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Abstract:

We investigate exact solutions of the NavierStokes equations for steady rectilinear pendent rivulets running under inclined surfaces. First we show how to find exact solutions for sessile or hanging rivulets for any profile of the substrate (transversally to the direction of flow) and with no restrictions on the contact angles. The free surface is a cylindrical meniscus whose shape is determined by the static equilibrium between gravity and surface tension, by the shape of the solid surface, and by the contact angles on both contact lines. Given this, the velocity field can be obtained by integrating numerically a Poisson equation. We then perform a systematic study of rivulets hanging below an inclined plane, computing some of their global properties, and discussing their stability. © 2010 Elsevier Masson SAS. All rights reserved.

Registro:

Documento: Artículo
Título:Navier-Stokes solutions for steady parallel-sided pendent rivulets
Autor:Tanasijczuk, A.J.; Perazzo, C.A.; Gratton, J.
Filiación:Universidad de Buenos Aires, Buenos Aires, Argentina
Dto. de Fsica y Qumica, Universidad Favaloro, Sols 453, 1078, Buenos Aires, Argentina
INFIPCONICET, Dto. de Fsica, Ciudad Universitaria, Pab. i, 1428, Buenos Aires, Argentina
Palabras clave:NavierStokes equations; Parallel flow; Pendent rivulet; Contact lines; Exact solution; Free surfaces; Global properties; Inclined planes; Inclined surface; Navier Stokes; Parallel flows; Pendent rivulet; Solid surface; Static equilibrium; Systematic study; Velocity field; Contact angle; Poisson equation; Surface tension; Parallel flow
Año:2010
Volumen:29
Número:6
Página de inicio:465
Página de fin:471
DOI: http://dx.doi.org/10.1016/j.euromechflu.2010.06.002
Título revista:European Journal of Mechanics, B/Fluids
Título revista abreviado:Eur J Mech B Fluids
ISSN:09977546
CODEN:EJBFE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09977546_v29_n6_p465_Tanasijczuk

Referencias:

