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Journal articles on the topic 'STOKES LAW'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Cartwright, Julyan H. E. "Stokes' law, viscometry, and the Stokes falling sphere clock." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2179 (2020): 20200214. http://dx.doi.org/10.1098/rsta.2020.0214.

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Clocks run through the history of physics. Galileo conceived of using the pendulum as a timing device on watching a hanging lamp swing in Pisa cathedral; Huygens invented the pendulum clock; and Einstein thought about clock synchronization in his Gedankenexperiment that led to relativity. Stokes derived his law in the course of investigations to determine the effect of a fluid medium on the swing of a pendulum. I sketch the work that has come out of this, Stokes drag, one of his most famous results. And to celebrate the 200th anniversary of George Gabriel Stokes’ birth I propose using the time

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2

Auerbach, David. "Some limits to Stokes’ law." American Journal of Physics 56, no. 9 (1988): 850–51. http://dx.doi.org/10.1119/1.15442.

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3

Nasyrov, V. V., and M. G. Nasyrova. "About the Stokes law applicability." Mathematical Structures and Modeling, no. 2 (54) (October 5, 2020): 40–48. http://dx.doi.org/10.24147/2222-8772.2020.2.40-48.

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We find the correction coefficient for the Stokes law that permit to use this formula in case of a spherical body in a tube with the glycerol. An interpolation formula for the correction coefficient for a motion with low-Reynolds-number is obtained.

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4

Nabarro, F. R. N. "Cottrell-stokes law and activation theory." Acta Metallurgica et Materialia 38, no. 2 (1990): 161–64. http://dx.doi.org/10.1016/0956-7151(90)90044-h.

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5

Wojnar, Ryszard. "Heuristic derivation of Brinkman's seepage equation." Technical Sciences 4, no. 20 (2017): 359–74. http://dx.doi.org/10.31648/ts.5433.

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Brinkman’s law is describing the seepage of viscous fluid through a porous medium and is more acurate than the classical Darcy’s law. Namely, Brinkman’s law permits to conform the flow through a porous medium to the free Stokes’ flow. However, Brinkman’s law, similarly as Schro¨dinger’s equation was only devined. Fluid in its motion through a porous solid is interacting at every point with the walls of pores, but the interactions of the fluid particles inside pores are different than the interactions at the walls, and are described by Stokes’ equation. Here, we arrive at Brinkman’s law from St

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6

Schiller, Robert. "The Stokes-Einstein law by macroscopic arguments." International Journal of Radiation Applications and Instrumentation. Part C. Radiation Physics and Chemistry 37, no. 3 (1991): 549–50. http://dx.doi.org/10.1016/1359-0197(91)90033-x.

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7

Djoko, J. K., J. Koko, M. Mbehou, and Toni Sayah. "Stokes and Navier-Stokes equations under power law slip boundary condition: Numerical analysis." Computers & Mathematics with Applications 128 (December 2022): 198–213. http://dx.doi.org/10.1016/j.camwa.2022.10.016.

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8

Yang, Hailing, and Yi Xia. "Hydrodynamic instability of nanofluids in round jet for small Stokes number." Modern Physics Letters B 33, no. 33 (2019): 1950419. http://dx.doi.org/10.1142/s0217984919504190.

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The flow instability of particle-laden jet has been widely studied for large Stokes numbers. However, there is little attention on the case with small Stoke number, which often occurs in practical applications with nanoparticle-laden fluid. In this paper, the instability of nanofluids in round jet is studied numerically for [Formula: see text]. The results show that the law of nanofluids instability is quite similar to regular particle instability for axisymmetric azimuthal mode [Formula: see text]. However, for asymmetric azimuthal mode [Formula: see text], the regular pattern of instability

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9

Barton, I. E. "Exponential-Lagrangian Tracking Schemes Applied to Stokes Law." Journal of Fluids Engineering 118, no. 1 (1996): 85–89. http://dx.doi.org/10.1115/1.2817520.

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The exponential-Lagrangian tracking scheme applied to Stokes Law is developed by introducing a predictor-corrector formulation. The new predictor-corrector schemes are more accurate than the original scheme and are estimated to give a better performance taking into account the increased computational effort. The schemes are tested on two simple problems and the results are compared with the analytical solutions.

