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| Title: Pressure-driven transient flows of Newtonian fluids through microtubes with slip boundary |
| Authors: |
| Author Full Names: Wu, Yong Hong; Wiwatanapataphee, B. |
| Source: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 387 (24): 5979-5990 OCT 15 2008 |
| Language: English |
| Document Type: Article |
| Author Keywords: fluid flow; microtube; slip boundary condition; Navier-Stokes equations; flow rate |
| Keywords Plus: LIQUID FLOW; TURBULENT-FLOW; SIMULATION; SURFACES; SIZE |
| Abstract: Recent advances in microscale experiments and molecular simulations confirm that slip of fluid on solid surface occurs at small scale, and thus the traditional no-slip boundary condition in fluid mechanics cannot be applied to flow in micrometer and nanometer scale tubes and channels. On the other hand, there is an urgent need to understand fluid flow in micrometer scale due to the emergence of biochemical lab-on-the-chip system and micro-electromechanical system fabrication technologies. In this paper, we study the pressure driven transient flow of an incompressible Newtonian fluid in microtubes with a Navier slip boundary condition. An exact solution is derived and is shown to include some existing known results as special cases. Through analysis of the derived solution, it is found that the influences of boundary slip on the flow behaviour are qualitatively different for different types of pressure fields driving the flow. For pressure fields with a constant pressure grad! ient, the boundary slip does not alter the interior material deformation and stress field; while, for pressure fields with a wave form pressure gradient, the boundary slip causes the change of interior material deformation and consequently the velocity profile and stress field. We also derive asymptotic expressions for the exact solution through which a parameter is identified to dominate the behaviour of the flow driven by the wave form pressure gradient, and an explicit formulae for the critical slip parameter leading to the maximum transient flow rate is established. (C) 2008 Elsevier B.V. All rights reserved. |
| Reprint Address: Wu, YH, Curtin Univ Technol, Dept Math & Stat, Perth, WA 6845, Australia. |
| Research Institution addresses: Curtin Univ Technol, Dept Math & Stat, Perth, WA 6845, Australia; Mahidol Univ, Fac Sci, Dept Math, Bangkok 10400, Thailand; Univ Sci & Technol China, Sch Engn Sci, Beijing, Peoples R China |
| E-mail Address: yhwu@maths.curtin.edu.au |
| Cited References: BOURLON B, 2007, NAT NANOTECHNOL, V2, P104, DOI 10.1038/nnano.2006.211. CAO BY, 2006, ACTA PHYS SIN-CH ED, V55, P5305. CAO BY, 2006, PHYS REV E 2, V74, ARTN 066311. CARPINLIOGLU MO, 2001, FLOW MEAS INSTRUM, V12, P163. CHAUVETEAU G, 1982, J RHEOL NY, V26, P111. CHRISTOPHE Y, 2007, PHYS FLUIDS, V19, UNSP 123601. DESHMUKH SR, 2005, IND ENG CHEM RES, V44, P4982, DOI 10.1021/ie0490987. DEVARGAS L, 1989, POLYM ENG SCI, V29, P1232. DONGHYUN Y, 2007, PHYS FLUIDS, V19, UNSP 081701. ERIC L, 2005, PHYS FLUIDS, V17, UNSP 103102. GADELHAK M, 1999, T ASME, V121, P5. HERWIG H, 2003, INT J HEAT MASS TRAN, V46, P935. HO CM, 1998, ANNU REV FLUID MECH, V30, P579. HUANG H, 2007, INT J NUMER METHOD H, V17, P587, DOI 10.1108/09615530710761225. HUANG P, 2007, PHYS FLUIDS, V19, ARTN 028104. KUO TC, 2003, SENSOR ACTUAT A-PHYS, V102, P223. LEE HB, 2007, GEOPHYS RES LETT, V34, P19401. MATTHEWS MT, 2007, ACTA MECH, V191, P195, DOI 10.1007/s00707-007-0454-8. NAKANE JJ, 2003, J PHYS-CONDENS MAT, V15, R1365. PASCAL JP, 2006, J NON-NEWTON FLUID, V133, P109, DOI 10.1016/j.jnnfm.2005.11.007. PIT R, 2000, PHYS REV LETT, V85, P980. RAY S, 2005, J FLUID ENG-T ASME, V127, P405, DOI 10.1115/1.1906265. SAHU KC, 2007, PHYS FLUIDS, V19, ARTN 122101. SAIDI F, 2006, ZAMM-Z ANGEW MATH ME, V86, P702, DOI 10.1002/zamm.200510275. SLATTERY JC, 1999, ADV TRANSPORT PHENOM. SU YC, 2004, J MICROELECTROMECH S, V13, P75, DOI 10.1109/JMEMS.2003.823215. SZALMAS L, 2006, PHYS REV E 2, V73, ARTN 066710. THOMPSON PA, 1997, NATURE, V389, P360. TUINIER R, 2005, J PHYS-CONDENS MAT, V17, L9, DOI 10.1088/0953-8984/17/2/L01. WIWATANAPATAPHEE B, 2004, J COMPUT APPL MATH, V166, P307, DOI 10.1016/j.cam.2003.09.020. WIWATANAPATAPHEE B, 2006, MATH BIOSCI ENG, V3, P371. WU YH, 2007, DISCRETE CONT DYN-B, V8, P695. XU JL, 2007, INT J HEAT MASS TRAN, V50, P2571, DOI 10.1016/j.ijheatmasstransfer.2006.11.031. YANG SP, 2006, J NON-NEWTON FLUID, V138, P173, DOI 10.1016/j.jnnfm.2006.05.007. YOUSIF HA, 1997, COMPUT PHYS COMMUN, V106, P199. ZHU YX, 2001, PHYS REV LETT, V87, ARTN 096105. |
