Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T23:09:31.850Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of a binary mixture subjected to a temperature gradient and oscillatory forcing

Published online by Cambridge University Press:  13 February 2015

V. Shevtsova ,
Y. A. Gaponenko ,
V. Sechenyh ,
D. E. Melnikov ,
T. Lyubimova  and
A. Mialdun
V. Shevtsova*
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
Y. A. Gaponenko
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
V. Sechenyh
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
D. E. Melnikov
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
T. Lyubimova
Affiliation:
Institute of Continuous Media Mechanics UB RAS, 1, Koroleva str., 614013 Perm, Russia
A. Mialdun
Affiliation:
Microgravity Research Centre, CP-165/62, Université Libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, B-1050 Brussels, Belgium
*
†Email address for correspondence: vshev@ulb.ac.be
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine the dynamics of a binary mixture in a cubic cell subjected to a temperature differential and oscillatory forcing. The Soret effect, which is negative in the present study, provides a coupling mechanism by which a temperature gradient establishes a concentration gradient in a mixture. We present the results of experiments that were performed on the International Space Station (ISS) and compare the observations with the results of direct numerical simulations. The evolution of temperature and concentration fields is investigated by optical digital interferometry. One advantage of the experimental technique is the observation of the fields along two perpendicular directions of the cell, allowing us to restore the three-dimensional field. Experimental evidence disproves speculations that the ISS microgravity environment always affects diffusion-controlled processes. Furthermore, we demonstrate that imposed vibrations with constant frequency and amplitude create slow mean flows and that they do influence the diffusion kinetics. The perturbation of the diffusive fields scales as the square of the vibrational velocity. In addition to calculations of the full three-dimensional Navier–Stokes equations, a two-time-scale computational methodology is used for situations in which the forcing period is very small compared to the natural time scales of the problem. The simulations show excellent agreement with experimental observations.

JFM classification

Instability: Instability Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 767 , 25 March 2015 , pp. 290 - 322
Check for updates
Copyright
© 2015 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