  • Towell, G.D., Rothfeld, L.B., Hydrodynamics of rivulet flow (1966) AIChE J., 12 (5), pp. 972-980
  • Allen, R.F., Biggin, C.M., Longitudinal flow of a lenticular liquid filament down an inclined plane (1974) Phys. Fluids, 17, p. 287
  • Duffy, B.R., Moffatt, H.K., Flow of a viscous trickle on a slowly varying incline (1995) Chem. Eng. J., 60 (13), pp. 141-146
  • Alekseenko, S.V., Geshev, P.I., Kuibin, P.A., Free-boundary fluid flow on an inclined cylinder (1997) Sov. Phys. Dokl., 42, pp. 269-272
  • Wilson, S.K., Duffy, B.R., On the gravity-driven draining of a rivulet of viscous fluid down a slowly varying substrate with variation transverse to the direction of flow (1998) Phys. Fluids, 10, p. 13
  • Holland, D., Duffy, B.R., Wilson, S.K., Thermocapillary effects on a thin viscous rivulet draining steadily down a uniformly heated or cooled slowly varying substrate (2001) J. Fluid Mech., 441, pp. 195-221
  • Wilson, S.K., Duffy, B.R., Strong temperature-dependent-viscosity effects on a rivulet draining down a uniformly heated or cooled slowly varying substrate (2003) Phys. Fluids, 15, pp. 827-840
  • Duffy, B.R., Wilson, S.K., A rivulet of perfectly wetting fluid with temperature-dependent viscosity draining down a uniformly heated or cooled slowly varying substrate (2003) Phys. Fluids, 15, pp. 3236-3239
  • Rosenblat, S., Rivulet flow of a viscoelastic liquid (1983) J. Non-Newton. Fluid Mech., 13 (3), pp. 259-277
  • Wilson, S.K., Duffy, B.R., Ross, A.B., On the gravity-driven draining of a rivulet of a viscoplastic material down a slowly varying substrate (2002) Phys. Fluids, 14, pp. 555-571
  • Myers, T.G., Liang, H.X., Wetton, B., The stability and flow of a rivulet driven by interfacial shear and gravity (2004) Internat. J. Non-Linear Mech., 39 (8), pp. 1239-1249
  • Sullivan, J.M., Wilson, S.K., Duffy, B.R., AirBlown rivulet flow of a perfectly wetting fluid on an inclined substrate (2008) Math. Ind., 12, pp. 774-778
  • Sullivan, J.M., Wilson, S.K., Duffy, B.R., A thin rivulet of perfectly wetting fluid subject to a longitudinal surface shear stress (2008) Q. J. Mech. Appl. Math., 61 (1), pp. 25-61
  • Mertens, K., Putkaradze, V., Vorobieff, P., Braiding patterns on an inclined plane (2004) Nature, 430 (6996), p. 165
  • Mertens, K., Putkaradze, V., Vorobieff, P., Morphology of a stream flowing down an inclined plane. Part 1. Braiding (2005) J. Fluid Mech., 531, pp. 49-58
  • Birnir, B., Mertens, K., Putkaradze, V., Vorobieff, P., Morphology of a stream flowing down an inclined plane. Part 2. Meandering (2008) J. Fluid Mech., 607, pp. 401-411
  • Perazzo, C.A., Gratton, J., NavierStokes solutions for parallel flow in rivulets on an inclined plane (2004) J. Fluid Mech., 507, pp. 367-379
  • Bashforth, F., Adams, J.C., (1892) An Attempt to Test the Theory of Capillary Action, , Cambridge University Press and Deighton, Bell & Co
  • Pitts, E., The stability of pendent liquid drops. Part 1. Drops formed in a narrow gap (1973) J. Fluid Mech., 59, pp. 753-767. , 101017/S0022112073001849
  • Indeikina, A., Veretennikov, I., Chang, H.C., Drop falloff from pendent rivulets (1997) J. Fluid Mech., 338, pp. 173-201
  • Michael, D.H., Meniscus stability (1981) Annu. Rev. Fluid Mech., 13 (1), pp. 189-216
  • Oron, A., Davis, S.H., Bankoff, S.G., Long-scale evolution of thin liquid films (1997) Rev. Modern Phys., 69 (3), pp. 931-980. , 101103/RevModPhys69931
  • Kolmakov, G.V., Lebedeva, E.V., Levchenko, A.A., Mezhov-Deglin, L.P., Trusov, A.B., Shikin, V.B., Stationary nonlinear waves at the surface of a thin liquid layer under inverted gravitation conditions (2004) Low Temp. Phys., 30 (1), pp. 58-69. , http://link.aip.org/link/?LTP/30/58/1, 101063/11645156 URL
  • Alekseenko, S.V., Markovich, D.M., Shtork, S.I., Wave flow of rivulets on the outer surface of an inclined cylinder (1996) Phys. Fluids, 8 (12), pp. 3288-3299. , http://link.aip.org/link/?PHF/8/3288/1, 101063/1869118 URL

Citas:

---------- APA ----------
Tanasijczuk, A.J., Perazzo, C.A. & Gratton, J. (2010) . Navier-Stokes solutions for steady parallel-sided pendent rivulets. European Journal of Mechanics, B/Fluids, 29(6), 465-471.
http://dx.doi.org/10.1016/j.euromechflu.2010.06.002
---------- CHICAGO ----------
Tanasijczuk, A.J., Perazzo, C.A., Gratton, J. "Navier-Stokes solutions for steady parallel-sided pendent rivulets" . European Journal of Mechanics, B/Fluids 29, no. 6 (2010) : 465-471.
http://dx.doi.org/10.1016/j.euromechflu.2010.06.002
---------- MLA ----------
Tanasijczuk, A.J., Perazzo, C.A., Gratton, J. "Navier-Stokes solutions for steady parallel-sided pendent rivulets" . European Journal of Mechanics, B/Fluids, vol. 29, no. 6, 2010, pp. 465-471.
http://dx.doi.org/10.1016/j.euromechflu.2010.06.002
---------- VANCOUVER ----------
Tanasijczuk, A.J., Perazzo, C.A., Gratton, J. Navier-Stokes solutions for steady parallel-sided pendent rivulets. Eur J Mech B Fluids. 2010;29(6):465-471.
http://dx.doi.org/10.1016/j.euromechflu.2010.06.002