DOI: 10.1017/s0022112093002290. On Marangoni drying: nonlinear kinematic waves in a thin film

On Marangoni drying: nonlinear kinematic waves in a thin film

10.1017/s0022112093002290

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

Abstract

In the field of industrial drying, a recent innovation has exploited the occurrence of Marangoni effects in such a way that the resultant free-surface flow enhances the drying process. To this end, alcohol vapour, soluble in water, is introduced above a drying film and as a result of diffusion through the air and water phases a favourable concentration gradient gives rise to the required shear flow. We consider here a simple process driven by this mechanism, and by means of asymptotic simplification and the concepts of singular perturbation theory a leading-order approximation is obtained in which the alcohol concentration in the water is a specified function of space and time. The evolution of the free surface thus reduces to a single nonlinear partial differential equation of a similar form to the Korteweg–de Vries and Burgers equations, higher-derivative terms corresponding to surface tension and gravity effects. Numerical solutions of this equation are obtained and are compared to the application of first order nonlinear kinematic wave theory with corresponding shock solutions.

Bibliography

OâBrien, S. B. G. M. (1993). On Marangoni drying: nonlinear kinematic waves in a thin film. Journal of Fluid Mechanics, 254, 649â670.

Authors 1

S. B. G. M. O'Brien (first)

References 19 Referenced 40

Myshkis, A. D. 1986 Low Gravity Fluid Mechanics .Springer. (10.1007/978-3-642-70964-7)
Marangoni, C. G. M. 1871 Ann. Phys. (Poggendorff) 143,337.
Halpern, D. & Grotberg, J. B. 1992 Dynamics and transport of a localized soluble surfactant on a thin film.J. Fluid Mech. 237,1. (10.1017/S0022112092003318)
Levich, V. G. & Krylov, V. S. 1969 Surface tension driven phenomena.Ann. Rev. Fluid Mech. 1,293.
Thomson, J. 1855 Phil. Mag. (4)10,330.
Kevorkian, J. & Cole, J. D. 1981 Perturbation Methods in Applied Mathematics .Springer. (10.1007/978-1-4757-4213-8)
Haydon, R. 1958 An investigation of droplet oscillation during mass transfer.Proc. R. Soc. Lond. A 243,483.
Scriven, L. E. & Sternling, C. V. 1960 The Marangoni effects.Nature 187,186.
Whitham, G. B. 1974 Linear and Nonlinear Waves .John Wiley & Sons.
Benney, D. J. 1966 Long waves in liquid films.J. Math. & Phys. 45,150.
Jensen, O. E. & Grotberg, J. B. 1992 Insoluble surfactant spreading on a thin viscous film; shock evolution and film rupture.J. Fluid Mech. 240,259.
Hansen, R. S. 1960 The theory of diffusion controlled absorption kinetics with accompanying evaporation.J. Colloid Si. 64,637.
Moriarty, J. A. , Schwartz, L. W. & Tuck, E. O. 1991 Unsteady spreading of thin liquid films with small surface tension.Phys. Fluids A 3,733.
Peregrine, D. H. 1966 Calculations of the development of an undular bore.J. Fluid Mech. 25,321.
Patberg, W. B. , Koers, A. , Steenge, W. D. E. & Drinkenburg, A. A. H. 1983 Chem. Engng Sci. 38,917.
Gaver, D. P. & Grotberg, J. B. 1990 The dynamics of a localized surfactant on a thin film.J. Fluid Mech. 213,127.
Overdiep, W. S. 1986 The levelling of paints.Prog. Organic Coatings 14,159.
Pimputkar, S. M. & Ostrach, S. 1980 Transient thermocapillary flow in thin liquid layers.Phys. Fluids 23,1281.
Leenaars, A. F. M. , Huethorst, J. A. M. & Oekel, J. J. van 1991 Marangoni drying: a new extremely clean process.Langmuir 7,2748. (10.1021/la00059a057)

Dates

Type	When
Created	19 years, 3 months ago (April 27, 2006, 9:21 a.m.)
Deposited	6 years, 2 months ago (June 7, 2019, 4:12 p.m.)
Indexed	1 year, 2 months ago (June 22, 2024, 12:40 p.m.)
Issued	31 years, 11 months ago (Sept. 1, 1993)
Published	31 years, 11 months ago (Sept. 1, 1993)
Published Online	19 years, 3 months ago (April 26, 2006)
Published Print	31 years, 11 months ago (Sept. 1, 1993)

Funders 0

None

BibTeX

@article{O_Brien_1993, title={On Marangoni drying: nonlinear kinematic waves in a thin film}, volume={254}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112093002290}, DOI={10.1017/s0022112093002290}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={O’Brien, S. B. G. M.}, year={1993}, month=sep, pages={649–670} }

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