Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-09T03:37:52.140Z Has data issue: false hasContentIssue false
  • English
  • Français

The teapot effect: sheet-forming flows with deflection, wetting and hysteresis

Published online by Cambridge University Press:  26 April 2006

S. F. Kistler  and
L. E. Scriven
S. F. Kistler
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA Present address: 3M Company, 236-1N-05 3M Center, St. Paul. MN 55144-1000, USA.
L. E. Scriven
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The flow of a two-dimensional viscous film falling from the edge of an inclined plane exhibits a distinctive set of phenomena which, in various combinations, have been referred to as the teapot effect. This paper makes plain that three basic mechanisms are at the root of these phenomena: deflection of the liquid sheet by hydrodynamic forces, contact-angle hysteresis, and multiple steady states that give rise to a purely hydrodynamic hysteresis. The evidence is drawn from Galerkin/finite-element analysis of the Navier-Stokes system, matched to a one-dimensional asymptotic approximation of the sheet flow downstream, and is corroborated experimentally by flow visualization and measurements of free-surface profiles and contact line position. The results indicate that the Gibbs inequality condition quantifies the inhibiting effect of sharp edges on spreading of static contact lines, even in the presence of flow nearby. The branchings, turning points, and isolas of families of solutions in parameter space explain abrupt flow transitions observed experimentally, and illuminate the stability of predicted flow states.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 263 , 25 March 1994 , pp. 19 - 62
Copyright
© 1994 Cambridge University Press

