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1

Jenkins, James T. "Rapid Granular Flow Down Inclines." Applied Mechanics Reviews 47, no. 6S (1994): S240—S244. http://dx.doi.org/10.1115/1.3124415.

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As an example of the activity in the field of rapid granular flow, we sketch an analysis of a rapid granular flow of identical frictionless spheres that is driven by gravity down an incline. The flow is assumed to be dense, collisional, steady, and fully developed. Because we employ conditions at the base of the flow that are appropriate for a bumpy, frictionless boundary, the analysis is slightly more complicated than that of Savage (1983a, in Theory of Dispersed Multiphase Flow, RE Meyer (ed), Academic Press, New York, 339-358). Because we restrict our attention to dense flows, it is somewha
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2

Fischer, Karen M. "Flow and fabric deep down." Nature 415, no. 6873 (2002): 745–47. http://dx.doi.org/10.1038/415745a.

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3

KOJIMA, Hideyuki, Satoshi OGATA, Teruyoshi TAKAYAMA, Nobushiro FUNAKOSHI, and Keizo WATANABE. "Flow characteristic of Down Flow for Indoor Ventilation." Proceedings of the Fluids engineering conference 2004 (2004): 206. http://dx.doi.org/10.1299/jsmefed.2004.206.

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4

Sisoev, Grigori M., Richard V. Craster, Omar K. Matar, and Sergei V. Gerasimov. "Film flow down a fibre at moderate flow rates." Chemical Engineering Science 61, no. 22 (2006): 7279–98. http://dx.doi.org/10.1016/j.ces.2006.08.033.

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5

Krol, S., A. Pekediz, and H. de Lasa. "Particle clustering in down flow reactors." Powder Technology 108, no. 1 (2000): 6–20. http://dx.doi.org/10.1016/s0032-5910(99)00196-5.

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6

Morin, Veronique M., David Z. Zhu, and Mark R. Loewen. "Supercritical Exchange Flow Down a Sill." Journal of Hydraulic Engineering 130, no. 6 (2004): 521–31. http://dx.doi.org/10.1061/(asce)0733-9429(2004)130:6(521).

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7

Higuera, F. J. "Steady creeping flow down a slope." Physics of Fluids 7, no. 11 (1995): 2918–20. http://dx.doi.org/10.1063/1.868668.

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8

Trifonov, Yu Ya. "Viscous Film Flow down Corrugated Surfaces." Journal of Applied Mechanics and Technical Physics 45, no. 3 (2004): 389–400. http://dx.doi.org/10.1023/b:jamt.0000025021.41499.e1.

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9

Mann, J. A., L. Romero, R. R. Rye, and F. G. Yost. "Flow of simple liquids down narrowssVgrooves." Physical Review E 52, no. 4 (1995): 3967–72. http://dx.doi.org/10.1103/physreve.52.3967.

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10

Alshaikhi, Abdulwahed S., Stephen K. Wilson, and Brian R. Duffy. "Rivulet flow down a slippery substrate." Physics of Fluids 32, no. 7 (2020): 072011. http://dx.doi.org/10.1063/5.0013572.

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11

Elgindi, M. B. M., and C. Y. Wang. "Viscous flow down a membrane trough." Journal of Fluids and Structures 27, no. 3 (2011): 467–70. http://dx.doi.org/10.1016/j.jfluidstructs.2010.11.012.

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12

ITAYA, Yoshinori, Nobusuke KOBAYASHI, Shigenobu HATANO, and Akina FUJIMORI. "B209 GASIFICATION OF COMBINED BIOMASS AND COAL IN DOWN-FLOW ENTRAINED BED(Combustion-6)." Proceedings of the International Conference on Power Engineering (ICOPE) 2009.2 (2009): _2–129_—_2–134_. http://dx.doi.org/10.1299/jsmeicope.2009.2._2-129_.

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13

An, Kwangman, Hyehyun Kang, Youngkuk An, Jinil Park, and Jonghwa Lee. "Methodology of Excavator System Energy Flow-Down." Energies 13, no. 4 (2020): 951. http://dx.doi.org/10.3390/en13040951.

