this ‘macro-transport’ equation takes the form of a macroscopic Fick's law with a constant effective diffusivity tensor. An asymptotic analysis in low volume fraction of the effective diffusivity in a bed of fixed spheres is carried out for all values of the Péclet number ℙ = Ua/Df, where U is the average velocity through the bed. a is the particle radius and Df is the molecular diffusivity of the solute in the fluid. Several physical mechanisms causing dispersion are revealed by this analysis. The stochastic velocity fluctuations induced in the fluid by the randomly positioned bed particles give rise to a convectively driven contribution to dispersion. At high Péclet numbers, this convective dispersion mechanism is purely mechanical, and the resulting effective diffusivities are independent of molecular diffusion and grow linearly with ℙ. The region of zero velocity in and near the bed particles gives rise to non-mechanical dispersion mechanisms that dominate the longitudinal diffusivity at very high Péclet numbers. One such mechanism involves the retention of the diffusing species in permeable particles, from which it can escape only by molecular diffusion, leading to a diffusion coefficient that grows as ℙ2. Even if the bed particles are impermeable, non-mechanical contributions that grow as ℙ ln ℙ and ℙ2 at high ℙ arise from a diffusive boundary layer near the solid surfaces and from regions of closed streamlines respectively. The results for the longitudinal and transverse effective diffusivities as functions of the Péclet number are summarized in tabular form in §6. Because the same physical mechanisms promote dispersion in dilute and dense fixed beds, the predicted Péclet-number dependences of the effective diffusivities are applicable to all porous media. The theoretical predictions are compared with experiments in densely packed beds of impermeable particles, and the agreement is shown to be remarkably good.
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Turetta, Lorenzo, and Marco Lattuada. "The role of hydrodynamic interactions on the aggregation kinetics of sedimenting colloidal particles." Soft Matter 18, no. 8 (2022): 1715–30. http://dx.doi.org/10.1039/d1sm01637g.
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Mao, Deming, Xueying Xie, Raymond M. Jones, Albert Harvey, and John M. Karanikas. "A Simple Approach for Quantifying Accelerated Production Through Heating Producer Wells." SPE Journal 22, no. 01 (July 11, 2016): 316–26. http://dx.doi.org/10.2118/181757-pa.
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Summary This paper focuses on techniques for quantifying accelerated-production rates achieved by installing wellbore heaters in heavy-oil-producer wells. The uniform injection of heat into the wellbore of heavy-oil producers reduces local near-well fluid viscosity, lowers dynamic pressure, and results in increased production rates. Wellbore heat penetrates into the surrounding reservoir through conduction. Because of the exponential dependence of heavy-oil viscosity on temperature, small changes in temperature can substantially reduce near-wellbore oil viscosity. Conduction-heat transfer into the formation is balanced by convection back into the wellbore by the inflowing produced fluids. The higher the flow rate, the lower the heat-penetration depth is for a fixed heater-injection rate. Schild (1957) presented a steady-state model that deploys boundary condition at an infinite radial location, resulting in the prediction of an infinite-influence region for the temperature when the Péclet number is smaller than unity. Production-improvement factor (PIF) on the order of 100 is reported and will be shown to be overoptimistic when the transient nature is properly represented. In this paper, a transient model is presented dependent on the boundary conditions at a finite radial distance from the wellbore. Predictions of the PIF suggest values on the order of three at small Péclet numbers. Influence of the formation thermal conductivity and permeability can be lumped into a defined Péclet number. The developed correlation is demonstrated to cover the effect of this Péclet number, together with the viscosity ratio, on the PIF.
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Alahmadi, Hani, and Shailesh Naire. "The Role of Thermoviscous and Thermocapillary Effects in the Cooling and Gravity-Driven Draining of Molten Free Liquid Films." Fluids 8, no. 5 (May 14, 2023): 153. http://dx.doi.org/10.3390/fluids8050153.
