Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T06:26:17.162Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of surface contamination on thermocapillary flow in a two-dimensional slot. Part 2. Partially contaminated interfaces

Published online by Cambridge University Press:  20 April 2006

Bradley Carpenter  and
G. M. Homsy
Bradley Carpenter
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
G. M. Homsy
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the flow driven by a thermally induced surface stress in a fluid held in a shallow two-dimensional slot, and show that, for low Maragoni number, the extent of surface stagnation due to the presence of a non-diffusing surfactant depends on a single parameter E, the elasticity number defined in Part 1 of this analysis (Homsy & Meiburg 1984). For situations in which the adsorbed species are insufficient to result in a fully covered surface, we find that the interface is either clean and subject to constant stress, or contaminated and no-slip. There is a region in which one type of surface is replaced by the other. The Wiener–Hopf technique is used to obtain an analytic expression for the stream function in the vicinity of the leading edge of the stagnant surface in the limit of creeping flow. This result shows that the flow dies off under the stagnant surface at a distance of the order of the depth of the fluid, in a series of vortices of exponentially decreasing magnitude.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 155 , June 1985 , pp. 429 - 439
Copyright
© 1985 Cambridge University Press

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

Adamson, A. W. 1982 The Physical Chemistry of Surfaces, 4th edn. Interscience.
Clark, P. A. & Wilcox, W. R. 1980 J. Crystal Growth 50, 461.
Davis, R. & Acrivos, A. 1966 Chem. Engng Sci. 21, 681.
Gaines, G. 1966 Insoluble Monolayers at Liquid–Gas Interfaces. Interscience.
Hardy, G. H. 1902 Mess. of Maths 31 (n.s.), 161.
Hillman, A. P. & Salzer, H. E. 1943 Phil. Mag. 34, 575.
Homsy, G. M. & Meiburg, E. 1984 J. Fluid Mech. 139, 443.
Hurle, D. T. J. 1983 J. Crystal Growth 65, 124.
Kenning, D. B. R. 1968 Appl. Mech. Rev. 21, 1101.
Levich, V. G. & Krylov, V. S. 1969 Ann. Rev. Fluid Mech. 1, 293.
Ostrach, S. 1982 Ann. Rev. Fluid Mech. 14, 313.
Richardson, S. 1970 Proc. Camb. Phil. Soc. 67, 477.
Sen, A. & Davis, S. H. 1982 J. Fluid Mech. 121, 163.
Strani, M., Piva, R. & Graziani, B. 1983 J. Fluid Mech. 130, 347.
Yih, C.-S. 1968 Phys. Fluids 11, 477.
Zebib, A., Homsy, G. M. & Meiburg, E. 1984 High Marangoni number convection in a square cavity, submitted to J. Fluid Mech.Google Scholar