Influence of Composition Dependent Diffusion Coefficient,Viscosity and Relaxation Time on EvaporativeRayleigh-Bénard-Marangoni Instabilities Induced by SolventEvaporation in a Polymer Solution

Rabani, Ramin; Machrafi, Hatim; Dauby, Pierre

doi:10.1007/s12217-019-09732-8

Article (Scientific journals)

Influence of Composition Dependent Diffusion Coefficient,Viscosity and Relaxation Time on EvaporativeRayleigh-Bénard-Marangoni Instabilities Induced by SolventEvaporation in a Polymer Solution

Rabani, Ramin; Machrafi, Hatim; Dauby, Pierre

2019 • In Microgravity Science and Technology

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/238733

DOI
10.1007/s12217-019-09732-8

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Keywords :

Drying of polymer solution; Rayleigh-Bénard-Marangoni instabilities; Monotonic and oscillatory modes

Abstract :

[en] In this study, a linear stability analysis is performed for both monotonic and oscillatory modes within a horizontal polymersolution layer, which solely the solvent evaporates into air. The approach is based on general thermodynamic principles and alsoon the physics of the gas phase and its interactions with the liquid phase. Due to evaporation, the solvent mass fraction changesand cooling occurs at the liquid-gas interface. This can trigger solutal and thermal Rayleigh-Bénard-Marangoni instabilities in thesystem. For the monotonic mode, the effects of composition dependent diffusion coefficient and dynamic viscosity on the onsetof Rayleigh-Bénard-Marangoni convection are studied. Moreover, the effect of different total heights of the liquid-gas system onthe behavior of convection onset is considered. The results show that a variable diffusion coefficient and a variable viscosity cannotably change the onset of instability for a polyisobutylene (PIB)/toluene solution. Our model for the monotonic mode is alsosatisfactorily compared with an experimental study. For the oscillatory mode, where the relaxation time is also compositiondependent, we observe that very thin layers will be susceptible to an oscillatory instability when drying occurs in the system.Finally, an approximate model is derived exploiting the fact that the solutal Marangoni is by far the most dominant instabilitymechanism here. A negligible difference with respect to the full model confirms the predominance of the solutal Marangonimechanism.

Research Center/Unit :

Thermodynamics of Irreversible Phenomena

Disciplines :

Mechanical engineering

Author, co-author :

Rabani, Ramin ; Université de Liège - ULiège > In silico-Model-based therapeutics, Critical Care Basic Sc.

Machrafi, Hatim ; Université de Liège - ULiège > In silico medecine-Thermodynamics of Irreversible Processes

Dauby, Pierre ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Thermodynamique des phénomènes irréversibles

Language :

English

Title :

Influence of Composition Dependent Diffusion Coefficient,Viscosity and Relaxation Time on EvaporativeRayleigh-Bénard-Marangoni Instabilities Induced by SolventEvaporation in a Polymer Solution

Alternative titles :

[en] Belgium

Publication date :

17 August 2019

Journal title :

Microgravity Science and Technology

ISSN :

0938-0108

eISSN :

1875-0494

Publisher :

Springer, Dordrecht, Netherlands

Special issue title :

Thirty Years ofMicrogravity Research - A Topical Collection Dedicated to J. C. Legros

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.springer.com/article/10.1007/s12217-019-09732-8

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique
BELSPO - Politique scientifique fédérale

Funding text :

Financial support from F.R.S.-FNRS (“DITRASOL” PDR T.0123.16) and from BELSPO (“EVAPORATION” MAP-PRODEX project) is also acknowledged.

Available on ORBi :

