Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2025-01-01T02:47:06.900Z Has data issue: false hasContentIssue false
  • English
  • Français

A new model to determine dynamic surface tension and elongational viscosity using oscillating jet measurements

Published online by Cambridge University Press:  26 April 2006

S.E. Bechtel ,
J.A. Cooper ,
M.G. Forest ,
N.A. Petersson ,
D.L. Reichard ,
A. Saleh  and
V. Venkataramanan
S.E. Bechtel
Affiliation:
Department of Engineering Mechanics, The Ohio State University, Columbus, OH 43210, USA
J.A. Cooper
Affiliation:
US Department of Agriculture, Agricultural Research Service, Wooster, OH 44691, USA
M.G. Forest
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA
N.A. Petersson
Affiliation:
Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
D.L. Reichard
Affiliation:
US Department of Agriculture, Agricultural Research Service, Wooster, OH 44691, USA
A. Saleh
Affiliation:
Department of Civil Engineering, The Ohio State University, Columbus, OH 43210, USA
V. Venkataramanan
Affiliation:
Department of Engineering Mechanics, The Ohio State University, Columbus, OH 43210, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We present an integro-differential equation model which, combined with experimental measurements of an oscillating free surface jet, calculates dynamic surface tension and elongational viscosity of a fluid. Our model builds upon previous models due to Rayleigh and Bohr in that it self-consistently incorporates the effects of viscosity and gravity. Further, surface tension and viscosity are allowed to be non-constant. The principal result of this paper is a technique for the measurement of surface tension of newly forming surfaces on the millisecond timescale relevant for agricultural spray mixtures. Coincidentally, our model independently yields the elongational viscosity of the fluid, although our present experimental apparatus limits the accuracy of measurement of this material property.

In this paper we take measurements from physical jet experiments and implement our inverse model to deduce these material properties. The model is first benchmarked against standard techniques on a well-characterized fluid with constant surface tension and Newtonian viscosity. We then apply our method to an agricultural spray mixture, with non-constant surface tension and non-Newtonian rheology. We measure (i) the rapid decay of surface tension from the newly formed surface (aged less than a millisecond) to the much lower equilibrium value, and (ii) the rate dependence of elongational viscosity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 293 , 25 June 1995 , pp. 379 - 403
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