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Due to the strengthening of air-quality regulations, researchers have been investigating methods to improve excavator energy efficiency. Many researchers primarily conducted simulation studies employing mathematical models to analyze the energy consumption of excavator systems, which is necessary to examine the fuel efficiency improvement margin and the improvement effect. However, to effectively study the improvement of excavator efficiency, the real-time energy consumption characteristics must be examined through simulations and analyses of actual equipment-based energy consumption. Accordin
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14

Bontozoglou, V., and G. Papapolymerou. "Laminar film flow down a wavy incline." International Journal of Multiphase Flow 23, no. 1 (1997): 69–79. http://dx.doi.org/10.1016/s0301-9322(96)00053-5.

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15

WANG, C. Y. "Maximum flow down a circular sector tube." Chemical Engineering Science 54, no. 7 (1999): 961–64. http://dx.doi.org/10.1016/s0009-2509(98)00311-x.

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16

Huthnance, John M. "Accelerating Dense-Water Flow down a Slope." Journal of Physical Oceanography 39, no. 6 (2009): 1495–511. http://dx.doi.org/10.1175/2008jpo3964.1.

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Abstract Where water is denser on a shallow shelf than in the adjacent deep ocean, it tends to flow down the slope from shelf to ocean. The flow can be in a steady bottom boundary layer for moderate combinations of upslope density gradient −ρx∞ and bottom slope (angle θ to horizontal):Here g is acceleration due to gravity, ρ0 is a mean density, and f is twice the component of the earth’s rotation normal to the sloping bottom. For stronger combinations of the horizontal density gradient and bottom slope, the flow accelerates. Analysis of an idealized initial value problem shows that, when b ≥ 1
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17

Sonar, Prasad, Ishan Sharma, and Jayant Singh. "Granular flow down a flexible inclined plane." EPJ Web of Conferences 140 (2017): 03074. http://dx.doi.org/10.1051/epjconf/201714003074.

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18

Velan, M., and T. K. Ramanujam. "Hydrodynamics in down flow jet loop reactor." Canadian Journal of Chemical Engineering 69, no. 6 (1991): 1257–61. http://dx.doi.org/10.1002/cjce.5450690605.

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19

Bennett, D. L., B. L. Hertzler, and C. E. Kalb. "Down-flow shell-side forced convective boiling." AIChE Journal 32, no. 12 (1986): 1963–70. http://dx.doi.org/10.1002/aic.690321205.

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20

Chawla, S. S., P. K. Srivastava, and A. S. Gupta. "Spin-down of the von Karman flow." International Journal of Non-Linear Mechanics 41, no. 3 (2006): 426–31. http://dx.doi.org/10.1016/j.ijnonlinmec.2005.09.003.

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21

BERTHO, Y., F. GIORGIUTTI-DAUPHINÉ, T. RAAFAT, E. J. HINCH, H. J. HERRMANN, and J. P. HULIN. "Powder flow down a vertical pipe: the effect of air flow." Journal of Fluid Mechanics 459 (May 25, 2002): 317–45. http://dx.doi.org/10.1017/s0022112002008042.

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The dynamics of dry granular flows down a vertical glass pipe of small diameter have been studied experimentally. Simultaneous measurements of pressure profiles, air and grain flow rates and volume fractions of particles have been realized together with spatio-temporal diagrams of the grain distribution down the tube. At large grain flow rates, one observes a stationary flow characterized by high particle velocities, low particle fractions and a downflow of air resulting in an underpressure in the upper part of the pipe. A simple model assuming a free fall of the particles slowed down by air f
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22

Thorwarth, J., A. Schleiss, J. Köngeter, and H. Schüttrumpf. "Flow patterns in nappe flow regime down low-gradient stepped chutes." Journal of Hydraulic Research 47, no. 6 (2009): 830–32. http://dx.doi.org/10.1080/00221686.2009.9522064.

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23

Toombes, L., Connell Wagner, and H. Chanson. "Flow patterns in nappe flow regime down low gradient stepped chutes." Journal of Hydraulic Research 46, no. 1 (2008): 4–14. http://dx.doi.org/10.1080/00221686.2008.9521838.

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24

Nguyen, Duyen, and Vemuri Balakotaiah. "Flow maldistributions and hot spots in down-flow packed bed reactors." Chemical Engineering Science 49, no. 24 (1994): 5489–505. http://dx.doi.org/10.1016/0009-2509(94)00360-2.

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25

DIMENSTEIN, D. M., and K. M. NG. "A MODEL FOR PULSING FLOW IN COCURRENT DOWN-FLOW TRICKLE-BED REACTORS." Chemical Engineering Communications 41, no. 1-6 (1986): 215–35. http://dx.doi.org/10.1080/00986448608911720.