since 19 August 2019

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Bibliography

Bassou, N., Rharbi, Y.: Role of Benard- Marangoni instabilities during solvent evaporation in polymer surface corrugations. Langmuir. 25(1), 624–632 (2008)
Bekezhanova, V.B., Shefer, I.A.: Influence of gravity on the stability of evaporative convection regimes. Microgravity Sci Technol. 30(4), 543–560 (2018)
Bird, R.B., Armstrong, R.C. and Hassager, O.: Dynamics of polymeric liquids. Vol. 1: Fluid mechanics (1987)
Bormashenko, E., Balter, S., Pogreb, R., Bormashenko, Y., Gendelman, O., Aurbach, D.: On the mechanism of patterning in rapidly evaporated polymer solutions: Is temperature-gradient-driven Marangoni instability responsible for the large-scale patterning? J. Colloid Interface Sci. 343(2), 602–607 (2010)
Bratsun, D., Kostarev, K., Mizev, A., Mosheva, E.: Concentration-dependent diffusion instability in reactive miscible fluids. Phys. Rev. E. 92(1), 011003 (2015)
Bratsun, D.A., Stepkina, O.S., Kostarev, K.G., Mizev, A.I., Mosheva, E.A.: Development of concentration-dependent diffusion instability in reactive miscible fluids under influence of constant or variable inertia. Microgravity Sci Technol. 28(6), 575–585 (2016)
Cantú, A.A.: A study of the evaporation of a solvent from a solution—application to writing ink aging. Forensic Sci. Int. 219(1–3), 119–128 (2012)
Chatterjee, B.K., Roy, S.C.: Viscosity divergence and gelation. Radiat. Phys. Chem. 74(6), 419–425 (2005)
Colinet, P., Legros, J.C. and Velarde, M.G.: Nonlinear dynamics of surface-tension-driven instabilities. Wiley-vch (2001)
Dauby, P.C., Parmentier, P., Lebon, G., Grmela, M.: Coupled buoyancy and thermocapillary convection in a viscoelastic Maxwell fluid. J. Phys. Condens. Matter. 5(26), 4343 (1993)
De Gans, B.J., Duineveld, P.C., Schubert, U.S.: Inkjet printing of polymers: state of the art and future developments. Adv. Mater. 16(3), 203–213 (2004)
De Gennes, P.G.: Instabilities during the evaporation of a film: Non-glassy polymer+ volatile solvent. Eur Phys J E. 6(1), 421–424 (2001)
Dondlinger, M., Colinet, P., Dauby, P.C.: Influence of a nonlinear reference temperature profile on oscillatory Bénard-Marangoni convection. Phys. Rev. E. 68(6), 066310 (2003)
Doumenc, F., Boeck, T., Guerrier, B., Rossi, M.: Transient Rayleigh-Bénard-Marangoni convection due to evaporation: a linear non-normal stability analysis. J. Fluid Mech. 648, 521–539 (2010)
Doumenc, F., Chénier, E., Trouette, B., Boeck, T., Delcarte, C., Guerrier, B., Rossi, M.: Free convection in drying binary mixtures: solutal versus thermal instabilities. Int. J. Heat Mass Transf. 63, 336–350 (2013)
Evans, P.L., Schwartz, L.W., Roy, R.V.: J. Colloid Interface Sci. 227, 191 (2000)
Foster, T.: Onset of convection in a layer of fluid cooled from above. Phys. Fluids. 8(10), 1770–1774 (1965a)
Foster, T.: Stability of a homogeneous fluid cooled uniformly from above. Phys. Fluids. 8(7), 1249–1257 (1965b)
de Gans, B.J., Schubert, U.S.: Inkjet printing of well-defined polymer dots and arrays. Langmuir. 20(18), 7789–7793 (2004)
Getachew, D., Rosenblat, S.: Thermocapillary instability of a viscoelastic liquid layer. Acta Mech. 55(1–2), 137–149 (1985)
Goussis, D.A., Kelly, R.E.: On the thermocapillary instabilities in a liquid layer heated from below. Int. J. Heat Mass Transf. 33(10), 2237–2245 (1990)
Guerrier, B., Bouchard, C., Allain, C., Bénard, C.: Drying kinetics of polymer films. AICHE J. 44(4), 791–798 (1998)
Guo, L.: Gelation and micelle structure changes of aqueous polymer solutions, Ph.D. thesis, The Pennsylvania State University, Pennsylvania, United states (2003)
Haut, B., Colinet, P.: Surface-tension-driven instabilities of a pure liquid layer evaporating into an inert gas. J. Colloid Interface Sci. 285(1), 296–305 (2005)
Howison, S.D., Moriarty, J.A., Ockendon, J.R., Terrill, E.L., Wilson, S.K.: A mathematical model for drying paint layers. J. Eng. Math. 32(4), 377–394 (1997)
Iorio, C.S., Kabov, O.A., Legros, J.C.: Thermal patterns in evaporating liquid. Microgravity Sci Technol. 19(3–4), 27–29 (2007)
