Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-23T15:47:47.180Z Has data issue: false hasContentIssue false

Spontaneous oscillations of a sessile lens

Published online by Cambridge University Press:  04 July 2007

ROMAN STOCKER
Affiliation:
Ralph M. Parsons Laboratory, Department of Civil and Environmental Engineering, MIT, Cambridge, MA, USAromans@mit.edu
JOHN W. M. BUSH
Affiliation:
Department of Mathematics, MIT, Cambridge, MA, USAbush@math.mit.edu

Abstract

When an oil drop is placed on a water surface, it assumes the form of a sessile lens. We consider the curious behaviour that may arise when the oil contains a water-insoluble surfactant: the lens radius oscillates in a quasi-periodic fashion. While this oscillatory behaviour has been reported elsewhere, a consistent physical explanation has yet to be given. We present the results of an experimental investigation that enable us to elucidate the subtle mechanism responsible. Videomicroscopy reveals that the beating behaviour is generated by a subtle process of partial emulsification at the lens edge and sustained by evaporation of surfactant from the water surface.

Type
Papers
Copyright
Copyright © Cambridge University Press 2007

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

REFERENCES

Blyth, M. G. & Pozrikidis, C. 2004 Effect of surfactant on the stability of two-layer channel flow. J. Fluid Mech. 505, 5986.CrossRefGoogle Scholar
DeBruijn, R. A. Bruijn, R. A. 1993 Tip-streaming of drops in simple shear flows. Chem. Engng Sci. 48, 277284.Google Scholar
Dupeyrat, M. & Nakache, E. 1978 Direct conversion of chemical energy into mechanical energy at oil water interface. Bioelectrochem. Bioenergetics 5, 134141.Google Scholar
Fernandez, J. M. & Homsy, G. M. 2004 Chemical reaction-driven tip-streaming phenomena in a pendant drop. Phys. Fluids 16, 25482555.CrossRefGoogle Scholar
Foda, M. & Cox, R. G. 1980 The spreading of thin liquid films on a water-air interface. J. Fluid Mech. 101, 3351.Google Scholar
Franklin, B. 1774 Of the stilling of waves by means of oil. Phil. Trans. 64, 445.Google Scholar
Frenkel, A. L. & Halpern, D. 2002 Stokes-flow instability due to interfacial surfactant. Phys. Fluids 14, L45L48.CrossRefGoogle Scholar
Frenkel, A. L. & Halpern, D. 2005 Effect of inertia on the insoluble-surfactant instability of shear flow. Phys. Rev. E 71, 016302.CrossRefGoogle ScholarPubMed
Friesen, W. O., Block, G. D. & Hocker, C. G. 1993 Formal approaches to understanding biological oscillators. Annu. Rev. Physiol. 55, 661681.CrossRefGoogle ScholarPubMed
Goldbeter, A. 1996 Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour. Cambridge University Press.CrossRefGoogle Scholar
Halpern, D. & Frenkel, A. L. 2003 Destabilization of a creeping flow by interfacial surfactant: linear theory extended to all wavenumbers. J. Fluid Mech. 485, 191220.Google Scholar
Kovalchuk, V. I., Kamusewitz, H., Vollhardt, D. & Kovalchuk, V. I. 1999 Auto-oscillations of surface tension. Phys. Rev. E 60, 20292036.Google Scholar
Krechetnikov, R. & Homsy, G. M. 2004 On physical mechanisms in chemical reaction-driven tip-streaming. Phys. Fluids 16, 25562566.Google Scholar
McBain, J. W. & Woo, T. 1937 Spontaneous emulsification, and reactions overshooting equilibrium. Proc. R. Soc. Lond. A 163, 182188.Google Scholar
Miksis, M. J. & Vanden-Broeck, J. 2001 Motion of a triple junction. J. Fluid Mech. 437, 385394.CrossRefGoogle Scholar
Mitchell, D. J., Tiddy, G. J. T., Waring, L., Bostock, T. & McDonald, M. P. 1983 Phase behaviour of polyoxyehtylene surfactants with water. J. Chem. Soc., Faraday Trans. I 79, 9751000.CrossRefGoogle Scholar
Pujado, P. R. & Scriven, L. E. 1972 Sessile lenticular configurations: translationally and rotationally symmetric lenses. J. Colloid Interface Sci. 40, 8298.Google Scholar
Scriven, L. E. & Sternling, C. V. 1960 The Marangoni effects. Nature 187, 186188.CrossRefGoogle Scholar
Sebba, F. 1975 Macrocluster gas-liquid an biliquid foams and their biological significance. A.C.S. Symposium Series 9, 1839.CrossRefGoogle Scholar
Sebba, F. 1979 A surface-chemical basis for cell motility. J. Theor. Biol. 78, 375391.Google Scholar
Sebba, F. & Briscoe, H. V. A. 1940 The variation of the solubility of unimolecular films with surface pressure, and its effect on the measurement of true surface pressure. J. Chem. Soc. 114–118.Google Scholar
Shioi, A., Kumagai, H., Sugiura, Y. & Kitayama, Y. 2002 Oscillation of interfacial tension and spontaneous interfacial flow at a water/oil interface composed of Di(2-ethylhexyl) phosphoric acid. Langmuir 18, 55165522.CrossRefGoogle Scholar
Smith, M. K. & Davis, S. H. 1983 Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities. J. Fluid Mech. 132, 119144.CrossRefGoogle Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146, 501523.Google Scholar
Yoshikawa, K. & Matsubara, Y. 1983 Spontaneous oscillation of pH and electrical potential in an oil–water system. J. Am. Chem. Soc. 105, 59675969.CrossRefGoogle Scholar