Abstract
This chapter describes the phenomenology and modeling of Bénard-like patterns and waves in liquid layers, including the case of thin films for which surface tension effects are dominant. Attention is also paid to the (generalized) one-sided description of instabilities in the presence of evaporation, with or without an inert component in the gas phase. Then, the focus is on simplified models of patterned structures, and on the role of symmetry properties of the physical system considered.
Research Associate (Fonds de la Recherche Scientique — FNRS)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
H. Bénard. Les tourbillons cellulaires dans une nappe liquide transportent de la chaleur par convection en régime permanent. Ann. Chim. Phys., 23:62, 1901.
M. Bestehorn and R. Friedrich. Rotationally invariant order parameter equations for natural patterns in nonequilibrium systems. Phys. Rev. E, 59:2642–2652, 1999.
R.B. Bird, W.E. Stewart, and E.N. Lightfoot. Transport Phenomena. Wiley, 1960.
M.J. Block. Surface tension as the cause of Bénard cells and surface deformation in a liquid film. Nature, 178:650–651, 1956.
J.P. Burelbach, S.G. Bankoff, and S.H. Davis. Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech., 195:463–494, 1988.
S. Chandrasekhar. Hydrodynamic and Hydromagnetic Stability. Dover, 1961.
C.I. Christov and M.G. Velarde. Dissipative solitons. Physica D, 86:323–347, 1995.
P. Colinet, J.C. Legros, and M.G. Velarde. Nonlinear Dynamics of Surface-Tension-Driven Instabilities. Wiley-VCH, 2001.
P. Colinet, A.A. Nepomnyashchy, and J.C. Legros. Multiplication of defects in hexagonal patterns. Europhys. Lett., 57:480–486, 2002.
M.C. Cross and P.C. Hohenberg. Pattern formation outside of equilibrium. Rev. Mod. Phys., 65:851–1112, 1993.
B. Echebarria and H. Riecke. Instabilities of hexagonal patterns with broken chiral symmetry. Physica D, 139:97–108, 2000.
K. Eckert and A. Grahn. Plumes and finger regimes driven by an exothermic interfacial reaction. Phys. Rev. Lett., 82:4436, 1999.
K. Eckert and A. Thess. Nonbound dislocations in hexagonal patterns: pentagon lines in surface-tension-driven Bénard convection. Phys. Rev. E, 60:4117–4124, 1999.
K. Eckert, M. Bestehorn, and A. Thess. Square cells in surface-tension-driven Bénard convection: experiment and theory. J. Fluid Mech., 356: 155–197, 1998.
K. Eckert, M. Acker, and Y. Shi. Chemical pattern formation driven by a neutralization reaction. Part I: Mechanism and basic features. Phys. Fluids, 16:385–399, 2004.
P.L. Garcia-Ybarra, J.L. Castillo, and M.G. Velarde. A nonlinear evolution equation for Bénard-Marangoni convection with deformable boundary. Phys. Lett. A, 122:107–110, 1987a.
P.L. Garcia-Ybarra, J.L. Castillo, and M.G. Velarde. Bénard-Marangoni convection with a deformable interface and poorly conducting boundaries. Phys. Fluids, 30:2655–2661, 1987b.
A.A. Golovin, A.A. Nepomnyashchy, and L.M. Pismen. Pattern formation in large-scale Marangoni convection with deformable interface. Physica D, 81:117–147, 1995.
E. Guyon, J.-P. Hulin, and L. Petit. Hydrodynamique Physique. Savoirs Actuels, Editions du CNRS, 1991.
B. Haut and P. Colinet. Surface-tension-driven instabilities of a pure liquid layer evaporating into an inert gas. J. Colloid Interface Sci., 285:296–305, 2005.
J. Israelachvili. Intermolecular and surface forces. Academic Press, 1992.
E. Knobloch. Pattern selection in long-wavelength convection. Physica D, 41:450–479, 1990.
M. Maillard, L. Motte, A.T. Ngo, and M.P. Pileni. Rings and hexagons made of nanocrystals: a Marangoni effect. J. Phys. Chem. B, 104: 11871–11877, 2000.
T. Molenkamp. Marangoni Convection, Mass Transfer and Microgravity. Rijksuniversiteit Groningen, 1998.
A.A. Nepomnyashchy. Order parameter equations for long-wavelength instabilities. Physica D, 86:90–95, 1995.
A.A. Nepomnyashchy, M.G. Velarde, and P. Colinet. Interfacial Phenomena and Convection. Chapman & Hall/CRC, 2002.
