Abstract
While the Rayleigh–Bénard convection in a pure liquid serves as a paradigmatic example of stationary patterns generated by monotonic instability, convection in a binary liquid provides a basic example of an oscillatory instability generating wave patterns.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
L.M. Pismen, Phys. Rev. A 38, 2564 (1988)
F.S. Gaeta, G. Perna, G. Scala, F. Bellucci, J. Phys. Chem. 86, 2967 (1982)
P. Kolodner, H. Williams, C. Moe, J. Chem. Phys. 88, 6512 (1988)
G.W.T. Lee, P. Lucas, A. Tyler, J. Fluid Mech. 135, 235 (1983)
W. Hort, S.J. Linz, M. Lücke, Phys. Rev. A 45, 3737 (1992)
J. Liu, G. Ahlers, Phys. Rev. E 55, 6950 (1997)
S. Hollinger, M. Lücke, H.W. Muller, Phys. Rev. E 57, 4250 (1998)
A. Bergeon, D. Henry, H. BenHadid, Microgravity Q. 5, 123 (1995)
D.A. Nield, J. Fluid Mech. 71, 411 (1975)
L. Shtilman, G.I. Sivashinsky, Physica D 52, 477 (1991)
S. Shklyaev, A.A. Nepomnyashchy, A. Oron, Phys. Rev. E 84, 056327 (2011)
M. Silber, E. Knobloch, Nonlinearity 4, 1063 (1991)
M. Roberts, J.W. Swift, D.H. Wagner, Contemp. Math. 56, 283 (1986)
A.H. Nayfeh, Perturbation Methods (Wiley, New York, 1973)
S. Shklyaev, A.A. Nepomnyashchy, A. Oron, Phys. Fluids 19, 072105 (2007)
T. Clune, M.C. Depassier, E. Knobloch, Instabilities and Nonequilibrium Structures (Kluwer, Dordrecht, 1996)
J.J. Jasper, J. Phys. Chem. Ref. Data 1, 841 (1972)
S. Shklyaev, A.A. Nepomnyashchy, A. Oron, Phys. Fluids 21, 054101 (2009)
A. Oron, A.A. Nepomnyashchy, Phys. Rev. E 69, 016313 (2004)
J.R.A. Pearson, J. Fluid Mech. 4, 489 (1958)
A. Podolny, A. Oron, A.A. Nepomnyashchy, Phys. Fluids 17, 104104 (2005)
A. Podolny, A. Oron, A.A. Nepomnyashchy, Math. Model. Nat. Phenom. 3(1), 1 (2008)
A. Podolny, A. Oron, A.A. Nepomnyashchy, Fluid Dyn. Mater. Process. 6, 13 (2010)
A.A. Golovin, A.A. Nepomnyashchy, L. Pismen, Physica D 81, 117 (1995)
S. Shklyaev, A.A. Nepomnyashchy, A. Oron, SIAM J. Appl. Math. 73, 2203 (2013)
S. Shklyaev, A.A. Nepomnyashchy, A. Oron, SIAM J. Appl. Math. 74, 1005 (2014)
M. Krupa, I. Melbourne, Ergodic Theory Dyn. Syst. 15, 121 (1995)
I. Melbourne, P. Chossat, M. Golubitsky, Proc. R. Soc. Edinb. Sec. A Math. 113, 315 (1989)
J.L. Castillo, M.G. Velarde, J. Fluid Mech. 125, 463 (1982)
J.L. Castillo, M.G. Velarde, J. Colloid Interface Sci. 108, 264 (1985)
M.-I. Char, K.-T. Chiang, Int. J. Heat Mass Transf. 39, 407 (1996)
J.K. Bhattacharjee, Phys. Rev. E 50, 1198 (1994)
S.W. Joo, J. Fluid Mech. 293, 127 (1995)
J.R.L. Skarda, F.E. McCaughan, Int. J. Heat Mass Transf. 42, 2387 (1999)
A. Podolny, A. Oron, A.A. Nepomnyashchy, Phys. Fluids 18, 054104 (2006)
A. Podolny, A. Oron, A.A. Nepomnyashchy, J. Non-Equilib. Thermodyn. 32, 1 (2007)
M. Morozov, A. Oron, A.A. Nepomnyashchy, Phys. Fluids 25, 052107 (2013)
A. Podolny, A. Oron, A.A. Nepomnyashchy, Phys. Rev. E 76, 026309 (2007)
