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Non-isothermal spreading of liquid drops on horizontal plates

Published online by Cambridge University Press:  26 April 2006

Peter Ehrhard  and
Stephen H. Davis
Peter Ehrhard
Affiliation:
Institut für Reaktorbauelemente, Kernforschungszentrum Karlsruhe GmbH Postfach 3640, D-7500 Karlsruhe 1, Germany
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
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Abstract

A viscous-liquid drop spreads on a smooth horizontal surface, which is uniformly heated or cooled. Lubrication theory is used to study thin drops subject to capillary, thermocapillary and gravity forces, and a variety of contact-angle-versus-speed conditions. It is found for isothermal drops that gravity is very important at large times and determines the power law for unlimited spreading. Predictions compare well with the experimental data on isothermal spreading for both two-dimensional and axisymmetric configurations. It is found that heating (cooling) retards (augments) the spreading process by creating flows that counteract (reinforce) those associated with isothermal spreading. For zero advancing contact angle, heating will prevent the drop from spreading to infinity. Thus, the heat transfer serves as a sensitive control on the spreading.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 229 , August 1991 , pp. 365 - 388
Copyright
© 1991 Cambridge University Press

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References

Alavyoon, F., Henningson, D. S. & Alfredsson, P. H. 1986 Turbulent spots in plane Poiseuille flow - flow visualization. Phys. Fluids 29, 1328–1331.Google Scholar
Barkley, D. 1990 Theory, and predictions for finite-amplitude waves in two-dimensional plane Poiseuille flow.. Phys. Fluids A 2, 955–970.Google Scholar
Carlson, D. R., Widnall, S. E. & Peeters, M. F. 1982 A flow visualization study of transition in plane Poiseuille flow. J. Fluid Mech. 121, 487–505.Google Scholar
Chen, T. S. & Joseph, D. D. 1973 Subcritical bifurcation of plane Poiseuille flow. J. Fluid Mech. 58, 337–351.Google Scholar
Davey, A., Hocking, L. M. & Stewartson, K. 1974 On the nonlinear evolution of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 63, 529–536.Google Scholar
Doedel, E. J. & Kernevez, J. D. 1985 Software for continuation and bifurcation problems. Applied Mathematics Tech. Rep., Caltech.Google Scholar
Drazin, P. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Goldshtik, M. A., Lifshitz, E. M. & Shtern, V. N. 1983 The transition Reynolds number for a plane channel, Akad. Nauk. SSSR, Dokl., 273, 75–79.Google Scholar
Gottlieb, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Application. SIAM-CBMS.
Herbert, Th. 1976 Periodic secondary motions in a plane channel In Proc. Fifth Intl Conf. on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol. 59, p. 235. Springer.
Herbert, Th. 1977 Finite amplitude stability of plane parallel flows. AGARD CP-224, pp. 3–110.Google Scholar
Jiménez, J. 1987 Bifurcation and bursting in two-dimensional Poiseuille flow. Phys. Fluids 30, 3644–3646.Google Scholar
Joseph, D. D. 1976 Stability of Fluid Motions. Springer.
Keller, H. B. 1988 Numerical Methods in Bifurcation Problems. Springer.
Kim, J. 1983 On the structure of wall-bounded turbulent flows. Phys. Fluids 26, 2088–2097.Google Scholar
Kleiser, L. 1982 Spectral simulations in laminar-turbulent transition in plane Poiseuille flow and comparison with experiments. In Proc. 8th Intl Conf. on Numerical Methods in Fluid Dynamics, Aachen (ed. E. Krause), Lecture Notes in Physics, vol. 170, p. 280. Springer.
Marsden, J. E. & McCracken, M. 1976 The Hopf Bifurcation and Its Applications. Applied Mathematical Sciences, vol. 19, Springer.
Meksyn, D. & Stuart, J. T. 1951 Stability of viscous motion between parallel surfaces for finite disturbances.. Proc. R. Soc. Lond. A 208, 517–526.Google Scholar
Milinazzo, F. & Saffman, P. G. 1985 Finite amplitude waves in plane viscous shear flows. J. Fluid Mech. 160, 281–295.Google Scholar
Nishioka, M. & Asai, M. 1985 Some observations of the subcritical transition in plane Poiseuille flow. J. Fluid Mech. 150, 441–450.Google Scholar
Noether, F. 1921 Das Turbulenzproblem. Z. Angew. Math. Mech. 1, 125–138, 218–219.Google Scholar
Orszag, S. A. 1971 Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech. 50, 689–703.Google Scholar
Orszag, S. A. & Kells, L. C. 1980 Transition to turbulence in plane Poiseuille flow and plane Couette flow. J. Fluid Mech. 96, 159–206.Google Scholar
Orszag, S. A. & Patera, A. T. 1983 Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128, 347–385.Google Scholar
Pugh, J. D. & Saffman, P. G. 1988 Two-dimensional subharmonic stability of finite amplitude waves in plane Poiseuille flow. J. Fluid Mech. 194, 295–308.Google Scholar
Reichardt, H. 1956 Über die Geschwindigkeitsverteilung in einer geradlinigen turbulenen Coutteströmung. Z. Angew. Math. Mech. 36, 454.Google Scholar
Saffman, P. G. 1983 Vortices, stability and turbulence. Ann. NY Acad. Sci. 404, 12–24.Google Scholar
Tuckerman, L. S. 1989 Steady-state solving via Stokes preconditioning: recursion relations for elliptic operators. In Proc. Eleventh Intl Conf. on Numerical Methods in Fluid Dynamics (ed. D. L. Dowyer, M. Y. Hussaini & R. G. Voight). Springer.
Zahn, J. P., Toomre, J., Spiegel, E. A. & Gough, D. O. 1974 Nonlinear cellular motions in plane Poiseuille channel flow. J. Fluid Mech. 64, 319–345.Google Scholar