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Local fluid and heat flow near contact lines

Published online by Cambridge University Press:  26 April 2006

D. M. Anderson  and
S. H. Davis
D. M. Anderson
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK.
S. H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
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Abstract

We consider steady two-dimensional fluid flow and heat transfer near contact lines in single-phase and two-phase systems. Both single- and double-wedge geometries admit separable solutions in plane polar coordinates for both thermal and flow fields. We consider the class of functions which have bounded temperatures and velocities at the corner. When free surfaces are present, we seek local solutions, those that satisfy all local boundary conditions, and partial local solutions, those that satisfy all but the normal-stress boundary condition. Our aim in this work is to describe local fluid and heat flow in problems where these fields are coupled by determining for which wedge angles solutions exist, identifying singularities in the heat flux and stress which are present at contact lines, and determining the dependence of these singularities on the wedge angles. For thermal fields in two phases we identify two modes of heat transfer that are analogous to the two modes identified by Proudman & Asadullah (1988) for two-fluid flow. For non-isothermal flow, locally, convection does not play a role but coupling through thermocapillary effects on non-isothermal free surfaces can arise. We find that under non-isothermal conditions a planar free surface must leave a planar rigid boundary at an angle of π, the same angle found by Michael (1958) for an isothermal rigid/free wedge, in order to satisfy all local boundary conditions. Finally, we find that situations arise where no coupled solutions of the form sought can be found; we discuss means by which alternative solutions can be obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 268 , 10 June 1994 , pp. 231 - 265
Copyright
© 1994 Cambridge University Press

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References

Anderson, D. M. 1993 Corner flows, heat transfer, and phase transformation. PhD thesis, Northwestern University, Evanston, IL.
Anderson, D. M. & Davis, S. H. 1993 Two-fluid viscous flow in a corner. J. Fluid Mech. 257, 1–31.Google Scholar
Brown, R. A. 1988 Theory of transport processes in single crystal growth from the melt. AIChE J. 34, 881–911.Google Scholar
Burggraf, O. R. 1966 Analytical and numerical studies of the structure of steady separated flows. J. Fluid Mech. 24, 113–151.Google Scholar
Dean, W. R. & Montagnon, P. E. 1949 On the steady motion of viscous liquid in a corner. Proc. Camb. Phil. Soc. 45, 389–394.Google Scholar
Ehrhard, P. & Davis, S. H. 1991 Non-isothermal spreading of liquid drops on horizontal plates. J. Fluid Mech. 229, 365–388.Google Scholar
Keller, J. B. 1987 Effective conductivity of periodic composites composed of two very unequal conductors. J. Math. Phys. 28, 2516–2520.Google Scholar
Michael, D. H. 1958 The separation of a viscous liquid at a straight edge. Mathematika 5, 82–84.Google Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1–18.Google Scholar
Proudman, I. & Asadullah, M. 1988 Steady viscous flow near a stationary contact line. J. Fluid Mech. 187, 35–43.Google Scholar
Zebib, A., Homsy, G. M. & Meiburg, E. 1985 High Marangoni number convection in a square cavity. Phys. Fluids 28, 3467–3476.Google Scholar