A. Oron, S.H. Davis, and S.G. Bankhoff. Long-scale evolution of thin liquid films. Rev. Mod. Phys., 69:931–980, 1997.
M. Paniconi and K.R. Elder. Stationary, dynamical and chaotic states of the two-dimensional damped Kuramoto-Sivashinsky equation. Phys. Rev. E, 56:2713–2721, 1997.
J.R.A. Pearson. On convection cells induced by surface tension. J. Fluid Mech., 4:489, 1958.
J. Pontes, C.I. Christov, and M.G. Velarde. Numerical study of patterns and their evolution in finite geometries. Int. J. Bif. Chaos, 6:1883–1890, 1996.
J. Pontes, C.I. Christov, and M.G. Velarde. Numerical approach to pattern selection in a model problem for Bénard convection in finite fluid layer. Ann. Univ. Sofia, 93:157–175, 1999.
A.Ye. Rednikov and M.G. Velarde. Nonlinear waves and (dissipative) solitons in thin liquid layers. In H.-C. Chang, editor, Nonlinear Waves in Multi-Phase Flow. Kluwer, 2000.
A.Ye. Rednikov, P. Colinet, M.G. Velarde, and J.C. Legros. Rayleigh-Marangoni oscillatory instability in a horizontal liquid layer heated from above: coupling and mode-mixing of internal and surface dilational waves. J. Fluid Mech., 405:57–77, 2000.
A.Ye. Rednikov, P. Colinet, M.G. Velarde, and J.C. Legros. Oscillatory thermocapillary instability in a liquid layer with deformable open surface: capillary-gravity waves, longitudinal waves and mode-mixing. J. Non-Eq. Thermodyn., 25:381–405, 2001.
M. F. Schatz and G.P. Neitzel. Experiments on thermocapillary instabilities. Annu. Rev. Fluid Mech., 33:93–127, 2001.
L. Shtilman and G. Sivashinsky. Hexagonal structure of large-scale Marangoni convection. Physica D, 52:477–488, 1991.
G.I. Sivashinsky. Nonlinear analysis of hydrodynamic instability of laminar flames. part 1. derivation of basic equations. Acta Astronautica, 4:1177–1206, 1977.
G.I. Sivashinsky. On cellular instability in the solidification of a dilute binary alloy. Physica D, 8:243–248, 1983.
P. Stephan and C.A. Busse. Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls. Int. J. Heat Mass Transfer, 35: 383–391, 1992.
J.B. Swift and P.C. Hohenberg. Hydrodynamic fluctuations at the convective instability. Phys. Rev. A, 15:319, 1977.
A. Thess and S.A. Orszag. Surface-tension-driven Bénard convection at infinite Prandtl number. J. Fluid Mech., 283:201–230, 1995.
A. Thess, D. Spirn, and B. Jüttner. Viscous flow at infinite Marangoni number. Phys. Rev. Lett., 75:4614–4617, 1995.
J. Thomson. On certain curious motions observable on the surfaces of wine and other alcoholic liquours. Philosophical Magazine, 10:330, 1855.
J.S. Turner. Buoyancy Effects in Fluids. Cambridge University Press, 1973.
S.J. VanHook, M.F. Schatz, J.B. Swift, W.D. McCormick, and H.L. Swin-ney. Long-wavelength surface-tension-driven Bénard convection: experiment and theory. J. Fluid Mech., 345:45, 1997.
L. Weh and H. Linde. Marangoni-stress-driven’ solitonic’ (periodic) wave trains rotating in an annular container during heat transfer. J. Colloid Interface Sci., 187:159–165, 1997.
A. Wierschem, H. Linde, and M.G. Velarde. Internal waves excited by the Marangoni effect. Phys. Rev. E, 62:6522–6530, 2000.
Y.-N. Young and H. Riecke. Penta-hepta defect chaos in a model for rotating hexagonal convection. Phys. Rev. Lett., 90:134502, 2003.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 CISM, Udine
About this chapter
Cite this chapter
Colinet, P. (2010). Interfacial patterns and waves in liquid layers and thin films. In: Colinet, P., Nepomnyashchy, A. (eds) Pattern Formation at Interfaces. CISM International Centre for Mechanical Sciences, vol 513. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0125-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-7091-0125-4_1
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-0124-7
Online ISBN: 978-3-7091-0125-4
eBook Packages: EngineeringEngineering (R0)