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We theoretically considered two-dimensional flow in a vertically aligned thick molten liquid film to investigate the competition between cooling and gravity-driven draining, which is relevant in the formation of metallic foams. Molten liquid in films cools as it drains, losing its heat to the surrounding colder air and substrate. We extended our previous model to include non-isothermal effects, resulting in coupled non-linear evolution equations for the film’s thickness, extensional flow speed and temperature. The coupling between the flow and cooling effect was via a constitutive relationship for temperature-dependent viscosity and surface tension. This model was parameterized by the heat transfer coefficients at the film–air free surface and film–substrate interface, the Péclet number, the viscosity–temperature coupling parameter and the slope of the linear surface tension–temperature relationship. A systematic exploration of the parameter space revealed that at low Péclet numbers, increasing the heat transfer coefficient and gradually reducing the viscosity with temperature was conducive to cooling and could slow down the draining and thinning of the film. The effect of increasing the slope of the surface tension–temperature relationship on the draining and thinning of the film was observed to be more effective at lower Péclet numbers, where surface tension gradients in the lamella region opposed the gravity-driven flow. At higher Péclet numbers, though, the surface tension gradients tended to enhance the draining flow in the lamella region, resulting in the dramatic thinning of the film in the later stages.
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Jha, Raman K., Steven L. Bryant, and Larry W. Lake. "Effect of Diffusion on Dispersion." SPE Journal 16, no. 01 (October 4, 2010): 65–77. http://dx.doi.org/10.2118/115961-pa.
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Summary It is known that dispersion in porous media results from an interaction between convective spreading and diffusion. However, the nature and implications of these interactions are not well understood. Dispersion coefficients obtained from averaged cup-mixing concentration histories have contributions of convective spreading and diffusion lumped together. We decouple the contributions of convective spreading and diffusion in core-scale dispersion and systematically investigate interaction between the two in detail. We explain phenomena giving rise to important experimental observations such as Fickian behavior of core-scale dispersion and power-law dependence of dispersion coefficient on Péclet number. We track movement of a swarm of solute particles through a physically representative network model. A physically representative network model preserves the geometry and topology of the pore space and spatial correlation in flow properties. We developed deterministic rules to trace paths of solute particles through the network. These rules yield flow streamlines through the network comparable to those obtained from a full solution of Stokes’ equation. Paths of all solute particles are deterministically known in the absence of diffusion. Thus, we can explicitly investigate purely convective spreading by tracking the movement of solute particles on these streamlines. Then, we superimpose diffusion and study dispersion in terms of interaction between convective spreading and diffusion for a wide range of Péclet numbers. This approach invokes no arbitrary parameters, enabling a rigorous validation of the physical origin of core-scale dispersion. In this way, we obtain an unequivocal, quantitative assessment of the roles of convective spreading and diffusion in hydrodynamic dispersion in flow through porous media. Convective spreading has two components: stream splitting and velocity gradient in pore throats in the direction transverse to flow. We show that, if plug flow occurs in the pore throats (accounting only for stream splitting), all solute particles can encounter a wide range of independent velocities because of velocity differences between pore throats and randomness of pore structure. Consequently, plug flow leads to a purely convective spreading that is asymptotically Fickian. Diffusion superimposed on plug flow acts independently of convective spreading (in this case, only stream splitting), and, consequently, dispersion is simply the sum of convective spreading and diffusion. In plug flow, hydrodynamic dispersion varies linearly with the pore-scale Péclet number when diffusion is small in magnitude compared to convective spreading. For a more realistic parabolic velocity profile in pore throats, particles near the solid surface of the medium do not have independent velocities. Now, purely convective spreading (caused by a combination of stream splitting and variation in flow velocity in the transverse direction) is non-Fickian. When diffusion is nonzero, solute particles in the low-velocity region near the solid surface can move into the main flow stream. They subsequently undergo a wide range of independent velocities because of stream splitting, and, consequently, dispersion becomes asymptotically Fickian. In this case, dispersion is a result of an interaction between convection and diffusion. This interaction results in a weak nonlinear dependence of dispersion on Péclet number. The dispersion coefficients predicted by particle tracking through the network are in excellent agreement with the literature experimental data for a broad range of Péclet numbers. Thus, the essential phenomena giving rise to hydrodynamic dispersion observed in porous media are (1) stream splitting of the solute front at every pore, causing independence of particle velocities purely by convection; (2) velocity gradient in pore throats in the direction transverse to flow; and (3) diffusion. Taylor's dispersion in a capillary tube accounts only for the second and third of these phenomena, yielding a quadratic dependence of dispersion on Péclet number. Plug flow in the bonds of a physically representative network accounts only for the first and third phenomena, resulting in a linear dependence of dispersion on Péclet number. When all the three phenomena are accounted for, we can explain effectively the weak nonlinear dependence of dispersion on Péclet number.
