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Transient Rayleigh–Bénard–Marangoni convection due to evaporation: a linear non-normal stability analysis

Published online by Cambridge University Press:  07 April 2010

F. DOUMENC ,
T. BOECK ,
B. GUERRIER  and
M. ROSSI
F. DOUMENC*
Affiliation:
UPMC Université Paris 06, Université Paris-Sud, CNRS, UMR 7608, Lab FAST, Bat 502, Campus Universitaire, Orsay F-91405, France
T. BOECK
Affiliation:
Institut für Thermo- und Fluiddynamik, Technische Universität Ilmenau, Postfach 100565, 98684 Ilmenau, Germany
B. GUERRIER
Affiliation:
UPMC Université Paris 06, Université Paris-Sud, CNRS, UMR 7608, Lab FAST, Bat 502, Campus Universitaire, Orsay F-91405, France
M. ROSSI
Affiliation:
UPMC Université Paris 06, CNRS, UMR 7190, IJLRA, 4 place Jussieu, Paris F-75005, France
*
†Email address for correspondence: frederic.doumenc@upmc.fr
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Abstract

The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal approach, and predicts the onset of instability, critical wavenumber and time. The method is applied to transient Rayleigh–Bénard–Marangoni convection due to cooling by evaporation. Numerical results as well as theoretical scalings for the critical parameters as function of the Biot number are presented for the limiting cases of purely buoyancy-driven and purely surface-tension-driven convection. Critical parameters from calculations are in good agreement with those from experiments on drying polymer solutions, where the surface cooling is induced by solvent evaporation.

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Papers
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Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 521 - 539
Copyright
Copyright © Cambridge University Press 2010

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References

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