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10

Greenwood, Margaret Stautberg, Frances Fazio, Marie Russotto, and Aaron Wilkosz. "Using the Atwood machine to study Stokes’ law." American Journal of Physics 54, no. 10 (1986): 904–6. http://dx.doi.org/10.1119/1.14786.

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11

Straub, Dieter, and Michael Lauster. "Angular momentum conservation law and Navier-Stokes theory." International Journal of Non-Linear Mechanics 29, no. 6 (1994): 823–33. http://dx.doi.org/10.1016/0020-7462(94)90055-8.

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12

Bochniak, W. "The cottrell-stokes law for F.C.C. single crystals." Acta Metallurgica et Materialia 41, no. 11 (1993): 3133–40. http://dx.doi.org/10.1016/0956-7151(93)90043-r.

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13

Hong, Sun Ig, and Campbell Laird. "Deviations from Cottrell-Stokes law in cyclic deformation." Scripta Metallurgica et Materialia 26, no. 7 (1992): 1113–18. http://dx.doi.org/10.1016/0956-716x(92)90239-b.

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14

Hu, Yuxi, and Reinhard Racke. "Compressible Navier–Stokes Equations with Revised Maxwell’s Law." Journal of Mathematical Fluid Mechanics 19, no. 1 (2016): 77–90. http://dx.doi.org/10.1007/s00021-016-0266-5.

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15

Marušić-Paloka, E. "On the Stokes Paradox for Power-Law Fluids." ZAMM 81, no. 1 (2001): 31–36. http://dx.doi.org/10.1002/1521-4001(200101)81:1<31::aid-zamm31>3.0.co;2-g.

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16

Hu, Yuxi, and Reinhard Racke. "Compressible Navier–Stokes Equations with hyperbolic heat conduction." Journal of Hyperbolic Differential Equations 13, no. 02 (2016): 233–47. http://dx.doi.org/10.1142/s0219891616500077.

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We investigate the system of compressible Navier–Stokes equations with hyperbolic heat conduction, i.e. replacing the Fourier’s law by Cattaneo’s law. First, by using Kawashima’s condition on general hyperbolic parabolic systems, we show that for small relaxation time [Formula: see text], global smooth solution exists for small initial data. Moreover, as [Formula: see text] goes to zero, we obtain the uniform convergence of solutions of the relaxed system to that of the classical compressible Navier–Stokes equations.

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17

Lushnikov, Pavel M. "Structure and location of branch point singularities for Stokes waves on deep water." Journal of Fluid Mechanics 800 (July 12, 2016): 557–94. http://dx.doi.org/10.1017/jfm.2016.405.

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The Stokes wave is a finite-amplitude periodic gravity wave propagating with constant velocity in an inviscid fluid. The complex analytical structure of the Stokes wave is analysed using a conformal mapping of a free fluid surface of the Stokes wave onto the real axis with the fluid domain mapped onto the lower complex half-plane. There is one square root branch point per spatial period of the Stokes wave located in the upper complex half-plane at a distance $v_{c}$ from the real axis. The increase of Stokes wave height results in $v_{c}$ approaching zero with the limiting Stokes wave formatio

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18

Wright, Steve. "Time‐dependent Stokes flow through a randomly perforated porous medium." Asymptotic Analysis 23, no. 3-4 (2000): 257–72. https://doi.org/10.3233/asy-2000-398.

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An incompressible fluid is assumed to satisfy the time‐dependent Stokes equations in a porous medium. The porous medium is modeled by a bounded domain in $R^n$ that is perforated for each ε > 0 by ε‐dilations of a subset of $R^n$ arising from a family of stochastic processes which generalize the homogeneous random fields. The solution of the Stokes equations on these perforated domains is homogenized as ε → 0 by means of stochastic two‐scale convergence in the mean, and the homogenized limit is shown to satisfy a two‐pressure Stokes system containing both deterministic and stochastic deriva

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19

Rana, Anirudh Singh, Vinay Kumar Gupta, and Henning Struchtrup. "Coupled constitutive relations: a second law based higher-order closure for hydrodynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2218 (2018): 20180323. http://dx.doi.org/10.1098/rspa.2018.0323.