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Tzella, Alexandra, and Jacques Vanneste. "FKPP Fronts in Cellular Flows: The Large-Péclet Regime." SIAM Journal on Applied Mathematics 75, no. 4 (January 2015): 1789–816. http://dx.doi.org/10.1137/15m1006714.
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Michelin, Sébastien, and Eric Lauga. "Optimal feeding is optimal swimming for all Péclet numbers." Physics of Fluids 23, no. 10 (October 2011): 101901. http://dx.doi.org/10.1063/1.3642645.
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Zinchenko, Alexander Z., and Robert H. Davis. "Gravity-induced coalescence of drops at arbitrary Péclet numbers." Journal of Fluid Mechanics 280 (December 10, 1994): 119–48. http://dx.doi.org/10.1017/s0022112094002879.
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The collision efficiency in a dilute suspension of sedimenting drops is considered, with allowance for particle Brownian motion and van der Waals attractive force. The drops are assumed to be of the same density, but they differ in size. Drop deformation and fluid inertia are neglected. Owing to small particle volume fraction, the analysis is restricted to binary interactions and includes the solution of the full quasi-steady Fokker—Planck equation for the pair-distribution function. Unlike previous studies on drop or solid particle collisions, a numerical solution is presented for arbitrary Péclet numbers, Pe, thus covering the whole range of particle size in typical hydrosols. Our technique is mainly based on an analytical continuation into the plane of complex Péclet number and a special conformal mapping, to represent the solution as a convergent power series for all real Péclet numbers. This efficient algorithm is shown to apply to a variety of convection—diffusion problems. The pair-distribution function is expanded into Legendre polynomials, and a finite-difference scheme with respect to particle separation is used. Two-drop mobility functions for hydrodynamic interactions are provided from exact bispherical coordinate solutions and near-field asymptotics. The collision efficiency is calculated for wide ranges of the size ratio, the drop-to-medium viscosity ratio, and the Péclet number, both with and without interdroplet forces. Solid spheres are considered as a limiting case; attractive van der Waals forces are required for non-zero collision rates in this case. For Pe [Gt ] 1, the correction to the asymptotic limit Pe → ∞ is O(Pe−1/2). For Pe [Lt ] 1, the first two terms in an asymptotic expansion for the collision efficiency are C/Pe + ½C2, where the constant C is determined from the Brownian solution in the limit Pe → 0. The numerical results are in excellent agreement with these limits. For intermediate Pe, the numerical results show that Brownian motion is important for Pe ≤ O(102). For Pe = 10, the trajectory analysis for Pe → ∞ may underestimate the collision rate by a factor of two. A simpler, approximate solution based on neglecting the transversal diffusion is also considered and compared to the exact solution. The agreement is within 2–3% for all conditions investigated. The effect of van der Waals attractions on the collision efficiency is studied for a wide range of droplet sizes. Except for very high drop-to-medium viscosity ratios, the effect is relatively small, especially when electromagnetic retardation is accounted for.
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MYDLARSKI, L., and Z. WARHAFT. "Passive scalar statistics in high-Péclet-number grid turbulence." Journal of Fluid Mechanics 358 (March 10, 1998): 135–75. http://dx.doi.org/10.1017/s0022112097008161.