J. Buongiorno, ASME Trans. J. Heat Transf. 128, 240 (2006)
L. Dong, D. Johnson, Langmuir 19, 10205 (2003)
L. Dong, D. Johnson, Adv. Space Res. 32, 149 (2003)
H. Xue, J. Fan, Y. Hu, R. Hong, K. Cen, J. Appl. Phys. 100, 104909 (2006)
F. Ravera, M. Ferrari, L. Liggieri, G. Loglio, E. Santini, A. Zanobini, Colloids Surf. A 323, 99 (2008)
G.I. Sivashinsky, Physica D 4, 227 (1982)
E. Knobloch, Physica D 41, 450 (1990)
A. Mikishev, A.A. Nepomnyashchy, Microgravity Sci. Technol. 22, 415 (2010)
A. Mikishev, A.A. Nepomnyashchy, Phys. Rev. E 82, 046306 (2010)
A.S.A. Hamid, S.A. Kechil, A.S.A. Aziz, World Acad. Sci. Eng. Technol. 58, 24 (2011)
S. Slavtchev, P. Kalitzova-Kurteva, A. Oron, J. Theor. Appl. Mech. (Sofia) 39, 63 (2009)
P. Kalitzova-Kurteva, S. Slavtchev, A. Oron, J. Theor. Appl. Mech. (Sofia) 39, 31 (2009)
R. Pan, J. Green, C. Maldarelli, J. Colloid Interface Sci. 205, 213 (1998)
S. Shklyaev, A.A. Nepomnyashchy, Eur. Phys. J. Spec. Top. 192, 155 (2011)
M.L. Agrawal, R.D. Neuman, J. Colloid Interface Sci. 121, 366 (1988)
D.S. Valkovska, K.D. Danov, J. Colloid Interface Sci. 223, 314 (2000)
S. Shklyaev, A.A. Nepomnyashchy, J. Fluid Mech. 718, 428 (2013)
D.S. Goldobin, D.V. Lyubimov, Sov. Phys. JETP 104, 830 (2007)
M. Morozov, A. Oron, A.A. Nepomnyashchy, Phys. Fluids 26, 112101 (2014)
M. Morozov, A. Oron, A.A. Nepomnyashchy, Phys. Fluids 27, 082107 (2015)
J.C. Berg, A.A. Acrivos, Chem. Eng. Sci. 20, 737 (1965)
H.J. Palmer, J.C. Berg, J. Fluid Mech. 51, 38 (1972)
V.G. Levich, Physicochemical Hydrodynamics (Prentice Hall, Englewood Cliffs, 1962)
A.Y. Gilev, A.A. Nepomnyashchy, I.B. Simanovskii, Zh. Prikl. Mekh. Tekhn. Fiz. 5, 76 (1986, in Russian)
A.A. Nepomnyashchy, I.B. Simanovskii, Fluid Dyn. 21, 169 (1986)
A.A. Nepomnyashchy, I.B. Simanovskii, Fluid Dyn. 23, 302 (1988)
A.A. Nepomnyashchy, I.B. Simanovskii, Zh. Prikl. Mekh. Tekhn. Fiz. 1, 146 (1989, in Russian)
A.A. Nepomnyashchy, I.B. Simanovskii, Sov. Phys. Dokl. 34, 420 (1989)
A.A. Nepomnyashchy, I.B. Simanovskii, Zh. Prikl. Mekh. Tekhn. Fiz. 3 73 (1992, in Russian)
A. Mikishev, A.A. Nepomnyashchy, Microgravity Sci. Technol. 23(Suppl 1), S59 (2011)
A. Mikishev, A.A. Nepomnyashchy, Phys. Fluids 25, 054109 (2013)
A. Mikishev, A.A. Nepomnyashchy, Fluid Dyn. Res. 46, 041420 (2014)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Shklyaev, S., Nepomnyashchy, A. (2017). Convection in Binary Liquids: Amplitude Equations for Stationary and Oscillatory Patterns. In: Longwave Instabilities and Patterns in Fluids. Advances in Mathematical Fluid Mechanics. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-7590-7_4
Download citation
DOI: https://doi.org/10.1007/978-1-4939-7590-7_4
Published:
Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-1-4939-7588-4
Online ISBN: 978-1-4939-7590-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)