Solutal driven flow is studied for a binary solution submitted to solvent evaporation at the upper free surface. Evaporation induces an increase in the solute concentration close to the free surface and solutal gradients may induce a convective flow driven by buoyancy and/or surface tension. This problem is studied numerically, using several assumptions deduced from previous experiments on polymer solutions. The stability of the system is investigated as a function of the solutal Rayleigh and Marangoni numbers, the evaporative flux and the Schmidt number. The sensitivity of the thresholds to initial perturbations is analyzed. The effect of viscosity variation during drying is also investigated. At last numerical simulations are presented to study the competition between buoyancy and Marangoni effects in the nonlinear regime.
REFERENCES
1.
P.
Colinet
, J. C.
Legros
, and M. G.
Verlade
, Nonlinear Dynamics of Surface-Tension-Driven Instabilities
(Wiley-VCH
, Berlin
, 2001
). 2.
P.
Manneville
, Dynamics of Spatio-Temporal Cellular Structures: Henri Bénard Centenary Review
, Springer Tracts in Modern Physics
Vol. 207
(Springer
, 2006
). 3.
D.
Merkt
and M.
Bestehorn
, “Bénard-Marangoni convection in a strongly evaporating fluid
,” Physica D
185
, 196
–208
(2003
). 4.
C.
Moussy
, G.
Lebon
, and J.
Margerit
, “Influence of evaporation on Bénard-Marangoni instability in a liquid-gas bilayer with a deformable interface
,” Eur. Phys. J. B
40
, 327
–335
(2004
). 5.
O.
Ozen
and R.
Narayanan
, “The physics of evaporative and convective instabilities in bilayer systems
,” Phys. Fluids
16
, 4644
–4652
(2004
). 6.
J.
Margerit
, M.
Dondlinger
, and P. C.
Dauby
, “Improved 1.5-sided model for the weakly nonlinear study of Bénard-Marangoni instabilities in an evaporating liquid layer
,” J. Colloid Interface Sci.
290
(1
), 220
–230
(2005
). 7.
G.
Toussaint
, H.
Bodiguel
, F.
Doumenc
, B.
Guerrier
, and C.
Allain
, “Experimental characterization of buoyancy- and surface tension-driven convection during the drying of a polymer solution
,” Int. J. Heat Mass Transfer
51
, 4228
–4237
(2008
). 8.
A.
Vidal
and A.
Acrivos
, “Effect of nonlinear temperature profiles on onset of convection driven by surface tension gradients
,” Ind. Eng. Chem. Fundam.
7
, 53
–58
(1968
). 9.
T. D.
Foster
, “Stability of a homogeneous fluid cooled uniformly from above
,” Phys. Fluids
8
, 1249
–1257
(1965
). 10.
F.
Doumenc
, T.
Boeck
, B.
Guerrier
, and M.
Rossi
, “Transient Rayleigh-Bénard-Marangoni convection due to evaporation: a linear non-normal stability analysis
,” J. Fluid Mech.
648
, 521
–539
(2010
). 11.
O.
Touazi
, E.
Chénier
, F.
Doumenc
, and B.
Guerrier
, “Simulation of transient Rayleigh-Bénard-Marangoni convection induced by evaporation
,” Int. J. Heat Mass Transfer
53
, 656
–664
(2010
). 12.
B.
Trouette
, E.
Chénier
, C.
Delcarte
, and B.
Guerrier
, “Numerical study of convection induced by evaporation in cylindrical geometry
,” Eur. Phys. J. Special Topics
192
, 83
–93
(2011
). 13.
J. C.
Berg
, M.
Boudart
, and A.
Acrivos
, “Natural convection in pools of evaporative liquids
,” J. Fluid Mech.
24
, 721
–735
(1966
). 14.
P.
Colinet
, L.
Joannes
, C. S.
Iorio
, B.
Haute
, M.
Bestehorn
, G.
Lebon
, and J. C.
Legros
, “Interfacial turbulence in evaporating liquids: theory and preliminary results of the ITEL-master 9 sounding rocket experiment
,” Adv. Space Res.
32
(2
), 119
–127
(2003
). 15.
H.
Mancini
and D.
Maza
, “Pattern formation without heating in an evaporative convection experiment
,” Europhys. Lett.
66
(6
), 812
–818
(2004
). 16.
V. M.
Ha
and C. L.
Lai
, “Onset of Marangony instability of a two-component evaporating droplet
,” Int. J. Heat Mass Transfer
45
, 5143
–5158
(2002
). 17.
H.
Machrafi
, A.
Rednikov
, P.
Colinet
, and P. C.
Dauby
, “Bénard instabilities in a binary-liquid layer evaporating into an inert gas
,” J. Colloid Interface Sci.
349
, 331
–353
(2010
). 18.
P. Y.
de Gennes
, “Instabilities during the evaporation of a film: Non-glassy polymer + volatile solvent
,” Eur. Phys. J. E
6
, 421
–424
(2001
). 19.
S.
Sakurai
, C.
Furukawa
, A.
Okutsu
, A.
Myoshi
, and S.
Nomura
, “Control of mesh pattern of surface corrugation via rate of solvent evaporation in solution casting of polymer film in the presence of convection
,” Polymer
43
, 3359
–3364
(2002
). 20.
N.
Bassou
and Y.
Rharbi
, “Role of Bénard-Marangoni instabilities during solvent evaporation in polymer surface corrugations
,” Langmuir
25
, 624
–632
(2009
). 21.
F.
Doumenc
, B.
Guerrier
, and C.
Allain
, “Mutual diffusion coefficient and vapor-liquid equilibrium data for the system PIB/Toluene
,” J. Chem. Eng. Data
50
, 983
–988
(2005
). 22.
Y.
Gorand
, F.
Doumenc
, B.
Guerrier
, and C.
Allain
, “Instabilités de plissement lors du séchage de films polymères plans
,” Rhéologie
3
, 22
–29
(2003
). 23.
V. C.
Regnier
, P. C.
Dauby
, and G.
Lebon
, “Linear and nonlinear Rayleigh-Bénard-Marangoni instability with surface deformations
,” Phys. Fluids
12
(11
), 2787
–2799
(2000
). 24.
C. W.
Hirt
, A. A.
Amsden
, and J. L.
Cook
, “An arbitrary Lagrangian-Eulerian computing method for all flow speeds
,” J. Comput. Phys.
135
(2
), 203
–216
(1997
)C. W.
Hirt
, A. A.
Amsden
, and J. L.
Cook
, J. Comput. Phys.
[reprinted from 14
(3
), 227
–253
(1974
)]. 25.
J.
Kim
and P.
Moin
, “Application of a fractional-step method to incompressible Navier-Stokes equations
,” J. Comput. Phys.
59
(2
), 308
–323
(1985
). 26.
B.
Trouette
, “Instabilités de Rayleigh-Bénard-Marangoni induites par évaporation en régime transitoire-Application aux solutions polymères
,” Doctorat de l’Université Paris-Sud, 2010
. 27.
E.
Chénier
, C.
Desceliers
, C.
Delcarte
, B.
Trouette
, F.
Doumenc
, and B.
Guerrier
, “Sensitivity of diffusive-convective transition to the initial conditions in a transient Bénard-Marangoni problem
,” in Proceedings of the International Heat Transfer Conference
, Washington, DC
, August 8–13, 2010
(IHTC14-22600). 28.
J. V.
Wehausen
and E. V.
Laitone
, “Surface waves
,” in Handbuch der Physiks
(Springer
, 1960
). © 2012 American Institute of Physics.
2012
American Institute of Physics
You do not currently have access to this content.
