On the modelling of the dynamic contact angle

The dynamic contact angle is a value of great significance for characterizing wetting processes. Three strategies have been developed for modelling this value; empirical models, models based on molecular kinetics and models based on flow mechanics.Models based on molecular kinetics start from the fact that the dynamic contact angle appears immediately at the Une of wetting, and that the curvature of the liquid surface can be neglected. Models based on flow mechanics show that near the line of wetting the curvature is very strong. These models require the presence of the static contact angle at the line of wetting and give a model of the dynamic contact angle as the slope of the interface. In the present paper, models based on flow mechanics are extended in two directions. For the case of flow in a tubular capillary, the model represents the effect of the adsorption kinetics of surfactants on the dynamic contact angle, assuming the adsorption to be kinetically controlled. Another model is concerned with the effect of the flow of the third phase on the dynamic contact angle and on the boundaries of dynamic wetting. It is demonstrated that coating under an inert liquid is possible only for small working ranges.

[1]  L. Scriven,et al.  Hydrodynamic Model of Steady Movement of a Solid / Liquid / Fluid Contact Line , 1971 .

[2]  D. v.,et al.  The moving contact line: the slip boundary condition , 1976, Journal of Fluid Mechanics.

[3]  Eli Ruckenstein,et al.  Slip velocity during wetting of solids , 1977 .

[4]  Richard L. Hoffman,et al.  A study of the advancing interface , 1983 .

[5]  R. Miller.  Zur Adsortvtionskinetik an der Oberfläche wachsender Tropfen , 1980 .

[6]  E. J. Watson,et al.  A theory of capillary rise of a liquid in a vertical cylindrical tube and in a parallel-plate channel , 1980 .

[7]  C. M. Holmes,et al.  Kinetics of wetting of surfaces by polymers , 1969 .

[8]  J. C. Slattery,et al.  Effect of interfacial viscosities upon displacement in capillaries with special application to tertiary oil recovery , 1983 .

[9]  J. C. Slattery,et al.  Correlation for dynamic contact angle , 1979 .

[10]  S. Dukhin,et al.  On the theory of adsorption kinetics of ionic surfactants at fluid interfaces , 1983 .

[11]  R. Burley,et al.  An experimental study of air entrainment at a solid/liquid/gas interface , 1976 .

[12]  R. Bogaert,et al.  Surface velocity of a flowing surfactant solution , 1979 .

[13]  D. F. Evans,et al.  Surfactant diffusion: New results and interpretations , 1983 .

[14]  T. Toong,et al.  Dynamic contact angle and its relationship to forces of hydrodynamic origin , 1971 .

[15]  K. Lunkenheimer,et al.  Ein Modell für die diffusionskontrollierte Adsorption von Tensidgemischen an fluiden Phasengrenzen , 1979 .

[16]  P. Joos,et al.  Theory on the determination of the dynamic surface tension with the drop volume and maximum bubble pressure methods , 1981 .

[17]  Darsh T. Wasan,et al.  The kinetics of adsorption of surface active agents at gas-liquid surfaces , 1983 .

[18]  M. Tempel,et al.  Damping of Waves by Surface‐Active Materials , 1965 .

[19]  Clarence A. Miller,et al.  Spreading kinetics of liquid drops on solids , 1976 .

[20]  Edgar B. Gutoff,et al.  Dynamic contact angles , 1982 .

[21]  James Lowndes,et al.  The numerical simulation of the steady movement of a fluid meniscus in a capillary tube , 1980, Journal of Fluid Mechanics.

[22]  Reinhard Miller.  On the solution of diffusion controlled adsorption kinetics for any adsorption isotherms , 1981 .

[23]  Chun Huh,et al.  The steady movement of a liquid meniscus in a capillary tube , 1977, Journal of Fluid Mechanics.

[24]  Clarence A. Miller,et al.  The origin of flow during wetting of solids , 1974 .

[25]  E. Lightfoot,et al.  Deformation of advancing menisci , 1968 .

[26]  R. Miller.  Adsorption kinetics of surfactants from micellar solutions , 1981 .

[27]  T. Blake,et al.  Kinetics of displacement , 1969 .

[28]  Motion of a droplet with a newtonian interface , 1981 .

[29]  L. M. Hocking.  A moving fluid interface. Part 2. The removal of the force singularity by a slip flow , 1977, Journal of Fluid Mechanics.

[30]  R. Burley,et al.  A study of the dynamic wetting behaviour of polyester tapes , 1976 .

[31]  B. J. McCoy.  Analytical solutions for diffusion-controlled adsorption kinetics with non-linear adsorption isotherms , 1983 .

[32]  H. K. Moffatt.  Viscous and resistive eddies near a sharp corner , 1964, Journal of Fluid Mechanics.

[33]  S. Whitaker,et al.  The effect of surfactants on the hydrodynamic development of thin liquid films , 1971 .

[34]  R. Miller,et al.  Numerische Lösung für ein gemischtes Modell der diffusions-kinetik-kontrollierten Adsorption , 1980 .

[35]  Clarence A. Miller,et al.  Spreading kinetics of a drop on a smooth solid surface , 1982 .

[36]  R. Miller.  Beschreibung der Ad- und Desorptionsvorgänge bei der Kompression von löslichen Tensidadsorptionsschichten , 1983 .