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In the classical framework, the Navier–Stokes–Fourier equations are obtained through the linear uncoupled thermodynamic force-flux relations which guarantee the non-negativity of the entropy production. However, the conventional thermodynamic descrip- tion is only valid when the Knudsen number is sufficiently small. Here, it is shown that the range of validity of the Navier–Stokes–Fourier equations can be extended by incorporating the nonlinear coupling among the thermodynamic forces and fluxes. The resulting system of conservation laws closed with the coupled constitutive relations is able to

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20

Guo, Xiaoyi. "New Exact Solutions for Stokes First Problem of a Generalized Jeffreys Fluid in a Porous Half Space." Applied Mechanics and Materials 477-478 (December 2013): 246–53. http://dx.doi.org/10.4028/www.scientific.net/amm.477-478.246.

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The fractional calculus approach has been taken into account in the Darcys law and the constitutive relationship of fluid model. Based on a modified Darcys law for a viscoelastic fluid, Stokes first problem is considered for a generalized Jeffreys fluid in a porous half space. By using the Fourier sine transform and the Laplace transform, two forms of exact solutions of Stokes first problem for a generalized Jeffreys fluid in the porous half space are obtained in term of generalized Mittag-Leffler function, and one of them is presented as the sum of the similar Newtonian solution and the corre

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21

Gorski, Patrick R., and Stanley I. Dodson. "Free-swimming Daphnia pulex can avoid following Stokes' law." Limnology and Oceanography 41, no. 8 (1996): 1815–21. http://dx.doi.org/10.4319/lo.1996.41.8.1815.

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22

Bar-Ziv, Ezra, Bin Zhao, Elaad Mograbi, David Katoshevski, and Gennady Ziskind. "Experimental validation of the Stokes law at nonisothermal conditions." Physics of Fluids 14, no. 6 (2002): 2015–18. http://dx.doi.org/10.1063/1.1476305.

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23

Pau, Paul Chi Fu, J. O. Berg, and W. G. McMillan. "Application of Stokes' law to ions in aqueous solution." Journal of Physical Chemistry 94, no. 6 (1990): 2671–79. http://dx.doi.org/10.1021/j100369a080.

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24

Carlson, Edward H. "A microscopic picture of Reynolds number and Stokes’ law." American Journal of Physics 56, no. 11 (1988): 1045–46. http://dx.doi.org/10.1119/1.15341.

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25

Pritchard, David, Catriona R. McArdle, and Stephen K. Wilson. "The Stokes boundary layer for a power-law fluid." Journal of Non-Newtonian Fluid Mechanics 166, no. 12-13 (2011): 745–53. http://dx.doi.org/10.1016/j.jnnfm.2011.04.011.

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26

Tanner, R. I. "Stokes paradox for power-law flow around a cylinder." Journal of Non-Newtonian Fluid Mechanics 50, no. 2-3 (1993): 217–24. http://dx.doi.org/10.1016/0377-0257(93)80032-7.

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27

Borggaard, Jeff, Traian Iliescu, and John Paul Roop. "An improved penalty method for power-law Stokes problems." Journal of Computational and Applied Mathematics 223, no. 2 (2009): 646–58. http://dx.doi.org/10.1016/j.cam.2008.02.002.

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28

Boukrouche, Mahdi, Imane Boussetouan, and Laetitia Paoli. "Unsteady 3D-Navier–Stokes system with Tresca’s friction law." Quarterly of Applied Mathematics 78, no. 3 (2019): 525–43. http://dx.doi.org/10.1090/qam/1563.

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29

Voronel, A., E. Veliyulin, V. Sh Machavariani, A. Kisliuk, and D. Quitmann. "Fractional Stokes-Einstein Law for Ionic Transport in Liquids." Physical Review Letters 80, no. 12 (1998): 2630–33. http://dx.doi.org/10.1103/physrevlett.80.2630.

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30

Rehmeier, Marco, and Andre Schenke. "Nonuniqueness in law for stochastic hypodissipative Navier–Stokes equations." Nonlinear Analysis 227 (February 2023): 113179. http://dx.doi.org/10.1016/j.na.2022.113179.