Alexander, J. I. D. 1990 Low gravity experiment sensitivity to residual accelerations: a review. Microgravity Sci. Technol. 3, 52–68.Google Scholar
Babushkin, I. A., Bogatyrev, G. P., Glukhov, A. F., Putin, A. F., Avdeev, S. V., Ivanov, A. I. & Maksimova, M. M. 2001 Investigation of thermal convection and low-frequency microgravity by the DACON sensor aboard the MIR orbital complex. Cosmic Res. 39 (2), 161–169.CrossRefGoogle Scholar
Bardan, G., Razi, Y. P. & Mojtabi, A. 2004 Comments on the mean flow averaged model. Phys. Fluids 16, 4535–4538.CrossRefGoogle Scholar
Beysens, D. 2006 Vibrations in space as an artificial gravity? Europhys. News 37 (3), 22–25.CrossRefGoogle Scholar
Christov, C. I. & Homsy, G. M. 2001 Nonlinear dynamics of two-dimensional convection in a vertically stratified slot with and without gravity modulation. J. Fluid Mech. 430, 335–360.CrossRefGoogle Scholar
de Groot, S. R. & Mazur, P. 1962 Non-Equilibrium Thermodynamics. North-Holland.Google Scholar
Gaponenko, Y., Mialdun, A. & Shevtsova, V. 2014 Experimental and numerical analysis of mass transfer in a binary mixture with Soret effect in the presence of weak convection. Eur. Phys. J. E 37, 90.CrossRefGoogle Scholar
Garandet, J. P., Alexander, J. I. D., Corre, S. & Favier, J. J. 2001 Composition variations induced by g-jitter in Bridgman growth of Sn–Bi alloys in microgravity. J. Cryst. Growth 22, 543–554.CrossRefGoogle Scholar
Garrabos, Y., Beysens, D., Lecoutre, C., Dejoan, A., Polezhaev, V. & Emelianov, V. 2007 Thermoconvectional phenomena induced by vibrations in supercritical $\text{SF}_{6}$ under weightlessness. Phys. Rev. E 75, 056317.CrossRefGoogle Scholar
Gershuni, G. Z., Kolesnikov, A. K., Legros, J. C. & Myznikova, B. I. 1997 On the vibrational convective instability of a horizontal, binary-mixture layer with the Soret effect. J. Fluid Mech. 330, 251–269.CrossRefGoogle Scholar
Gershuni, G. Z. & Lyubimov, D. V. 1998 Thermal Vibrational Convection. Wiley.Google Scholar
Gusev, V., Wu, B. & Diebold, G. J. 2011 Dynamics of thermal diffusion in a linear temperature field. J. Appl. Phys. 110, 044908.CrossRefGoogle Scholar
Higuera, M., Porter, J., Varas, F. & Vega, J. M. 2014 Nonlinear dynamics of confined liquid systems with interfaces subject to forced vibrations. Adv. Colloid Interface Sci. 206, 106–115.CrossRefGoogle ScholarPubMed
Hipp, M., Woisetschläger, J., Reiterer, P. & Neger, T. 2004 Digital evaluation of interferograms. Measurement 36, 53–66.CrossRefGoogle Scholar
Hirata, K., Fujita, S., Okaji, A. & Tanigawa, H. 1995 Thermal convection in an oscillating cube at various frequencies and amplitudes. J. Therm. Sci. Tech. 8, 309–322.CrossRefGoogle Scholar
Hirata, K., Sasaki, T. & Tanigawa, H. 2013 Vibrational effects on convection in a square cavity at zero gravity. J. Fluid Mech. 445, 327–344.CrossRefGoogle Scholar
Huke, B., Lücke, M., Büchel, P. & Jung, Ch. 2000 Stability boundaries of roll and square convection in binary fluid mixtures with positive separation ratio. J. Fluid Mech. 408, 121–147.CrossRefGoogle Scholar
Ito, Y. & Komori, S. 2006 Microfluidic mixing under low frequency vibration. Lab on a Chip 9, 1435–1438.Google Scholar
Jules, K., McPherson, K., Hrovat, K., Kelly, E. & Reckart, T. 2004 A status report on the characterization of the microgravity environment of the International Space Station. Acta Astronaut. 55, 335–364.CrossRefGoogle ScholarPubMed
Kak, A. C. & Slaney, M. 1988 Principles of Computerized Tomographic Imaging. IEEE.Google Scholar
Kerr, O. & Zebib, A. 2006 The effect of vibrations on sideways double-diffusive instabilities: strong stratification asymptotics. J. Fluid Mech. 559, 299–306.CrossRefGoogle Scholar