References

Abbott, J. P. 1978 An efficient algorithm for the determination of certain bifurcation points. J. Comput. Appl. Math. 4, 19–26.Google Scholar
Adamson, A. W. 1982 Physical Chemistry of Surfaces, 4th edn. Wiley.
Benner, R. E., Scriven, L. E. & Davis, H. T. 1982 Structure and stress in the gas—liquid—solid contact region. In Structure of the Interfacial Region (ed. M. Lal). Faraday Symp. No. 16, pp 169–190. The Royal Society of Chemistry, London.
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.Google Scholar
Brown, D. R. 1961 A study of the behaviour of a thin sheet of moving liquid. J. Fluid Mech. 10, 297–305.Google Scholar
Chang, P. W., Patten, T. W. & Finlayson, B. A. 1979 Collocation and Galerkin finite element methods for viscoelastic fluid flow - II. Die swell problem with a free surface. Comput. Fluids 7, 285–303.Google Scholar
Christodoulou, K. N. & Scriven, L. E. 1994 Operability limits of free surface flow systems by solving nonlinear eigenvalue problems. Intl J. Num. Meth. Fluids (to appear).Google Scholar
Clarke, N. S. 1968 Two-dimensional flow under gravity in a jet of viscous liquid. J. Fluid Mech. 31, 481–500.Google Scholar
Cruickshank, J. O. & Munson, B. R. 1981 Viscous buckling of plane and axisymmetric jets. J. Fluid Mech. 113, 221–239.Google Scholar
Cullen, E. J. & Davidson, J. F. 1957 Absorption of gas in liquid jets. Trans. Faraday Soc. 53, 113–120.Google Scholar
Dittmann, D. A., Griswold, G. L., Wright, S. E. & Winkler, D. E. 1976 Curtain coating apparatus. Research Disclosure 147, 19 (No. 14715, July 1976).Google Scholar
Dupret, F. 1982 A method for the computation of viscous flow by finite elements with free boundaries and surface tension. In Finite Element Flow Analysis, Proc. Fourth Intl Conf. on Finite Element Methods in Flow Problems Tokyo, 26–29 July 1982 (ed. T. Kawai), pp. 495–502. University of Tokyo Press.
Gear, R. L. Keentok, M., Milthorpe, J. F. & Tanner, R. I. 1983 The shape of low Reynolds number jets. Phys. Fluids. 26, 7–25.Google Scholar
Gibbs, J. W. 1906 The Scientific Papers of J. Willard Gibbs. Vol. I: Thermodynamics. Longmans Green & Co. (Dover Reprint, 1961).
Grifford, W. A. 1982 A finite element analysis of isothermal fiber formation. Phys. Fluids 25, 219–225.Google Scholar
Greiller, G. F. 1972 Method for Making Photographic Elements. US Patent No. 3,632,374.
Gutoff, E. B. & Kendrick, C. E. 1982 Dynamic contact angles. AIChE J. 28, 459–466.Google Scholar
Harlow, F. H. & Amsden, A. A. 1971 Fluid Dynamics. Los Alamos Scientific Laboratory Monograph LA-4700.
Higgins, B. G. & Scriven, L. E. 1979 Interfacial shape and evolution equations for liquid films and other viscocapillary flows. I & EC Fundam. 18, 208–215.Google Scholar
Hirt, C. W. & Shannon, J. P. 1968 Free surface stress conditions for incompressible flow calculations. J. Comput. Phys. 2, 403–411.Google Scholar
Hood, P. 1976 Frontal solution program for unsymmetric matrices. Intl J. Num. Meth. Engng 10, 379–393; and Correction. Intl J. Num. Meth. Engng. 11, (1977) 1055.Google Scholar
Huh, C. & Mason, S. G. 1977 Effects of surface roughness on wetting. J. Colloid Interface Sci. 60, 11–38.Google Scholar
Huyakorn, P. S., Taylor, C., Lee, R. L. & Grresho, P. M. 1978 A comparison of various mixed interpolation finite elements in the velocity-pressure formulation of the Navier-Stokes equations. Comput. Fluids 6, 25–35.Google Scholar
Iooss, G. & Joseph, D. D. 1980 Elementary Stability and Bifurcation Theory. Springer.
Johnson, R. E. & Dettre, R. H. 1969 Wettability and contact angles. In Surface and Colloid Science (ed. E. Matijevic), Vol. 2, pp. 85–153. Wiley Interscience.
Joseph, D. D., Ngyen, K. & Matta, J. E. 1983 Jets into liquid under gravity. J. Fluid Mech. 128, 443–468.Google Scholar
Keller, H. B. 1977 Numerical solution of bifurcation and non-linear eigenvalue problems. In Applications in Bifurcation Theory (ed. P. H. Rabinowitz), pp. 359–384. Academic.
Keller, J. B. 1957 Teapot effect. J. Appl. Phys. 28, 859–864.Google Scholar
Kheshgi, H. S., Basaran, O. A., Benner, R. E., Kistler, S. F. & Scriven, L. E. 1983 Continuation in a parameter: experience with viscous and free surface flows. In Numerical Methods in Laminar and Turbulent Flow, Proc. Third. Intl Conf. on Finite Element Methods in Flow Problems, Seattle 8–11 August 1983 (ed. C. Taylor et al.). Pineridge Press.
Kistler, S. F. 1984 The fluid mechanics of curtain coating and related viscous free surface flows with contact lines. PhD dissertation, University of Minnesota, Minneapolis, USA.
Kistler, S. F. & Scriven, L. E. 1983 Coating flows. In Computational Analysis of Polymer Processing (ed. J. R. A. Pearson & S. M. Richardson), pp. 243–299. Applied Science Publishers.
Kistler, S. F. & Scriven, L. E. 1984 Coating flow theory by finite element and asymptotic analysis of the Navier—Stokes system. Intl J. Num. Meth. Fluids 4, 207–229.Google Scholar
Lin, S. P. 1981 Stability of a falling curtain. J. Fluid Mech. 104, 111–118.Google Scholar
Lin, S. P. & Krishna, M. V. G. 1978 Deflection of a viscous liquid curtain. Phys. Fluids 21, 2367–2368.Google Scholar
Martin, H. R. & Friedman, S. B. 1974 A review of research related to the development of liquid jet fluidics. Fluidics Q. 6, 67–79.Google Scholar
Michael, D. H. 1958 The separation of a viscous liquid at a straight edge. Mathematika 5, 82–84.Google Scholar
Mohanty, K. K. 1981 Fluid in porous media: two-phase distribution and flow. PhD dissertation, University of Minnesota, Minneapolis, USA.
Newman, A. A. 1968 Glycerol. Morgan-Grampian.
Nickell, R. E., Tanner, R. I. & Caswell, B. 1974 Solution of viscous incompressible jet and free surface flows using finite element method. J. Fluid Mech. 65, 189–206.Google Scholar
Novy, R. A., Davis, H. T. & Scriven, L. E. 1990 Upstream and downstream boundary conditions for continuous-flow systems. Chem. Engng Sci. 45, 1515–1524.Google Scholar
Ogawa, S. & Scriven, L. E. 1994 An analysis of curtain coating flow. AIChE J. (in press).Google Scholar
Oliver, J. F., Huh, C. & Mason, S. G. 1977 Resistance to spreading of liquids by sharp edges. J. Colloid Interface Sci. 59, 568–581.Google Scholar
Oliver, J. F., Huh, C. & Mason, S. G. 1980 Experimental study of some effects of solid surface roughness on wetting. Colloids and Surfaces 1, 79–90.Google Scholar
Pritchard, W. G. 1986 Instability and chaotic behaviour in a free surface flow. J. Fluid Mech. 165, 1–60.Google Scholar
Raux, R. 1976 Appareil de Revêtement par Rideau Liquide. Brevet d’Invention 833.851, Royaume de Belgique.
Reiner, M. 1956 The teapot effect. Physics Today 9, 16–20 (September).Google Scholar
Reiner, M. 1969 Deformation, Strain and Flow, .3rd edn. H. K. Lewis & Co.
Richardson, S. 1970 The die swell phenomenon. Rheol. Acta 9, 193–199.Google Scholar
Rubin, H. & Wharshavsky, M. 1970 A note on the break-up of viscoelastic liquid jets. Israel J. Technol. 8, 285–288.Google Scholar
Ruschak, K. J. 1978 Flow of a falling film into a pool. AIChE J. 24, 705–709.Google Scholar
Ruschak, K. J. 1980 A method for incorporating free boundaries with surface tension in finite element fluid flow simulators. Lntl J. Num. Meth. Engng 15, 639–648.Google Scholar
Saito, H. & Scriven, L. E. 1981 Study of coating flow by the finite element method. J. Comput. Phys. 42, 53–76.Google Scholar
Silliman, W. J. & Scriven, L. E. 1980 Separating flow near a static contact line: slip at wall and the shape of the free surface. J. Comput. Phys. 34, 287–313.Google Scholar
Taylor, G. I. 1968 Instability of jets, threads and sheets of viscous fluids. In Proc. Intl Congr. Appl. Mech. Stanford 1968 (ed. M. Hetenyi & W. G. Vicenti), p 382. Springer.
Teletzke, G. F., Davis, H. T. & Scriven, L. E. 1987 How liquids spread on solids. Chem. Engng Commun. 55, 41–81.Google Scholar
Teletzke, G. F., Davis, H. T. & Scriven, L. E. 1988 Wetting hydrodynamics. Rev. Phys. Appl. 23, 989–1007.Google Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1986 Pouring flows. Phys. Fluids 29, 3958–3961.Google Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1988 Pouring flows with separation. Phys. Fluids A 1, 156–158.Google Scholar
Walker, J. 1984 The troublesome teapot effect, or why a poured liquid clings to the container. Scientific American 251, 144–152 (October).Google Scholar
Walters, R. A. 1980 The frontal method in hydrodynamic simulations. Comput. Fluids 8, 265–272.Google Scholar