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31

Darvell, B. W., and N. B. Wong. "Viscosity of dental waxes by use of Stokes' Law." Dental Materials 5, no. 3 (1989): 176–80. http://dx.doi.org/10.1016/0109-5641(89)90009-2.

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32

OGOLO, NAOMI A., MIKE O. ONYEKONWU, and ABBEY T. MICHAEL. "Problems of Stokes’ law application in determining the settling velocity of clays." Journal of Engineering Sciences and Innovation 9, no. 3 (2024): 277–86. https://doi.org/10.56958/jesi.2024.9.3.277.

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Clay sedimentation is important for various applications including settling of drilling mud during downtime in drilling operations, and it is essential to model such processes. A widely accepted theory that explains the kinetics of dispersed particles under gravitational pull in a quiescent medium is Stokes’ law. This law is commendable and reliable for modelling the settling velocity of particles but has been reported to be inadequate for modelling the settling velocity of clays. This has prompted a re-examination of the law with regard to assumptions made in deriving it, and it was found tha

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33

Palaniappan, D., S. D. Nigam, and T. Amaranath. "Shear-free boundary in Stokes flow." International Journal of Mathematics and Mathematical Sciences 19, no. 1 (1996): 145–50. http://dx.doi.org/10.1155/s016117129600021x.

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A theorem of Harper for axially symmetric flow past a sphere which is a stream surface, and is also shear-free, is extended to flow past a doubly-body𝔅consisting of two unequal, orthogonally intersecting spheres. Several illustrative examples are given. An analogue of Faxen's law for a double-body is observed.

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34

Neumann, Wladimir, Doris Breuer, and Tilman Spohn. "Water-Rock Differentiation of Icy Bodies by Darcy law, Stokes law, and Two-Phase Flow." Proceedings of the International Astronomical Union 11, A29A (2015): 261–66. http://dx.doi.org/10.1017/s174392131600301x.

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AbstractThe early Solar system produced a variety of bodies with different properties. Among the small bodies, objects that contain notable amounts of water ice are of particular interest. Water-rock separation on such worlds is probable and has been confirmed in some cases. We couple accretion and water-rock separation in a numerical model. The model is applicable to Ceres, icy satellites, and Kuiper belt objects, and is suited to assess the thermal metamorphism of the interior and the present-day internal structures. The relative amount of ice determines the differentiation regime according

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35

Ouya, Jules, and Arouna Ouedraogo. "Rigorous justification of hydrostatic approximation of compressible fluid flow equations." Gulf Journal of Mathematics 18, no. 1 (2024): 72–94. https://doi.org/10.56947/gjom.v18i1.2239.

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In this paper, we obtain the 3D compressible primitive equations approximation with gravity by taking the small aspect ratio limit to the Navier-Stokes equations. We use the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier-Stokes equations with a pressure law of the form p(ρ) = ρ2 to the compressible primitive equations.

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36

Saeger, R. B., L. E. Scriven, and H. T. Davis. "Transport processes in periodic porous media." Journal of Fluid Mechanics 299 (September 25, 1995): 1–15. http://dx.doi.org/10.1017/s0022112095003399.

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The Stokes equation system and Ohm's law were solved numerically for fluid in periodic bicontinuous porous media of simple cubic (SC), body-centred cubic (BCC) and face-centred cubic (FCC) symmetry. The Stokes equation system was also solved for fluid in porous media of SC arrays of disjoint spheres. The equations were solved by Galerkin's method with finite element basis functions and with elliptic grid generation. The Darcy permeability k computed for flow through SC arrays of spheres is in excellent agreement with predictions made by other authors. Prominent recirculation patterns are found

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37

Wei, Yizheng, and Chao Sun. "The Depth Distribution Law of the Polarization of the Vector Acoustic Field in the Ocean Waveguide." Journal of Marine Science and Engineering 12, no. 8 (2024): 1325. http://dx.doi.org/10.3390/jmse12081325.