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26

Zvyagin, A. V., and V. P. Kolpakov. "Flow of a viscous fluid down a slope." Moscow University Mechanics Bulletin 66, no. 5 (2011): 99–104. http://dx.doi.org/10.3103/s0027133011050013.

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27

Šutalo, I. D., A. Bui, and M. Rudman. "The flow of non-Newtonian fluids down inclines." Journal of Non-Newtonian Fluid Mechanics 136, no. 1 (2006): 64–75. http://dx.doi.org/10.1016/j.jnnfm.2006.02.011.

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28

Shapiro, Howard M., and Howard M. Shapiro. "Gently Down The Stream: Flow Cytometry As Microscopy." Microscopy and Microanalysis 7, S2 (2001): 610–11. http://dx.doi.org/10.1017/s1431927600029123.

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Flow cytometry is an analytical technique in which optical measurements are made of cells or other biological particles as the cells or particles flow, ideally in single file, in a fluid stream past one or more optical measurement stations. Modern optical flow cytometers typically measure light scattered at small (1-5°) and large (15°-135°) angles to an illuminating laser beam, and fluorescence emitted in three or more discrete spectral bands; the most complex instruments employ three or four spatially separated illuminating beams at different wavelengths and can measure twelve fluorescence si
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29

Moszynski, Peter. "High prices drive down flow of food aid." BMJ 336, no. 7658 (2008): 1397.2–1397. http://dx.doi.org/10.1136/bmj.a372.

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30

Wang, C. Y. "Maximum Flow Down a Partially Filled Elliptic Tube." ZAMM 80, no. 5 (2000): 351–55. http://dx.doi.org/10.1002/(sici)1521-4001(200005)80:5<351::aid-zamm351>3.0.co;2-t.

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31

Pop, I., D. B. Ingham, and D. Lesnic. "Conjugate Film Flow Down a Heated Vertical Wall." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 77, no. 2 (1997): 151–54. http://dx.doi.org/10.1002/zamm.19970770214.

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32

Giovine, P., A. Minervini, and P. Andreussi. "Stability of liquid flow down an inclined tube." International Journal of Multiphase Flow 17, no. 4 (1991): 485–96. http://dx.doi.org/10.1016/0301-9322(91)90044-4.

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33

Gudhe, R., R. C. Yalamanchili, and M. Massoudi. "Flow of granular materials down a vertical pipe." International Journal of Non-Linear Mechanics 29, no. 1 (1994): 1–12. http://dx.doi.org/10.1016/0020-7462(94)90047-7.

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34

Ng, K. M. "A model for flow regime transitions in cocurrent down-flow trickle-bed reactors." AIChE Journal 32, no. 1 (1986): 115–22. http://dx.doi.org/10.1002/aic.690320113.

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35

SATO, Susumu, Masayuki FUKAGAWA, Hiroshi NAGAKURA, and Takeshi MATSUO. "Prevention of Steam Flow Disturbance in Heated Down Flow Tube at Minimum Load." Transactions of the Japan Society of Mechanical Engineers Series B 71, no. 704 (2005): 1140–47. http://dx.doi.org/10.1299/kikaib.71.1140.

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36

Salkar, V. D., and A. R. Tembhurkar. "Experimental evaluation of ripening behavior: Down-Flow vs. Up-Flow rapid sand filters." KSCE Journal of Civil Engineering 20, no. 4 (2015): 1221–27. http://dx.doi.org/10.1007/s12205-015-0736-y.

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37

Hansen, Erik B. "Stokes flow down a wall into an infinite pool." Journal of Fluid Mechanics 178 (May 1987): 243–56. http://dx.doi.org/10.1017/s0022112087001204.

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The two-dimensional flow of a thin film down a vertical or tilted plane wall into an infinite pool is studied in the Stokes approximation, the principal aim being to determine the shape of the fluid surface. Results are obtained for fluids with or without surface tension. Earlier results by Ruschak, that the surface tension gives rise to thickness variation of the film, are confirmed. For small or vanishing surface tension a dip of the pool surface is found to exist close to the wall. The case of a wall moving downwards is also considered.
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38

O'Malley, K., A. D. Fitt, T. V. Jones, J. R. Ockendon, and P. Wilmott. "Models for high-Reynolds-number flow down a step." Journal of Fluid Mechanics 222, no. -1 (1991): 139. http://dx.doi.org/10.1017/s0022112091001039.

