3619
DIMPLING OF THINLIQUID FILMS
Acknowledgment. The author is indebted to the Lever Rrothers Co. for permission to publish this
paper and to Dr. S. Goldwasscr for discussions on infrared spectroscopy.
Experimental Investigation on the “Dimpling” of Thin Liquid Films
by D. Platikanov Institute of Physical Chemistry, Bulgarian Academy o j Sciences, So&, Bulgaria
(Received April 19,1964)
In order to provide an experimental check of the Frankel-RIysels theory for the shape of the “dimpling” during the approach of two interfaces, measureinents were carried out on microscopic, circular, thinning liquid films on a solid substrate and on similar foam (soap) films, The shape of t,he “dimple” was given by the interference picture obtained by photographing the films in reflected monochromatic light. The decreasing of the thickness in the center of the film was measured iiitel.feron~etricallywith a photoinultiplier. Films of water, aqueous KCl, aniline, ethanol, and oleic acid were used. A shape corresponding to the l+ankel-Mysels theory but with a slightly smaller “dimple” was obtained for films on a substrate. For foam filnis the shape evolved in a different way. In all cases practically plane-parallel films were obtained when the diameters of the films and their thicknesses were sufficiently small. This is in accordance with the assumptions used in the dynamic method for measuring the disjoining pressure in thin liquid films.
The properties of thin microscopic circular films, formed when a gas bubble or a liquid drop approaches an interface, are of utmost importance for the behavior of the respective disperse systems (foams, emulsions, flotation systems, etc.). When the films are sufficiently thin, an additional pressure arises-the socalled disjoining pressure-caused by the deformation of the double electric layers and by van der Waals forces. a dynamic method has been developed for the measurenient of the disjoining pressure in thin liquid films as a function of their thickness. This method is based on the assumption that thin liquid films are plancparallel and that the liquid flows out of them as if between two parallel rigid disks. Thus the equation of Reynolds can be used for the rate of thinning of the film d(l/h2) dt
=
-p4 3V02
where h is the thickness of the film, r0 is its radius, and
q is the viscosity. As shown earlier,g when one of the surfaces of the film dilutes freely, the numerical factor is 16/a. For both cases the general equation will be
d(1/h2) l6 P dt 3n2nro2
(1)
where n is the number of surfaces a t which the flow rate PI is a sum of the is zero. The pressure P = P , capillary pressure P,, = 2 u / R (u is the surface tension, R is the radius of the bubble or the drop) and of the disjoining pressure II. To apply eq. 1 to the dynamic method for the measurement of 11, the experinicntal conditions in previous were chosen so that in the thickness range under investigation the films were plane-parallel, which was controlled visually.
+
(1) A. Scheludko, Kolloid-Z., 155, 39 (1957). (2) A. Scheludko and D. Exerowa, ibid., 165, 148 (1959); 168, 24 (1960). (3) A. Scheludko and D. Platikanov, ibid., 175, 150 (19131).
Volume 68,Number 1.9 December, 1966
3620
D. PLATIKANOV
It is established, however14-7that when a bubble or a drop approaches an interface, the film obtained between the latter and the flattened part of the bubble is not plane, but has a central part thicker than its periphery. Thus a “dimple” is formed, entrapped by a thinner ‘‘barrier ring.” A hydrodynamic theory for the profile and evolution of this dimple was developed by Frankel and Rllysels.* This theory takes into consideration only the capillary pressure, but neglects the disjoining pressure which arises at low filin thicknesses and depends on this thickness. According to this theory the thickness h in the center of the film (the maximum thickness) is given by the equation 0.0096n2~ro6 ‘I‘
=
[
UR
]
1 (t
(2)
-
and the thickness zo a t the barrier ring (the minimum thickness) by zo =
[0.090n2~~02R]’/’ 1
(3)
(t - to)”’
U
where to is the time of formation of the hypothetic dimple with infinite thickness. The last equation coincides alniost completely with eq. 1, which on integration becomes
h =
[0.094n2~ro2R]’:’ (t
U
(for a flat film h the expression
= zo).
1
-
t
p
(4)
From eq. 2 and 3 one obtains
20
R
h
To2
- = 3.066 - h
(5)
which indicates, that the dimple should become relalively more pronounced as the film thins. The disagreement between these results and the experimental data which serve as a base of the dynamic methodl--3 for the measurement of the disjoining pressure requires elucidation. In the present work thin liquid circular films on a solid substrate, as well as free foam films were studied and the results compared with the Frankel and JIysels theory.8
Experimental A number of liquids with different viscosity were examined : water, aqueous KC1 solutions, ethanol, aniline, and oleic acid. The microscopic circular filnis on solid substrate were obtained in cell a (Fig. 1). A small glass plate, e, with well-polished surfaces was laid down on the bottom of the cell and the liquid under study was poured in (f). A vertical tube with a radius R = 2.4 X The Journal of Physical Chemistry
Figure 1. Cell for the investigations of circular liquid films on a solid substrate.
loM2cm. was placed above the plate so that the gap between its lower end and the plate was smaller than the radius R. With the aid of a mercury-sealed micrometric screw, air is pressed slowly through the capillary, d, until the concave liquid meniscus is lowered sufficiently to approach the glass plate. Thereupon a circular film is formed a t point g. The micrometric screw makes it possible to obtain films with different radii, ro, although the radius R of the “semibubble” remains constant. In this case the capillary pressure dependsgon ro
P,
=
R R2 - ro2
2u-
When ro