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The statistics of a turbulent passive scalar (temperature) and their Reynolds number dependence are studied in decaying grid turbulence for the Taylor-microscale Reynolds number, Rλ, varying from 30 to 731 (21[les ]Peλ[les ]512). A principal objective is, using a single (and simple) flow, to bridge the gap between the existing passive grid-generated low-Péclet-number laboratory experiments and those done at high Péclet number in the atmosphere and oceans. The turbulence is generated by means of an active grid and the passive temperature fluctuations are generated by a mean transverse temperature gradient, formed at the entrance to the wind tunnel plenum chamber by an array of differentially heated elements. A well-defined inertial–convective scaling range for the scalar with a slope, nθ, close to the Obukhov–Corrsin value of 5/3, is observed for all Reynolds numbers. This is in sharp contrast with the velocity field, in which a 5/3 slope is only approached at high Rλ. The Obukhov–Corrsin constant, Cθ, is estimated to be 0.45–0.55. Unlike the velocity spectrum, a bump occurs in the spectrum of the scalar at the dissipation scales, with increasing prominence as the Reynolds number is increased. A scaling range for the heat flux cospectrum was also observed, but with a slope around 2, less than the 7/3 expected from scaling theory. Transverse structure functions of temperature exist at the third and fifth orders, and, as for even-order structure functions, the width of their inertial subranges dilates with Reynolds number in a systematic way. As previously shown for shear flows, the existence of these odd-order structure functions is a violation of local isotropy for the scalar differences, as is the existence of non-zero values of the transverse temperature derivative skewness (of order unity) and hyperskewness (of order 100). The ratio of the temperature derivative standard deviation along and normal to the gradient is 1.2±0.1, and is independent of Reynolds number. The refined similarity hypothesis for the passive scalar was found to hold for all Rλ, which was not the case for the velocity field. The intermittency exponent for the scalar, μθ, was found to be 0.25±0.05 with a possible weak Rλ dependence, unlike the velocity field, where μ was a strong function of Reynolds number. New, higher-Reynolds-number results for the velocity field, which smoothly follow the trends of Mydlarski & Warhaft (1996), are also presented.
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Coti Zelati, Michele. "Stable mixing estimates in the infinite Péclet number limit." Journal of Functional Analysis 279, no. 4 (September 2020): 108562. http://dx.doi.org/10.1016/j.jfa.2020.108562.
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Guzman-Sepulveda, Jose R., Samiul Amin, E. Neil Lewis, and Aristide Dogariu. "Full Characterization of Colloidal Dynamics at Low Péclet Numbers." Langmuir 31, no. 38 (September 16, 2015): 10351–57. http://dx.doi.org/10.1021/acs.langmuir.5b02665.
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Alexandrov, D. V., E. A. Titova, and P. K. Galenko. "A shape of dendritic tips at high Péclet numbers." Journal of Crystal Growth 515 (June 2019): 44–47. http://dx.doi.org/10.1016/j.jcrysgro.2019.03.008.
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Novikov, Alexei, George Papanicolaou, and Lenya Ryzhik. "Boundary layers for cellular flows at high Péclet numbers." Communications on Pure and Applied Mathematics 58, no. 7 (October 21, 2004): 867–922. http://dx.doi.org/10.1002/cpa.20058.
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Oliveira, Rafael M., and Eckart Meiburg. "Miscible displacements in Hele-Shaw cells: three-dimensional Navier–Stokes simulations." Journal of Fluid Mechanics 687 (October 12, 2011): 431–60. http://dx.doi.org/10.1017/jfm.2011.367.
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AbstractThree-dimensional Navier–Stokes simulations of viscously unstable, miscible Hele-Shaw displacements are discussed. Quasisteady fingers are observed whose tip velocity increases with the Péclet number and the unfavourable viscosity ratio. These fingers are widest near the tip, and become progressively narrower towards the root. The film of resident fluid left behind on the wall decreases in thickness towards the finger tip. The simulations reveal the detailed mechanism by which the initial spanwise vorticity of the base flow, when perturbed, gives rise to the cross-gap vorticity that drives the fingering instability in the classical Darcy sense. Cross-sections at constant streamwise locations reveal the existence of a streamwise vorticity quadrupole along the length of the finger. This streamwise vorticity convects resident fluid from the wall towards the centre of the gap in the cross-gap symmetry plane of the finger, while it transports injected fluid laterally away from the finger centre within the mid-gap plane. In this way, it results in the emergence of a longitudinal, inner splitting phenomenon some distance behind the tip that has not been reported previously. This inner splitting mechanism, which leaves the tip largely intact, is fundamentally different from the familiar tip-splitting mechanism. Since the inner splitting owes its existence to the presence of streamwise vorticity and cross-gap velocity, it cannot be captured by gap-averaged equations. It is furthermore observed that the role of the Péclet number in miscible displacements differs in some ways from that of the capillary number in immiscible flows. Specifically, larger Péclet numbers result in wider fingers, while immiscible flows display narrower fingers for larger capillary numbers. Furthermore, while higher capillary numbers are known to promote tip-splitting, inner splitting is delayed for larger Péclet numbers.