Kang, K.H., Choi, C.K.: A theoretical analysis of the onset of surface-tension-driven convection in a horizontal liquid layer cooled suddenly from above. Phys. Fluids. 9(1), 7–15 (1997)
Kawase, T., Shimoda, T., Newsome, C., Sirringhaus, H., Friend, R.H.: Inkjet printing of polymer thin film transistors. Thin Solid Films. 438, 279–287 (2003)
Lebon, G., Parmentier, P., Teller, O., Dauby, P.C.: Bénard-Marangoni instability in a viscoelastic Jeffreys' fluid layer. Rheol. Acta. 33(4), 257–266 (1994)
Litvinov, V.M. and De, P.P.: Spectroscopy of rubbers and rubbery materials. iSmithers Rapra Publishing (2002)
Machrafi, H., Rednikov, A., Colinet, P., Dauby, P.C.: Bénard instabilities in a binary-liquid layer evaporating into an inert gas. J. Colloid Interface Sci. 349(1), 331–353 (2010)
Machrafi, H., Rednikov, A., Colinet, P., Dauby, P.C.: Bénard instabilities in a binary-liquid layer evaporating into an inert gas: Stability of quasi-stationary and time-dependent reference profiles. Eur Phys J Spec Top. 192(1), 71–81 (2011)
Machrafi, H., Rednikov, A., Colinet, P., Dauby, P.C.: Time-dependent Marangoni-Bénard instability of an evaporating binary-liquid layer including gas transients. Phys. Fluids. 25(8), 084106 (2013)
Machrafi, H., Rednikov, A., Colinet, P., Dauby, P.C.: Importance of wave-number dependence of Biot numbers in one-sided models of evaporative Marangoni instability: Horizontal layer and spherical droplet. Phys. Rev. E. 91(5), 053018 (2015)
Mokarian-Tabari, P., Geoghegan, M., Howse, J.R., Heriot, S.Y., Thompson, R.L., Jones, R.A.L.: Quantitative evaluation of evaporation rate during spin-coating of polymer blend films: Control of film structure through defined-atmosphere solvent-casting. Eur Phys J E. 33(4), 283–289 (2010)
Münch, A., Please, C.P., Wagner, B.: Spin coating of an evaporating polymer solution. Phys. Fluids. 23(10), 102101 (2011)
Nield, D.A.: Surface tension and buoyancy effects in cellular convection. J. Fluid Mech. 19(3), 341–352 (1964)
Ozawa, K.Y., Okuzono, T., Doi, M.: Diffusion process during drying to cause the skin formation in polymer solutions. Jpn. J. Appl. Phys. 45(11R), 8817 (2006)
Pearson, J.R.A.: On convection cells induced by surface tension. J. Fluid Mech. 4(5), 489–500 (1958)
Rabani, R., Machrafi, H., Dauby, P.: Effect of including a gas layer on the gel formation process during the drying of a polymer solution. Eur Phys J E. 40(10), 89 (2017)
Reichenbach, J., Linde, H.: Linear perturbation analysis of surface-tension-driven convection at a plane interface (Marangoni instability). J. Colloid Interface Sci. 84(2), 433–443 (1981)
Sakurai, S., Furukawa, C., Okutsu, A., Miyoshi, A., Nomura, S.: 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(11), 3359–3364 (2002)
Simanovskii, I.B., Viviani, A., Dubois, F., Legros, J.C.: Symmetric and asymmetric convective oscillations in a multilayer system. Microgravity Sci Technol. 22(3), 257–263 (2010)
Simanovskii, I.B., Viviani, A., Dubois, F., Legros, J.C.: The influence of the horizontal component of the temperature gradient on nonlinear oscillatory convective regimes in multilayer system. Microgravity Sci Technol. 23(1), 25 (2011)
Tan, C.T., Homsy, G.M.: Stability of miscible displacements in porous media: Rectilinear flow. Phys Fluids. 29(11), 3549–3556 (1986)
Tanner, R.I.: Engineering rheology (Vol. 52). OUP Oxford (2000)
Toussaint, G., Bodiguel, H., Doumenc, F., Guerrier, B., Allain, C.: Experimental characterization of buoyancy-and surface tension-driven convection during the drying of a polymer solution. Int. J. Heat Mass Transf. 51(17–18), 4228–4237 (2008)
Trouette, B., Chénier, E., Doumenc, F., Delcarte, C., Guerrier, B.: Transient Rayleigh-Bénard-Marangoni solutal convection. Phys. Fluids. 24(7), 074108 (2012)
Vidal, A., Acrivos, A.: Effect of nonlinear temperature profiles on onset of convection driven by surface tension gradients. Ind Eng Chem Fundam. 7(1), 53–58 (1968)
Walheim, S., Schäffer, E., Mlynek, J., Steiner, U.: Nanophase-separated polymer films as high-performance antireflection coatings. Science. 283(5401), 520–522 (1999)
Ye, H.Y., Yang, L.J., Fu, Q.F.: Spatial instability of viscous double-layer liquid sheets. Phys. Fluids. 28(10), 102101 (2016)