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39

Snow, Kate, and B. R. Sutherland. "Particle-laden flow down a slope in uniform stratification." Journal of Fluid Mechanics 755 (August 14, 2014): 251–73. http://dx.doi.org/10.1017/jfm.2014.413.

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AbstractLock–release laboratory experiments are performed to examine saline and particle-laden flows down a slope into both constant-density and linearly stratified ambients. Both hypopycnal (surface-propagating) currents and hyperpycnal (turbidity) currents are examined, with the focus being upon the influence of ambient stratification on turbidity currents. Measurements are made of the along-slope front speed and the depth at which the turbidity current separates from the slope and intrudes into the ambient. These results are compared to the predictions of a theory that characterizes the flo
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40

Yang, Fengguang, Vijay P. Singh, Xiekang Wang, and Xingnian Liu. "Nappe Flow Surges down a Rough-Stepped Sloping Channel." Journal of Hydrologic Engineering 22, no. 10 (2017): 04017044. http://dx.doi.org/10.1061/(asce)he.1943-5584.0001570.

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41

Li, Xiaofan, and C. Pozrikidis. "Film flow of a suspension down an inclined plane." Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 361, no. 1806 (2003): 847–69. http://dx.doi.org/10.1098/rsta.2003.1171.

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42

Bauer, Ronald J., and C. H. von Kerczek. "Stability of Liquid Film Flow Down an Oscillating Wall." Journal of Applied Mechanics 58, no. 1 (1991): 278–82. http://dx.doi.org/10.1115/1.2897164.

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The stability of a liquid film flowing down an inclined oscillating wall is analyzed. First, the linear theory growth rates of disturbances are calculated to second order in a disturbance wave number. It is shown that this growth rate is simply the sum of the same growth rate expansions for a nonoscillating film on an inclined plate and an oscillating film on a horizontal plate. These growth rates were originally calculated by Yih (1963, 1968). The growth rate formula derived here shows that long wavelength disturbances to a vertical falling film, which are unstable at all nonzero values of th
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43

Nova, Samuel, Stephan Krol, and Hugo de Lasa. "Particle velocity and particle clustering in down-flow reactors." Powder Technology 148, no. 2-3 (2004): 172–85. http://dx.doi.org/10.1016/j.powtec.2004.09.008.

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44

Savoie, Rodrigue, Yves Gagnon, and Yves Mercadier. "Numerical simulation of the starting flow down a step." ESAIM: Proceedings 1 (1996): 377–86. http://dx.doi.org/10.1051/proc:1996028.

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45

Harper Jr, George R., and David W. Pfennig. "Selection overrides gene flow to break down maladaptive mimicry." Nature 451, no. 7182 (2008): 1103–6. http://dx.doi.org/10.1038/nature06532.

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46

Lin, T. S., L. Kondic, and A. Filippov. "Thin films flowing down inverted substrates: Three-dimensional flow." Physics of Fluids 24, no. 2 (2012): 022105. http://dx.doi.org/10.1063/1.3682001.

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47

Cheng, Yi-Lung, Wei-Yuan Chang, and Ying-Lang Wang. "Electromigration Characteristics for Electron Down-Flow in Copper Interconnects." ECS Transactions 35, no. 8 (2019): 211–21. http://dx.doi.org/10.1149/1.3567752.

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48

Geldart, D., N. Broodryk, and A. Kerdoncuff. "Studies on the flow of solids down cyclone diplegs." Powder Technology 76, no. 2 (1993): 175–83. http://dx.doi.org/10.1016/s0032-5910(05)80025-7.

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49

Lin, Te-Sheng, and Lou Kondic. "Thin films flowing down inverted substrates: Two dimensional flow." Physics of Fluids 22, no. 5 (2010): 052105. http://dx.doi.org/10.1063/1.3428753.

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50

Rousset, F., S. Millet, V. Botton, and H. Ben Hadid. "Temporal Stability of Carreau Fluid Flow Down an Incline." Journal of Fluids Engineering 129, no. 7 (2007): 913–20. http://dx.doi.org/10.1115/1.2742737.

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This paper deals with the temporal stability of a Carreau fluid flow down an inclined plane. As a first step, a weakly non-Newtonian behavior is considered in the limit of very long waves. It is found that the critical Reynolds number is lower for shear-thinning fluids than for Newtonian fluids, while the celerity is larger. In a second step, the general case is studied numerically. Particular attention is paid to small angles of inclination for which either surface or shear modes can arise. It is shown that shear dependency can change the nature of instability.
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