Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-09T07:33:14.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Onset of Rayleigh-Bénard convection in binary liquid mixtures of 3He in 4He

Published online by Cambridge University Press:  20 April 2006

G. W. T. Lee ,
P. Lucas  and
A. Tyler
G. W. T. Lee
Affiliation:
Schuster Laboratory, Department of Physics, University of Manchester, Manchester M13 9PL Present address: VG Analytical Ltd, Altrincham, Cheshire WA14 5REZ.
P. Lucas
Affiliation:
Schuster Laboratory, Department of Physics, University of Manchester, Manchester M13 9PL
A. Tyler
Affiliation:
Schuster Laboratory, Department of Physics, University of Manchester, Manchester M13 9PL
Get access Rights & Permissions [Opens in a new window]

Abstract

We describe experiments in which we have observed the onset of Rayleigh-Bénard convection in normal liquid 3He–4He mixtures. Evidence of overstability was seen when heating from below but only stationary convection was observed when heating from above. Measurements of the critical Rayleigh number are presented and compared with the predictions of current theories of marginal stability in a binary mixture. These experiments exemplify liquid 3He–4He mixtures as a system for the study of convective instabilities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 135 , October 1983 , pp. 235 - 259
Copyright
© 1983 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahlers, G. 1970 Thermal conductivity of a 3He-4He mixture near the superfluid transition. Phys. Rev. Lett. 24, 1333–1336.Google Scholar
Ahlers, G. 1975 Fluctuations, Instabilities and Phase Transitions (ed. T. Riste), p. 323. Plenum.
Ahlers, G. 1976 In The Physics of Liquid and Solid Helium, vol. 1 (ed. J. B. Ketterson and K. H. Benneman), chap. 2. Wiley.
Ahlers, G. & Pobell, F. 1974 Mass diffusivity of 3He-4He mixtures near the superfluid transition. Phys. Rev. Lett. 32, 144–147.Google Scholar
Barenghi, C. F., Lucas, P. & Donnelly, R. J. 1981 Cubic spline fits to thermodynamic and transport properties of liquid 4He above the λ-transition. J. Low Temp. Phys. 44, 491–504.Google Scholar
Caldwell, D. R. 1970 Non-linear effects in a Rayleigh-Bénard experiment J. Fluid Mech. 42, 161–175.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Chablson, G. S. & Sani, R. L. 1970 Thermoconvective instability in a bounded cylindrical fluid layer Intl J. Heat Mass Transfer 13, 1479–1496.Google Scholar
Da Costa, L. N., Knobloch, E. & Weiss, N. O. 1971 Oscillations in double-diffusive convection J. Fluid Mech. 109, 25–43.Google Scholar
De Groot, S. R. & Mazur, P. 1962 Non-Equilibrium Thermodynamics, chaps. 3 and 11. North-Hollond.
Fetter, A. L. 1981 Onset of convection in dilute superfluid 3He-4He mixtures. Physica 107B, 149–150. Also preprints to be published.Google Scholar
Gasparini, F. & Moldover, M. R. 1969 Specific heat of 3He-4He mixtures very near the λ-line. Phys. Rev. Lett. 23, 749–752.Google Scholar
Gershuni, G. Z. & Zhukhovitskii, E. M. 1976 Convective Stability of Incompressible Fluids, chap. 7. Israel Program for Scientific Translations, Jerusalem.
Gestrich, D. & Meyer, H. 1982 Transport properties in 3He-4He mixtures near the superfluid transition. Bull. Am. Phys. Soc. 27, 516.Google Scholar
Gestrich, D., Walsworth, R. & Meyer, H. 1983 Transport properties in 3He-4He mixtures near the superfluid transition. Preprint.
Gutkowicz-Krusin, D., Collins, M. A. & Ross, J. 1979a Rayleigh-Bénard instability in nonreactive fluids. I. Theory Phys. Fluids 22, 1443–1450.Google Scholar
Gutkowicz-Krusin, D., Collins, M. A. & Ross, J. 1979b Rayleigh-Bénard instability in nonreactive fluids. II. Results Phys. Fluids 22, 1451–1460.Google Scholar