Adamson, A. W. 1982 Physical Chemistry of Surfaces, 4th edn. John Wiley & Sons.
Baker, G. R., Meiron, D. I. & Orszag, S. A. 1982 Generalized vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477–501.Google Scholar
Basaran, O. A. 1992 Nonlinear oscillations of a viscous liquid drop. J. Fluid Mech. 241, 169–198.Google Scholar
Bechtel, S. E. 1989 The oscillation of slender elliptical inviscid and Newtonian jets: Effects of surface tension, inertia, viscosity and gravity. Trans. ASME E: J. Appl. Mech. 56, 968–974.Google Scholar
Bechtel, S. E., Cao, J. Z. & Forest, M. G. 1992a Practical application of a higher order perturbation theory for slender viscoselastic jets and fibers. J. Non-Newtonian Fluid Mech. 41, 201–273.Google Scholar
Bechtel, S. E., Forest, M. G., Holm, D. D. & Lin, K. J. 1988 One-dimensional closure models for three-dimensional incompressible viscoelastic free jets: Von Kármán flow geometry and elliptical cross-section. J. Fluid Mech. 196, 241–262.Google Scholar
Bechtel, S. E., Forest, M. G. & Lin, K. J. 1992b Closure to all orders in 1-D models for slender viscoelastic free jets I. An integrated theory for axisymmetric torsionless flows. Stability Appl. Anal. Cont. Media 2, 59–100.Google Scholar
Bendure, R. L. 1971 Dynamic surface tension determination with the maximum bubble pressure method. J. Colloid Interface Sci. 35, 238–248.Google Scholar
Bleys, G. & Joos, P. 1983 Desorbtion from a slightly soluble monolayer. Colloid Polymer Sci. 261, 1038–1042.Google Scholar
Bleys, G. & Joos, P. 1985 Absorption kinetics of Bolaform surfactants at an air/water interface. J. Phys. Chem. 89, 1027–1033.Google Scholar
Bohr, N. 1909 Determination of dynamic surface tension by the method of jet vibration. Phil. Trans. R. Soc. Lond. 209, 281–317.Google Scholar
Borwanker, R. P. & Wasan, D. T. 1983 The kinetics of adsorbtion of surface-active agents at gas-liquid surfaces. Chem. Engng Sci. 38, 1637–1649.Google Scholar
Caskey, J. L. & Barlage, W. B. 1971 An improved experimental technique for determining dynamic surface tensions of water and surfactant solutions. J. Colloid Interface Sci. 35, 46–52.Google Scholar
Chang, Y. C., Hou, T. Y., Merriman, B. & Osher, S. 1995 A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. J. Comput. Phys. to appear.Google Scholar
Defay, R. & Hommelen, J. 1958 Measurements of dynamic surface tensions of aqueos solutions by the oscillating jet method. J. Colloid Sci. 13, 553–564.Google Scholar
Edwards, D. A., Brenner, H. & Wasan, D. T. 1991 Interfacial Transport Processes and Rheology. Butterworth-Heinemann.
Flick, E. W. (ed.) 1985 Industrial Solvents Handbook 3rd edn. Park Ridge, New Jersey, USA: Noyes Data Corporation.
Garret, P. R. & Ward, D. R. 1988 A reexamination of the measurement of dynamic surface tensions using the maximum bubble pressure method. J. Colloid Interface Sci. 132, 475–490.Google Scholar
Geer, J. F. 1977 Slender streams with gravity: Outer asymptotic expansions. I. Phys. Fluids 20, 1613–1621.Google Scholar
Geer, J. F. & Strikwerda, J. C. 1983 Vertical slender jets with surface tension. J. Fluid Mech. 135, 155–169.Google Scholar
Hansen, R. S., Purchase, M. E., Wallace, T. C. & Woody, R. C. 1958 Extension of the vibrating jet method for surface tension measurements to jets of non-uniform velocity profile. J. Phys. Chem. 62, 210–214.Google Scholar
Hou, T. Y, Lowengrub, J. S. & Krasny, R. 1991 Convergence of a point vortex method for vortex sheets. SIAM J. Numer. Anal. 28, 308–320.Google Scholar
Hou, T. Y., Lowengrub, J. S. & Shelley, M. J. 1994 Removing stiffness from interfacial flows with surface tension. J. Comput. Phys. 114, 312–338.Google Scholar
Joos, P. & Serrien, G. 1989 Adsorbtion kinetics of lower alkanols at air/water interface: effect of structure makers and structure breakers. J. Colloid Interface Sci. 127, 97–103.Google Scholar
Kao, R. L., Edwards, D. A., Wasan, D. T. & Chen, E. 1991 Measurement of the interfacial dilatational viscosity at high rates of interfacial expansion using the maximum bubble pressure method I. Gas liquid surface. J. Colloid Interface Sci. 148, 247.Google Scholar
Kármán, T. Von 1921 Über Laminare and Turbulente Reibung. Z. angew. Math. Mech. 1, 233–252.Google Scholar
Keller, J. B. 1983 Capillary waves on a vertical jet. J. Fluid Mech. 135, 171–173.Google Scholar
Kochurova, N. N. & Rusanov, A. K. 1981 Dynamic surface tension of water: Surface tension and surface potential. J. Colloid Interface Soc. 81, 297–303.Google Scholar
Langmuir, I. 1917 The constitution and fundamental properties of solids and liquids II. Liquids. J. Am. Chem. Soc. 39, 1848–1906.Google Scholar
Lin, S. Y, McKeigue, K. & Maldarelli, C. 1990 Diffusion-controlled surfactant adsorbtion studied by pendant drop digitization. AIChE J. 36, 1785–1795.Google Scholar
Lukenheimer, K., Serrien, G. & Joos, P. 1990 The adsorbtion kinetics of octanol at the air/solution interface measured with the oscillating bubble and the oscillating jet methods. J. Colloid Interface Sci. 34, 407–411.Google Scholar
Lundgren, T. S. & Mansour, N. N. 1988 Oscillations of drops in zero gravity with weak viscous effects. J. Fluid Mech. 194, 479–510.Google Scholar
Mansour, N. N. & Lundgren, T. S. 1990 Satellite formation in capillary jet breakup. Phys. Fluids A, 2, 1141–1144.Google Scholar
Milliken, W. J., Stone, H. A. & Leal, L. G. 1993 The effect of surfactant on the transient motion of Newtonian drops. Phys. Fluids A, 5, 69–79.Google Scholar
Pedersen, P. O. 1907 On the surface tension of liquids investigated by the method of jet vibration. Phil. Trans. R. Soc., Lond. 207, 342–397.Google Scholar
Petersson, N. A. 1994 Fast numerical computation of 2-D free surface jet flow with surface tension. CAM report 94—32, Department of Mathematics, University of California, Los Angeles. J. Comput. Phys. to appear.Google Scholar
Petrie, C. J. S. 1979 Elongational flows. Pitman.
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearised Viscous Flow. Cambridge University Press.
Probstein, R. F. 1989 Physicochemical Hydrodynamics. Butterworths.
Rayleigh, Lord 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. 29, 71–97.Google Scholar
Rayleigh, Lord 1890 On the tension of recently formed surfaces. Proc. R. Soc. Lond. 41, 281–287.Google Scholar
Rideal, E. K. & Sutherland, K. L. 1952 The variations of surface tension of solutions with time. Trans. Faraday Soc. 48, 1109–1123.Google Scholar
Rosen, M. J. 1988 Surfactants and Interfacial Phenomena, 2nd edn. John Wiley & Sons.
Scheflan, L. & Jacobs, M. 1953 Handbook of Solvents. D. Van Nostrand Company Inc.
Stone, H. A. & Leal, L. G. 1990 The effect of surfactants on drop deformation and breakup. J. Fluid Mech. 220, 161–186.Google Scholar
Swean, T. F. Jr. & Beris, A. N. 1994 Dynamics of free-surface flows with surfactants. In Proc. Twelfth US National Congress of Applied Mechanics. (ed. A. S. Kobayashi), pp. 173–177. ASME
Thomas, W. D. E. & Potter, L. 1975 Solution/air interfaces 1. An oscillating jet relative method for determining dynamic surface tension. J. Colloid Interface Sci. 50, 397–412.Google Scholar
Tuck, E. O. 1976 The shape of free jets of water under gravity. J. Fluid Mech. 76, 625–640.Google Scholar
Zhang, L. H. & Zhao, G. X. 1989 Dynamic surface tension of the aqueos solutions of cationicanionic surfactant mixtures. J. Colloid Interface Sci. 127, 353–361.Google Scholar
Zhang, X., Harris, M. T. & Basaran, O. A. 1994 Measurement of dynamic surface tension by a growing drop technique. J. Colloid Interface Sci. 168, 47–60.Google Scholar