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The polarization of the acoustic field in the ocean waveguide environment is a unique property that can provide new ideas for locating and detecting the underwater target, so it is interesting to study the polarization. This paper extends the Stokes parameters to a broadband form, and uses the non-stationary phase approximation method to simplify the expressions, reducing the complexity of theoretical derivation. A physical phenomenon is observed where polarization exhibits significant variations concerning the sea surface, seafloor, source depth, and the source symmetrical depth. Simulation r

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38

Smoleń, Jakub, Piotr Olesik, Jakub Jała, Hanna Myalska-Głowacka, Marcin Godzierz, and Mateusz Kozioł. "Application of Mathematical and Experimental Approach in Description of Sedimentation of Powder Fillers in Epoxy Resin." Materials 14, no. 24 (2021): 7520. http://dx.doi.org/10.3390/ma14247520.

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In this paper, sedimentation inhibition attempts were examined using colloidal silica in a mathematical and experimental approach. Experimental results were validated by a two-step verification process. It was demonstrated that application of quantitative metallography and hardness measurements in three different regions of samples allows us to describe the sedimentation process using modified Stokes law. Moreover, proper application of Stokes law allows one to determine the optimal colloidal silica amount, considering characteristics of applied filler (alumina or graphite). The results of mat

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39

Chapuis, Robert P., François Duhaime, and Simon Weber. "Simplifying the calculation of equivalent diameter in sedimentation tests." Canadian Geotechnical Journal 52, no. 8 (2015): 1186–89. http://dx.doi.org/10.1139/cgj-2013-0467.

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In sedimentation tests, the equivalent diameter of particles, D, is calculated using an equation derived from Stokes’ law and a factor K interpolated from a table listing values of suspension temperature and the specific gravity of solids. This paper explains how to start with Stokes’ law and obtain the equation used in standards. Then it provides two equations for K, both of which are accurate for the usual temperature range for hydrometer tests, and for any specific gravity. The two equations can be used in spreadsheets to automatically calculate D, an easier process than obtaining or interp

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40

BOURGEAT, ALAIN, EDUARD MARUŠIĆ-PALOKA, and ANDRO MIKELIĆ. "WEAK NONLINEAR CORRECTIONS FOR DARCY’S LAW." Mathematical Models and Methods in Applied Sciences 06, no. 08 (1996): 1143–55. http://dx.doi.org/10.1142/s021820259600047x.

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We consider the Navier-Stokes system in a periodic porous medium Ωε where ε is the characteristic pore size. The viscosity is of order εβ with 0≤β<3/2, sufficiently close to the critical exponent β=3/2. An asymptotic expansion for the velocity and the pressure, in terms of the local Reynolds number Reε=ε3−2βis set and a second-order error estimate is proved.

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41

Shevchenko, Heorhii, Valentyna Cholyshkina, Vladyslav Kurilov, Halyna Lipska, and Oleksandr Havrosh. "Patterns of constrained particle settling in water mineral suspensions of different densities." Geo-Technical Mechanics, no. 169 (2024): 140–52. https://doi.org/10.15407/geotm2024.169.140.

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The settling velocity of particles in mineral suspensions is a crucial parameter for calculating the design of various hydraulic devices and equipment used for mineral pulp benefication. In studies of gravity separation of heterogeneous particles by settling, the determination of mass settling velocity, the influence of suspension density on the process, and the applicability of classical hydrodynamics laws remain the least explored aspects. Often, free settling conditions are used for calculating hydraulic separation processes, but this introduces significant error in the velocity magnitude,

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42

Sinha, Nityanand, Andres E. Tejada-Martínez, Cigdem Akan, and Chester E. Grosch. "Toward a K-Profile Parameterization of Langmuir Turbulence in Shallow Coastal Shelves." Journal of Physical Oceanography 45, no. 12 (2015): 2869–95. http://dx.doi.org/10.1175/jpo-d-14-0158.1.

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AbstractInteraction between the wind-driven shear current and the Stokes drift velocity induced by surface gravity waves gives rise to Langmuir turbulence in the upper ocean. Langmuir turbulence consists of Langmuir circulation (LC) characterized by a wide range of scales. In unstratified shallow water, the largest scales of Langmuir turbulence engulf the entire water column and thus are referred to as full-depth LC. Large-eddy simulations (LESs) of Langmuir turbulence with full-depth LC in a wind-driven shear current have revealed that vertical mixing due to LC erodes the bottom log-law veloc

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43

Alam, M., S. Saha, and R. Gupta. "Unified theory for a sheared gas–solid suspension: from rapid granular suspension to its small-Stokes-number limit." Journal of Fluid Mechanics 870 (May 15, 2019): 1175–93. http://dx.doi.org/10.1017/jfm.2019.304.