Kolodner, P. 1994 Stable, unstable, and defected confined states of traveling-wave convection. Phys. Rev. E 50, 2731–2755.CrossRefGoogle ScholarPubMed
Lyubimov, D. V. 1995 Convective flows under the influence of high-frequency vibrations. Eur. J. Mech. (B/Fluids) 14, 439–458.Google Scholar
Lyubimova, T. P., Shklyaeva, E., Legros, J. C., Shevtsova, V. & Roux, B. 2005 Numerical study of high frequency vibration influence on measurement of Soret and diffusion coefficients in low gravity conditions. Adv. Space Res. 36, 70–74.CrossRefGoogle Scholar
Mazzoni, S., Shevtsova, V., Mialdun, A., Melnikov, D., Gaponenko, Yu., Lyubimova, T. & Saghir, M. Z. 2010 Vibrating liquids in space. Europhys. News 41, 14–16.CrossRefGoogle Scholar
Melnikov, D. E., Pushkin, D. & Shevtsova, V. 2011 Accumulation of particles in oscillatory convective flow in liquid bridge. Eur. Phys. J. Spec. Top. 192 (1), 29–39.CrossRefGoogle Scholar
Melnikov, D. E., Shevtsova, V. & Legros, J. C. 2008 Impact of conditions at start-up on thermovibrational convective flow. Phys. Rev. E 78, 056306.CrossRefGoogle ScholarPubMed
Mialdun, A., Ryzhkov, I. I., Melnikov, D. E. & Shevtsova, V. 2008 Experimental evidence of thermal vibrational convection in a non-uniformly heated fluid in a reduced gravity environment. Phys. Rev. Lett. 101, 084501.CrossRefGoogle Scholar
Mialdun, A. & Shevtsova, V. 2011 Measurement of the Soret and diffusion coefficients for benchmark binary mixtures by means of digital interferometry. J. Chem. Phys. 134, 044524.CrossRefGoogle ScholarPubMed
Mialdun, A., Yasnou, V., Shevtsova, V., Königer, A., Köhler, W., Alonso de Mezquia, D. & Bou-Ali, M. M. 2012 A comprehensive study of diffusion, thermodiffusion, and Soret coefficients of water–isopropanol mixtures. J. Chem. Phys. 136, 244512.CrossRefGoogle ScholarPubMed
Moses, E. & Steinberg, V. 1986 Competing patterns in a convective binary mixture. Phys. Rev. Lett. 57 (16), 2018–2021.CrossRefGoogle Scholar
Naumann, R. J., Haulenbeek, G., Kawamura, H. & Matsunaga, K. 2002 The JUSTSAP experiment on STS-95. Microgravity Sci. Technol. 13 (2), 22–32.CrossRefGoogle Scholar
Oberti, S., Neild, A. & Wah Ng, T. 2006 A vibration technique for promoting liquid mixing and reaction in a microchannel. AIChE J. 52, 3011–3017.Google Scholar
Platten, J. K. & Legros, J. C. 1984 Convection in Liquids. Springer.CrossRefGoogle Scholar
Poty, P., Legros, J. C. & Thomaes, G. 1974 Thermal diffusion in some binary liquid mixtures by the flowing cell methods. Z. Naturforsch. 29A, 1915–1916.CrossRefGoogle Scholar
Saez, N., Ruiz, X., Pallar, s. J. & Shevtsova, V. 2013 On the accuracy of the interdiffusion coefficient measurements of high temperature binary mixtures under ISS condition. C. R. Méc. 341, 405–416.CrossRefGoogle Scholar
Savino, R. & Monti, R. 2001 Fluid–dynamics experiment sensitivity to accelerations prevailing on microgravity platforms. In Physics of Fluids in Microgravity (ed. Monti, R.), vol. 178. Taylor & Francis.Google Scholar
Senchenkov, A.2010 61th IAC Congress, IAC-10-A2.4.9, Prague, Czech Republic 2010.Google Scholar
Shevtsova, V. 2010c IVIDIL experiment onboard the ISS. Adv. Space Res. 46 (5), 672–679.CrossRefGoogle Scholar
Shevtsova, V., Gaponenko, Yu., Melnikov, D., Ryzhkov, I. I. & Mialdun, A. 2010a Study of thermoconvective flows induced by vibrations in reduced gravity. Acta Astronaut. 66, 166–173.CrossRefGoogle Scholar
Shevtsova, V., Lyubimova, T., Saghir, Z., Melnikov, D., Gaponenko, Y., Sechenyh, V., Legros, J. C. & Mialdun, A. 2011a IVIDIL: on-board g-jitters and diffusion controlled phenomena. J. Phys.: Conf. Ser. 327, 012031.Google Scholar
