Comptes Rendus
Instability of Navier slip flow of liquids
Comptes Rendus. Mécanique, Volume 332 (2004) no. 11, pp. 895-900.

We investigate the stability problem related to the basic slip flows of liquids in plane microchannels by using the Navier slip concept. We found that if the Navier slip parameter (Ns) equals 0.06, the critical Reynolds number (Recr) becomes 213.6. There are short-wave instabilities, however, when we further increase Ns to 0.07 or 0.08. Recr becomes 132.9 for Ns=0.08 if we neglect the short-wave instability.

Nous étudions la stabilité de l'écoulement de base d'un liquide dans un microcanal plan en présence de glissement aux parois, en utilisant le concept de glissement de Navier. Nous trouvons que le nombre de Reynolds critique (Recr) diminue à 213,6 quand le paramètre de glissement de Navier (Ns) augmente à 0,06. Cependant, il existe des instabilités à courte longueur d'onde quand nous augmentons le paramètre Ns à des valeurs de 0,07 et 0,08. Recr décroît à 132,9 pour Ns=0,08 si on néglige les instabilités d'onde courte.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2004.06.010
Keywords: Fluid mechanics, MEMS (MicroElectroMechanical systems), Preconditioning, Spectral method, Degeneracies, Slip velocity
Mot clés : Mécanique des fluides, Stabilité, Transition à la turbulence, Microfluidique, Glissement

A. Kwang-Hua Chu 1, 2

1 Department of Physics, Xinjiang University, Wulumuqi 830046, PR China
2 P.O. Box 30-15, Shanghai 200030, PR China
@article{CRMECA_2004__332_11_895_0,
     author = {A. Kwang-Hua Chu},
     title = {Instability of {Navier} slip flow of liquids},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {895--900},
     publisher = {Elsevier},
     volume = {332},
     number = {11},
     year = {2004},
     doi = {10.1016/j.crme.2004.06.010},
     language = {en},
}
TY  - JOUR
AU  - A. Kwang-Hua Chu
TI  - Instability of Navier slip flow of liquids
JO  - Comptes Rendus. Mécanique
PY  - 2004
SP  - 895
EP  - 900
VL  - 332
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crme.2004.06.010
LA  - en
ID  - CRMECA_2004__332_11_895_0
ER  - 
%0 Journal Article
%A A. Kwang-Hua Chu
%T Instability of Navier slip flow of liquids
%J Comptes Rendus. Mécanique
%D 2004
%P 895-900
%V 332
%N 11
%I Elsevier
%R 10.1016/j.crme.2004.06.010
%G en
%F CRMECA_2004__332_11_895_0
A. Kwang-Hua Chu. Instability of Navier slip flow of liquids. Comptes Rendus. Mécanique, Volume 332 (2004) no. 11, pp. 895-900. doi : 10.1016/j.crme.2004.06.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.06.010/

[1] D.C. Tretheway; C.D. Meinhart Phys. Fluids, 14 (2002), p. L9

[2] V.S.J. Craig; C. Neto; D.R.M. Williams Phys. Rev. Lett., 87 (2001), p. 054504

[3] Y.X. Zhu; S. Granick Phys. Rev. Lett., 87 (2001), p. 096105

[4] Y.X. Zhu; S. Granick Phys. Rev. Lett., 88 (2002), p. 106102

[5] H. Hervet; L. Léger C. R. Physique, 4 (2003), p. 241

[6] H. Lamb Hydrodynamics, Cambridge University Press, 1932 (sections 327 and 332)

[7] S. Succi Phys. Rev. Lett., 89 (2002), p. 064502

[8] W.K.-H. Chu Z. Angew. Math. Phys., 47 (1996), p. 591

[9] A.R. Wazzan; R.C. Lind; C.Y. Liu Phys. Fluids, 11 (1968), p. 1271

[10] M.v. Smoluchowski Wied. Ann. Phys., 64 (1898), p. 101

[11] M.v. Smoluchowski Akad. Wiss. Wien., 107 (1898), p. 304

[12] M. Knudsen Ann. Phys.-Leipzig, 28 (1909), p. 75

[13] W. Gaede Ann. Phys.-Leipzig, 41 (1913), p. 289

[14] W.A. Gross Gas Film Lubrication, Wiley, 1962

[15] C. Cercignani Mathematical Methods in Kinetic Theory, Plenum, New York, 1990

[16] J.-T. Jeong Phys. Fluids, 13 (2001), p. 1884

[17] K.-H.W. Chu Eur. J. Appl. Phys., 17 (2002), p. 131

[18] J. Pfahler; J. Harley; H.H. Bau; J. Zemel ASME Proceedings HTD-116, 1989

[19] J. Maurer; P. Tabeling; P. Joseph; H. Willaime Phys. Fluids, 15 (2003), p. 2613

[20] M. Esashi; K. Minami; T. Ono Cond. Matter News, 6 (1998), pp. 31-44

[21] K. Komvopoulos Wear, 200 (1996), pp. 305-327

[22] R. Zbikowski Philos. T. Math. Phys. Eng. Sci., 360 (2001), p. 273

[23] C. Cercignani Acta Mech. (Suppl.), 4 (1994), pp. 39-46

[24] A. Georgescu Hydrodynamic Stability Theory, Martinus Nijhoff, Dordrecht, The Netherlands, 1985 (translation edited by Prof. D. Sattinger)

[25] C.H. Choi; K.J.A. Westin; K.S. Breuer Phys. Fluids, 15 (2003), p. 2897

[26] E. Lauga; H.A. Stone J. Fluid Mech., 489 (2003), p. 55

[27] D. Lumma et al. Phys. Rev. E, 67 (2003), p. 056313

[28] H. Spikes; S. Granick Langmuir, 19 (2003), p. 5065

[29] S.A. Orszag J. Fluid Mech., 50 (1971), pp. 689-703

[30] J.K. Platten; J.C. Legros Convection in Liquids, Springer, Berlin, 1984

[31] V.C. Patel; M.R. Head J. Fluid Mech., 38 (1969), pp. 181-201

[32] P. Sun Q. Appl. Math., LIX (2001), p. 667

[33] P.G. de Gennes Langmuir, 18 (2002), p. 3013

[34] C.L.M. Navier C. R. Acad. Sci. Paris, 6 (1827), p. 389

[35] A.K.-H. Chu P. IEE Nanobiotechn., 150 (2003), p. 21

[36] A.K.-H. Chu, Preprint, 2002

[37] W.K.-H. Chu J. Phys. A, 34 (2001), pp. 3389-3392

[38] D. Gottlieb; S.A. Orszag Numerical Analysis of Spectral Methods: Theory and Applications, NSF-CBMS Monograph, vol. 26, SIAM, New York, 1977

[39] S.A. Orszag; A.T. Patera Phys. Rev. Lett., 45 (1980), p. 989

[40] D. Meksyn; J.T. Stuart Proc. Roy. Soc. London Ser. A, 208 (1951), p. 517

Cited by Sources:

Comments - Policy