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A non-perturbative nonlinear theory for moderately dense gas–solid suspensions is outlined within the framework of the Boltzmann–Enskog equation by extending the work of Saha & Alam (J. Fluid Mech., vol. 833, 2017, pp. 206–246). A linear Stokes’ drag law is adopted for gas–particle interactions, and the viscous dissipation due to hydrodynamic interactions is incorporated in the second-moment equation via a density-corrected Stokes number. For the homogeneous shear flow, the present theory provides a unified treatment of dilute to dense suspensions of highly inelastic particles, encompassin

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44

McKenna, Brian. "Outsourcing stokes financial crime threat." Computer Fraud & Security 2004, no. 12 (2004): 1–2. http://dx.doi.org/10.1016/s1361-3723(05)70177-9.

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45

Aguayo, Jorge, and Hugo Carrillo Lincopi. "Analysis of Obstacles Immersed in Viscous Fluids Using Brinkman's Law for Steady Stokes and Navier--Stokes Equations." SIAM Journal on Applied Mathematics 82, no. 4 (2022): 1369–86. http://dx.doi.org/10.1137/20m138569x.

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46

Szücs, Mátyás, and Róbert Kovács. "Gradient-dependent transport coefficients in the Navier-Stokes-Fourier system." Theoretical and Applied Mechanics, no. 00 (2022): 9. http://dx.doi.org/10.2298/tam221005009s.

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In the engineering praxis, Newton?s law of viscosity and Fourier?s heat conduction law are applied to describe thermomechanical processes of fluids. Despite several successful applications, there are some obscure and unexplored details, which are partly answered in this paper using the methodology of irreversible thermodynamics. Liu?s procedure is applied to derive the entropy production rate density, in which positive definiteness is ensured via linear Onsagerian equations; these equations are exactly Newton?s law of viscosity and Fourier?s heat conduction law. The calculations point out that

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47

Bresch, Didier, Pierre—Emmanuel Jabin, and Fei Wang. "Global Existence of Weak Solutions for Compresssible Navier—Stokes—Fourier Equations with the Truncated Virial Pressure Law." Communications in Applied and Industrial Mathematics 14, no. 1 (2023): 17–49. http://dx.doi.org/10.2478/caim-2023-0002.

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Abstract This paper concerns the existence of global weak solutions á la Leray for compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new const

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48

Batsanov, Stepan S., Dmitry A. Dan’kin, Sergey M. Gavrilkin, Anna I. Druzhinina, and Andrei S. Batsanov. "Structural changes in colloid solutions of nanodiamond." New Journal of Chemistry 44, no. 4 (2020): 1640–47. http://dx.doi.org/10.1039/c9nj05191k.

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49

Robbins, M. L., R. Varadaraj, J. Bock, and S. J. Pace. "EFFECT OF STOKES’ LAW SETTLING ON MEASURING OIL DISPERSION EFFECTIVENESS." International Oil Spill Conference Proceedings 1995, no. 1 (1995): 191–96. http://dx.doi.org/10.7901/2169-3358-1995-1-191.

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ABSTRACT Industry laboratory tests to measure dispersion effectiveness for oil spills on water measure only the volume percentage of oil dispersed and not the dispersed particle size. The effect of particle size on settling behavior is particularly pronounced in tests that use long settling times to superimpose a dispersion stability criterion on the effectiveness rating. The authors have studied the effect of settling time on the volume cumulative particle size distribution measured by the Coulter Multisizer II. Using Stokes’ law settling to analyze the results, we have demonstrated the effec

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50

Kim, Jae-Myoung. "3D Navier-Stokes equations of power law type with damping." Archiv der Mathematik 118, no. 3 (2022): 323–35. http://dx.doi.org/10.1007/s00013-021-01684-z.

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