Shevtsova, V., Melnikov, D. E. & Legros, J. C. 2006 Onset of convection in Soret-driven instability. Phys. Rev. E 73, 047302.CrossRefGoogle ScholarPubMed
Shevtsova, V., Melnikov, D., Legros, J. C., Yan, Y., Saghir, Z., Lyubimova, T., Sedelnikov, G. & Roux, B. 2007 Influence of vibrations on thermodiffusion in binary mixture: a benchmark of numerical solutions. Phys. Fluids 19, 017111.CrossRefGoogle Scholar
Shevtsova, V., Mialdun, A., Melnikov, D., Ryzhkov, I., Gaponenko, Y., Saghir, Z., Lyubimova, T. & Legros, J. C. 2011b IVIDIL experiment onboard ISS: thermodiffusion in presence of controlled vibrations. C. R. Méc. 339, 310–317.CrossRefGoogle Scholar
Shevtsova, V., Ryzhkov, I. I., Melnikov, D. E., Gaponenko, Yu. & Mialdun, A. 2010b Experimental and theoretical study of vibration induced thermal convection in low gravity. J. Fluid Mech. 648, 53–82.CrossRefGoogle Scholar
Shirkhanzadeh, M. 2009 Analysis of the data obtained from liquid metal diffusion experiments conducted on the MIR space station. Acta Astronaut. 64, 256–263.CrossRefGoogle Scholar
Shliomis, M. I. & Souhar, M. 2000 Self-oscillatory convection caused by the Soret effect. Europhys. Lett. 49, 55.CrossRefGoogle Scholar
Smith, R. W., Zhu, X., Tunnicliffe, M. C., Smith, T. J. N., Misener, L. & Adamson, J. 2002 The influence of gravity on the precise measurement of solute diffusion coefficients in dilute liquid metals and metalloids. Ann. N.Y. Acad. Sci. 974, 57.CrossRefGoogle ScholarPubMed
Smorodin, B. L., Myznikova, B. I. & Keller, I. O. 2002 On the Soret-Driven Thermosolutal Convection in a Vibrational Field of Arbitrary Frequency (ed. Köhler, W. & Wiegand, S.), Lecture Notes in Physics, vol. 584, p. 372. Springer.Google Scholar
Smorodin, B. L., Myznikova, B. I. & Legros, J. C. 2008 Evolution of convective patterns in a binary-mixture layer subjected to a periodical change of the gravity field. Phys. Fluids 20, 094102.CrossRefGoogle Scholar
Tanner, C. C. 1927 The Soret effect. Part I. Trans. Faraday Soc. 23, 75–95.CrossRefGoogle Scholar
Van Vaerenbergh, S. & Legros, J. C. 1990 Kinetics of the Soret effect: transient in the transport process. Phys. Rev. A 41, 67276731.CrossRefGoogle Scholar
Zebib, A. 2001 Low-gravity sideways double-diffusive instabilities. Phys. Fluids 13, 1829–1832.CrossRefGoogle Scholar
Zenkovskaya, S. M. & Simonenko, I. B. 1966 Effect of high-frequency vibration on convection initiation. Fluid Dyn. 1 (5), 35–37.CrossRefGoogle Scholar

Shevtsova et al. supplementary movie

Full caption: Evolution of the concentration field in two orthogonal planes obtained on the ISS by means of interferometry when f=2 Hz and A=44mm. Short caption: IVIDIL, two views in diffusive regime

Download Shevtsova et al. supplementary movie(Video)
Video 20.7 MB

Shevtsova et al. supplementary movie

Full caption: Evolution of the concentration field in two orthogonal planes obtained on the ISS by means of interferometry when f=2 Hz and A=44mm. Short caption: IVIDIL, two views in diffusive regime

Download Shevtsova et al. supplementary movie(Video)
Video 8.7 MB

Shevtsova et al. supplementary movie

Full caption: 3D evolution of the concentration field restored from the experiment on the ISS when f=1 Hz and A=68mm. Short caption: IVIDIL, 3D evolution in diffusive regime

Download Shevtsova et al. supplementary movie(Video)
Video 11.4 MB

Shevtsova et al. supplementary movie

Full caption: 3D evolution of the concentration field restored from the experiment on the ISS when f=1 Hz and A=68mm. Short caption: IVIDIL, 3D evolution in diffusive regime

Download Shevtsova et al. supplementary movie(Video)
Video 5.9 MB