| Cited Reference Count: 36 |
| Times Cited: 0 |
| Publisher: ELSEVIER SCIENCE BV; PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS |
| Subject Category: Physics, Multidisciplinary |
| ISSN: 0378-4371 |
| DOI: 10.1016/j.physa.2008.06.043 |
| IDS Number: 356IT |
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| Title: Motion of a spheroidal particle in a micropolar fluid contained in a spherical envelope |
| Authors: |
| Author Full Names: Saad, E. I. |
| Source: CANADIAN JOURNAL OF PHYSICS 86 (9): 1039-1056 SEP 2008 |
| Language: English |
| Document Type: Article |
| Keywords Plus: BOUNDARY-CONDITIONS; STOKES-FLOW; SLIP; WALL; SURFACE; DRAG |
| Abstract: This paper investigates first the Stokes' axisymmetrical translational motion of a spheroid particle, whose shape differs slightly from that of a sphere, in an unbounded micropolar fluid. A linear slip, Basset-type, boundary condition has been used. The drag acting on the spheroid is evaluated and discussed for the various parameters of the problem. Also, the terminal velocity is evaluated and tabulated for the slip, deformity, and micropolarity parameters. Secondly, the motion of a spheroidal particle at the instant it passes the centre of a spherical envelope filled with a micropolar fluid is investigated using the slip condition at the surface of the particle. The analytical expressions for the stream function and microrotation component are obtained to first order in the small parameter characterizing the deformation. As an application, we consider an oblate spheroidal particle and the drag acting on the body is evaluated. Its variation with respect to the diameter ratio! , deformity, micropolarity, and slip parameters is tabulated and displayed graphically. Well-known cases are deduced, the wall effect is then examined and comparisons are attempted between the classical fluid and micropolar fluid. |
| Reprint Address: Saad, EI, Univ Alexandria, Fac Sci, Dept Math, Damanhour 22511, Egypt. |
| Research Institution addresses: Univ Alexandria, Fac Sci, Dept Math, Damanhour 22511, Egypt |
| E-mail Address: elsayedsaad74@yahoo.com |
| Cited References: BASSET AB, 1961, TREATISE HYDRODYNAMI, V2. CUNNINGHAM E, 1910, P R SOC LOND A-CONTA, V83, P357. ERINGEN AC, 1966, J MATH MECH, V16, P1. ERINGEN AC, 1999, MICROCONTINUUM FIELD, V1. ERINGEN AC, 2001, MICROCONTINUUM FIELD, V2. FALTAS MS, 2005, INT J ENG SCI, V43, P953, DOI 10.1016/j.ijengsci.2005.02.002. HABERMAN WL, 1958, 1143 US NAV DEP. HAPPEL J, 1965, LOW REYNOLDS NUMBER. HAYAKAWA H, 2000, PHYS REV E B, V61, P5477. HOFFMANN KH, 2007, J FLUID MECH, V590, P319, DOI 10.1017/S0022112007008099. KEH HJ, 2004, INT J ENG SCI, V42, P1621, DOI 10.1016/j.ijensci.2004.03.007. KISTLER SF, 1993, WETTABILITY, P311. NAVIER CLM, 1823, MEMOIRES ACAD ROYALE, V1, P414. NIEFER R, 1980, J ENG MATH, V14, P107. RAMKISSOON H, 1976, PHYS FLUIDS, V19, P16. RAMKISSOON H, 1988, Z ANGEW MATH MECH, V68, P155. RAMKISSOON H, 1997, J MATH SCI, V8, P59. RAMKISSOON H, 2003, INT J ENG SCI, V41, P283. RAMKISSOON H, 2003, Z ANGEW MATH MECH, V83, P773, DOI 10.1002/zamm.200310102. SENCHENKO S, 2006, PHYS FLUIDS, V18, ARTN 088104. SHERIF HH, 2008, Z ANGEW MATH PHYS, V59, P293, DOI 10.1007/s00033-007-6078-y. TERRILL RM, 1984, IMA J APPL MATH, V33, P169. THOMPSON PA, 1989, PHYS REV LETT, V63, P766. THOMPSON PA, 1990, PHYS REV A, V41, P6830. THOMPSON PA, 1990, SCIENCE, V250, P792. THOMPSON PA, 1993, J ADHES SCI TECHNOL, V7, P535. THOMPSON PA, 1997, NATURE, V389, P360. WILLIAMS WE, 1915, PHILOS MAG, V29, P526. |
| Cited Reference Count: 28 |
| Times Cited: 0 |
| Publisher: NATL RESEARCH COUNCIL CANADA-N R C RESEARCH PRESS; BUILDING M 55, OTTAWA, ON K1A 0R6, CANADA |
| Subject Category: Physics, Multidisciplinary |
| ISSN: 0008-4204 |
| DOI: 10.1139/P08-045 |
| IDS Number: 357XH |
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