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Measurements of the concentration field in nonlinear travelling-wave convection

Published online by Cambridge University Press:  26 April 2006

Bernhard L. Winkler  and
Paul Kolodner
Bernhard L. Winkler
Affiliation:
AT & T Bell Laboratories, Murray Hill, NJ 07974-2070, USA Present address: Universität Bayreuth, D-8580 Bayreuth, Germany.
Paul Kolodner
Affiliation:
AT & T Bell Laboratories, Murray Hill, NJ 07974-2070, USA
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Abstract

We present observations of travelling-wave convection in ethanol/water mixtures in a rectangular container using shadowgraphic flow visualization along the axes of the convective rolls. The entrainment of solute into the centre of the fluid layer from the boundary layers at the top and bottom of the cell is clearly observed in the shadowgraph images as sharp features at the roll boundaries. The shadowgraph images are integrated to yield a map of the two-dimensional refractive-index field. The contributions to this field from the convective temperature and the concentration fields have sufficiently different spatial character to be reliably separated using image-processing techniques. This has allowed us to produce a map of these two flow fields that is in good quantitative agreement with numerical integrations of the full Navier–Stokes equations in the Boussinesq approximation. We also present qualitative visualizations of transients caused by abruptly triggering and quenching travelling-wave convection. These experiments illustrate the formation of concentration boundary layers and reveal the existence of large-scale currents which are an inherent part of travelling-wave convection.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 240 , July 1992 , pp. 31 - 58
Copyright
© 1992 Cambridge University Press

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References

Barten, W., Lücke, M., Hort, W. & Kamps, M. 1989 Fully developed traveling-wave convection in binary fluid mixtures. Phys. Rev. Lett. 63, 376–379.Google Scholar
Barten, W., Lücke, M. & Kamps, M. 1990 Structure and dynamics of nonlinear convective states in binary fluid mixtures. In Proc. NATO Advanced Research Workshop on Nonlinear Evolution of Spatio-temporal Structures in Dissipative Continuous Systems (ed. F. H. Busse & L. Kramer), pp. 131–148. Plenum.
Barten, W., Lücke, M. & Kamps, M. 1991 Localized traveling-wave convection in binary-fluid mixtures. Phys. Rev. Lett. 66, 2621–2625.Google Scholar
Bensimon, D., Kolodner, P., Surko, C. M., Williams, H. L. & Croquette, V. 1990 Competing and coexisting dynamical states of traveling-wave convection in an annulus. J. Fluid Mech. 217, 441–467.Google Scholar
Bensimon, D., Pumir, A. & Shraiman, B. I. 1989 Nonlinear theory of traveling wave convection in binary mixtures. J. Phys. Paris 50, 3089–3108.Google Scholar
Eaton, K. D., Ohlsen, D. R., Yamamoto, S. Y., Surko, C. M., Barten, W., Lücke, M., Kamps, M. & Kolodner, P. 1991 Concentration field in traveling-wave and stationary convection in fluid mixtures.. Phys. Rev. A 43, 7105–7108.Google Scholar
Hurle, D. T. J. & Jakeman, E. 1971 Soret-driven thermosolutal convection. J. Fluid Mech. 47, 667–689.Google Scholar
Kolodner, P. 1990 Neutrally stable fronts of slow convective traveling waves.. Phys. Rev. A 42, 2475–2478.Google Scholar
Kolodner, P. 1991 Drift, shape, and intrinsic destabilization of pulses of traveling-wave convection.. Phys. Rev. A 43, 6448–6465.Google Scholar
Kolodner, P., Passner, A., Surko, C. M. & Walden, R. W. 1986 Onset of oscillatory convection in a binary fluid mixture. Phys. Rev. Lett. 56, 2621–2624.Google Scholar
Kolodner, P., Passner, A., Williams, H. L. & Surko, C. M. 1987 The transition to finite-amplitude traveling-wave convection in binary fluid mixtures. Nucl. Phys. B (Proc. Suppl.) 2, 97–108.Google Scholar
Kolodner, P. & Williams, H. L. 1990 Complex demodulation techniques for experiments on traveling-wave convection. In Proc. NATO Advanced Research Workshop on Nonlinear Evolution of Spatio-temporal Structures in Dissipative Continuous Systems (ed. F. H. Busse & L. Kramer), pp. 73–92. Plenum.
Kolodner, P., Williams, H. & Moe, C. 1988 Optical measurement of the Soret coefficient of ethanol/water solutions. J. Chem. Phys. 88, 6512–6524.Google Scholar
Linz, S. J. & Lücke, M. 1987 Convection in binary mixtures: a Galerkin model with impermeable boundary conditions.. Phys. Rev. A 35, 3997–4000.Google Scholar
Linz, S. J., Lücke, M., Müller, H. W. & Niederländer, J. 1988 Convection in binary fluid mixtures: traveling waves and lateral currents.. Phys. Rev. A 38, 5727–5741.Google Scholar
Moses, E., Fineberg, J. & Steinberg, V. 1987 Multistability and confined traveling-wave patterns in a convecting binary mixture.. Phys. Rev. A 35, 2757–2760.Google Scholar
Moses, E. & Steinberg, V. 1988 Mass transport in propagating patterns of convection. Phys. Rev. Lett. 60, 2030–2033.Google Scholar
Moses, E. & Steinberg, V. 1989 Mass transport in propagating patterns of convection. Physica 37D, 341–358.Google Scholar
Ohlsen, D. R., Yamamoto, S. Y., Surko, C. M. & Kolodner, P. 1990 Transition from traveling-wave to stationary convection in fluid mixtures. Phys. Rev. Lett. 65, 1431–1434.Google Scholar
Rasenat, S., Hartung, G., Winkler, B. L. & Rehberg, I. 1989 The shadowgraph method in convection experiments. Exp. Fluids 7, 412–419.Google Scholar
Steinberg, V. & Kaplan, E. 1991 Localized and ‘blinking’ traveling wave patterns in a convective binary mixture. In Proc. NATO Advanced Research Workshop on Spontaneous Formation of Space—Time Structures and Criticality (ed. T. Riste & D. Sherrington), pp. 207–244. Plenum.
Steinberg, V., Moses, E. & Fineberg, J. 1987 Spatio-temporal complexity at the onset of convection in a binary fluid. Nucl. Phys. B (Proc. Suppl.) 2, 109–124.Google Scholar
Surko, C. M. & Kolodner, P. 1987 Oscillatory traveling-wave convection in a finite container. Phys. Rev. Lett. 58, 2055–2058.Google Scholar
Surko, C. M., Ohlsen, D. R., Yamamoto, S. Y. & Kolodner, P. 1991 Confined states of traveling-wave convection.. Phys. Rev. A 43, 7101–7104.Google Scholar
Walden, R. W., Kolodner, P., Passner, A. & Surko, C. M. 1985 Traveling waves and chaos in convection in binary fluid mixtures. Phys. Rev. Lett. 55, 496–499.Google Scholar