Haucke, H., Maeno, Y., Warkentin, P. & Wheatley, J. 1981 Time-dependent thermal convection in dilute solutions of 3He in superfluid 4He. J. Low Temp. Phys. 44, 505–533.Google Scholar
Huppert, H. E. & Moore, D. R. 1976 Non-linear double-diffusive convection J. Fluid Mech. 78, 821–854.Google Scholar
Huppert, H. E. & Moore, D. R. 1976 Non-linear diffusive convection J. Fluid Mech. 78, 821–854.Google Scholar
Hurle, D. T. J. & Jakeman, E. 1969 Significance of the Soret effect in the Rayleigh-Jeffreys problem Phys. Fluids 12, 2704–2705.Google Scholar
Hurle, D. T. J. & Jakeman, E. 1971 Soret-driven thermosolutal convection J. Fluid Mech. 47, 667–687.Google Scholar
Hurle, D. T. J., Jakeman, E. & Pike, E. R. 1967 On the solution of the Bénard problem with boundaries of finite conductivity. Proc. R. Soc. Lond A 296, 469–475.Google Scholar
Kierstead, H. A. 1976 Dielectric constant, molar volume, and phase diagram of saturated liquid 3He-4He mixtures. J. Low Temp. Phys. 24, 497–512.Google Scholar
Knobloch, E. 1980 Convection in binary fluids Phys. Fluids 23, 1918–1920.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, chap. 6. Pergamon.
Lee, G., Lucas, P., Tyler, A. & Vavasour, E. 1978 The Bénard instability in a 3He-4He mixture. J. Phys. (Paris) 41 (C6), 178–179.Google Scholar
Lee, G., Lucas, P. & Tyler, A. 1979 Bénard instability measurements in 3He-4He mixtures near their lambda temperatures. Phys. Lett. 75A, 81–84.Google Scholar
Lucas, P. & Tyler, A. 1977 Thermal diffusion ratio of a 3He-4He mixture near its λ-transition: the onset of heat flush. J. Low Temp. Phys. 27, 281–303.Google Scholar
Mountain, R. D. 1965 Spectral structure of critical opalescence: binary mixture. J. Res. Natl Bur. Standards 69A, 523–525.Google Scholar
Nield, D. A. 1967 The thermohaline Rayleigh-Jeffreys problem J. Fluid Mech. 29, 545–558.Google Scholar
Roberts, T. H. & Sydoriak, S. J. 1960 Sound velocity, phase separation, and lambda transitions of 3He-4He mixtures. Phys. Fluids 3, 895–902.Google Scholar
Ryskewitsch, M. G. & Meyer, H. 1979 Concentration susceptibility of 3He-4He mixtures near the superfluid transition. J. Low Temp. Phys. 35, 103–133.Google Scholar
Schechter, R. S., Prigogine, I. & Hamm, J. R. 1972 Thermal diffusion and convective stability Phys. Fluids 15, 379–386.Google Scholar
Schechter, R. S., Verlahde, M. G. & Platten, J. K. 1974 The two component Bénard problem Adv. Chem. Phys. 26, 265–301.Google Scholar
Steinberg, V. 1981a Stationary convective instability in a superfluid 3He-4He mixture. Phys. Rev. A24, 975–987.Google Scholar
Steinberg, V. 1981b Oscillatory convective instability in a superfluid 3He-4He mixture. Phys. Rev. A24, 2584–2594.Google Scholar
Tanaka, M. & Ikushima, A. 1978 Thermal transport coefficients in 3He-4He mixtures near the lambda line. Phys. Lett. 64A, 402–403.Google Scholar
Tanaka, M., Ikushima, A. & Kawasaki, K. 1977 Thermal conductivities of 3He-4He mixtures on the lambda line at low 3He concentrations. Phys. Lett. 61A, 119–121.Google Scholar
Verlarde, M. G. & Schechter, R. S. 1972 Thermal diffusion and convective stability. II. An analysis of the convected fluxes Phys. Fluids 15, 1707–1714.Google Scholar
Warkentin, P. A., Haucke, H. J., Lucas, P. & Wheatley, J. C. 1980 Stationary convection in dilute solutions of 3He in superfluid 4He. Proc. Natl Acad. Sci. 77, 6983–6987.Google Scholar
Webeler, R. W. H. & Allen, G. 1972 Lambda-point measurements of rHn for pure 3He and for three 3He-4He mixtures. Phys. Rev. A5, 1820–1827.Google Scholar
White, G. K. 1979 Experimental Techniques in Low-Temperature Physics. Clarendon.