Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-20T08:50:52.947Z Has data issue: false hasContentIssue false
  • English
  • Français

The interaction of a moving fluid/fluid interface with a flat plate

Published online by Cambridge University Press:  26 April 2006

J. Billingham  and
A. C. King
J. Billingham
Affiliation:
Schlumberger Cambridge Research, High Cross, Madingley Road, Cambridge CB3 0EL, UK
A. C. King
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A well-known technique for metering a multiphase flow is to use small probes that utilize some measurement principle to detect the presence of different phases surrounding their tips. In almost all cases of relevance to the oil industry, the flow around such local probes is inviscid and driven by surface tension, with negligible gravitational effects. In order to study the features of the flow around a local probe when it meets a droplet, we analyse a model problem: the interaction of an infinite, initially straight, interface between two inviscid fluids, advected in an initially uniform flow towards a semi-infinite thin flat plate oriented at 90° to the interface. This has enabled us to gain some insight into the factors that control the motion of a contact line over a solid surface, for a range of physical parameter values.

The potential flows in the two fluids are coupled nonlinearly at the interface, where surface tension is balanced by a pressure difference. In addition, a dynamic contact angle boundary condition is imposed at the three-phase contact line, which moves along the plate. In order to determine how the interface deforms in such a flow, we consider the small- and large-time asymptotic limits of the solution. The small-time and linearized large-time problems are solved analytically, using Mellin transforms, whilst the general large-time problem is solved numerically, using a boundary integral method.

The form of the dynamic contact angle as a function of contact line velocity is the most important factor in determining how an interface deforms as it meets and moves over the plate. Depending on this, the three-phase contact line may, at one extreme, hang up on the leading edge of the plate or, at the other extreme, move rapidly along the surface of the plate. At large times, the solution asymptotes to an interface configuration where the contact line moves at the far-field velocity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 296 , 10 August 1995 , pp. 325 - 351
Copyright
© 1995 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

Cox, R. G. 1986 The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169–194.Google Scholar
Dussan, V. E. B. 1976 The moving contact line: the slip boundary condition. J. Fluid. Mech. 77, 665–684.Google Scholar
Dussan, V. E. B. 1979 On the spreading of liquids on solid surfaces: Static and dynamic contact lines. Ann. Rev. Fluid Mech. 77, 371–400.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1980 Tables of Integrals, Series, and Products, Corrected and Enlarged Edition. Academic Press.
Jeffreys, H. & Jeffreys, B. S. 1962 Methods of Mathematical Physics. Cambridge University Press.
Keller, J. B. & Miksis, M. K. 1983 Surface tension driven flows. SIAM J. Appl. Maths 43, 268–277.Google Scholar
King, A. C. 1991 Moving contact lines in slender fluid wedges. Q. J. Mech. Appl. Maths 44, 173–192.Google Scholar
King, L. V. 1914 Convection of heat from small cylinders in a stream of fluid. Proc. R. Soc. Lond. A 214, 373–432.Google Scholar
Moujaes, S. 1990 Testing of a spherical dual-tipped optical fibre probe for local measurements of void fraction and gas velocity in two-phase flows. Can. J. Chem. Engng 68, 504–510.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1986 Numerical Recipes. Cambridge University Press.
Sekoguchi, K., Takeishi, M., Nishiura, T., Kano, H. & Nomura, T. 1985 Multiple optical fiber probe technique for measuring profiles of gas-liquid interface and its velocity. In Proc. Winter Annual Meeting of the ASME, FED Vol. 23.
Serizawa, A., Kataoka, I. & Michiyoshi, I. 1974 Turbulence structure of air-water bubbly flow. Intl J. Multiphase Flow 2, 221–259.Google Scholar