Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-24T02:40:38.376Z Has data issue: false hasContentIssue false

Capillary waves and air-sea gas transfer

Published online by Cambridge University Press:  10 February 1997

Andrew J. Szeri*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3975, USA

Extract

The effects of capillary waves are considered on the transfer of gas into (or out of) solution through a gas-liquid interface. The bulk liquid is assumed to be otherwise motionless in the analysis of a preliminary problem; in this problem, a concentration boundary layer is developed as a consequence of a first-order chemical reaction that is assumed to deplete the dissolved gas in the liquid. The reaction rate determines the asymptotic thickness of the concentration boundary layer. It is shown that gas transfer through the concentration boundary layer is most enhanced by the presence of capillary waves when there is vigorous removal of dissolved gases by chemical reaction - i.e. when the reaction is fast and the boundary layer is thin. The results of this theory are then measured against gas transfer through a turbulent, sheared interface in the context of a surface renewal model. Here it is the exchange, from time to time, of fluid between the interface and the bulk that leads to the development of a thin concentration boundary layer when the bulk fluid is not saturated with dissolved gas. Capillary waves are shown to thicken the concentration boundary layer at the interface and to increase the rate of gas transfer.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aranson, I. S., Ezersky, A. B., Rabinovich, M. I. & Tsimring, L. S. 1991 Impurity transport in parametrically excited capillary ripples. Phys. Lett. A 153, 211218.Google Scholar
Asher, W. E. & Pankow, J. F. 1991 Prediction of gas/water mass transport coefficients by a surface renewal model. Environ. Sci. Technol. 25, 12941300.CrossRefGoogle Scholar
Back, D. D. & McCready, M. J. 1988 Theoretical study of interfacial transport in gas-liquid flows. AIChE J. 34, 17891802.Google Scholar
Carrier, G. F., Krook, M. & Pearson, C. E. 1983 Functions of a Complex Variable. Hod Books.Google Scholar
Coantic, M. 1986 A model of gas transfer across air-water interfaces with capillary waves. J. Geophys. Res. 91(C3), 39253943.Google Scholar
Crapper, G. D. 1957 An exact solution for progressive capillary waves of arbitrary amplitude. J. Fluid Mech. 2, 532540.Google Scholar
Crapper, G. D. 1970 Nonlinear capillary waves generated by steep gravity waves. J. Fluid Mech. 40, 149159.Google Scholar
Danckwerts, P. V. 1951 Significance of liquid-film coefficients in gas absorption. Ind. Engng Chem. 43, 14601467.CrossRefGoogle Scholar
Fan, L. T., Shen, B. C. & CHOU, S. T. 1993 The surface renewal theory of interphase transport: a stochastic treatment. Chem. Engng Sci. 48, 39713982.Google Scholar
Fann Hang|A. & Papanicolaou, G. 1994 Convection enhanced diffusion for periodic flows. SIAM J. Appl. Maths 54, 333408.Google Scholar
Feng, Z. C. & Wiggins, S. 1995 Fluid particle dynamics and Stokes drift in gravity and capillary waves generated by the Faraday instability. Nonlinear Dynamics 8, 141160.CrossRefGoogle Scholar
Fyrillas, M. M. & Szeri, A. J. 1994 Dissolution or growth of soluble spherical oscillating bubbles. J. Fluid Mech. 277, 38107.Google Scholar
Fyrillas, M. M. & Szeri, A. J. 1995 Dissolution or growth of soluble spherical oscillating bubbles. The effect of surfactants. J. Fluid Mech. 289, 295314.CrossRefGoogle Scholar
Fyrillas, M. M. & Szeri, A. J. 1996 Surfactant dynamics and rectified diffusion of microbubbles. J. Fluid Mech. 311, 361378.Google Scholar
Jahne, B., Munnich, K. O., Bosinger, R., Dutzi, A., HUBER, W. & Libner, P. 1987 On the parameters influencing air-water gas exchange. J. Geophys. Res. 92(C2), 19371949.CrossRefGoogle Scholar
Knobloch, E. & Merryfield, W. J. 1992 Enhancement of diffusive transport in oscillatory flows. Astrophys. J. 401, 196205.CrossRefGoogle Scholar
Komori, S., Nagaosa, R. & MURAKAMI, Y. 1993 Turbulence structure and mass transfer across a sheared air-water interface in wind-driven turbulence. J. Fluid Mech. 249, 161183.CrossRefGoogle Scholar
LISS, P. S. 1983 Gas transfer: experiments and geochemical implications. In Air-Sea Exchange of Gases and Particles (ed. Liss, P. S. & Slinn, W. G. N.). D. Reidel Publishing Co. Google Scholar
Macintyre, F. 1971 Enhancement of gas transfer by interfacial ripples. Phys. Fluids 14, 15961604.CrossRefGoogle Scholar
Mccready, M. J. & Hanratty, T. J. 1985 Effect of air shear on gas absorption by a liquid film. AIChE J. 31, 20662074.Google Scholar
Mesquita, O. N., Kane, S. & Gollub, J. P. 1992 Transport by capillary waves -fluctuating Stokes drift. Phys. Rev. A 45, 37003705.Google Scholar
Perlin, M., LIN, H. & Ting, C.-L. 1993 On parasitic capillary waves generated by steep gravity waves: an experimental investigation with spatial and temporal measurements. J. Fluid Mech. 255, 597620.CrossRefGoogle Scholar
Ramshankar, R., Berlin, D. & Gollub, J. P. 1990 Transport by capillary waves. Part I. Particle trajectories. Phys. Fluids A 2, 19551965.CrossRefGoogle Scholar
Ramshankar, R. & Gollub, J. P. 1991 Transport by capillary waves. Part II. Scalar dispersion and the structure of the concentration field. Phys. Fluids A 3, 13441350.CrossRefGoogle Scholar
Witting, J. 1971 Effects of plane progressive irrotational waves on thermal boundary layers. J. Fluid Mech. 50, 321334.Google Scholar