Soap film vertical

Fig. 1.3. Vertical soap film in contact with soap solution A, film without contact angle B, film with contact angle 9.

The transitions from an unstable thick film to black films arc easily demonstrated by allowing a vertical soap film supported on a frame to drain (Figure 12.11). Initially the whole film shows interference colours, then a dark boundary, separated from the... 

If we dip a wire ring into a soap solution and hold it as shown in Fig. 17.19, we have a vertical soap film. From a force balance on a small section of the film, we see that it is acted on by gravity force downward, and lif it is to stay in place, it must be acted on by an upward surface force. How can this upward surface force be generated From this consideration, can we conclude that it is impossible to" form such a film from an absolutely pure liquid This t pic is discussed in detail by Ross [15]. 

An approach that is almost diametrically opposed to the earlier models of Khan and Armstrong, and Kraynik and Hansen, was advanced by Schwartz and Princen (108). In this model, the films are negligibly thin, so that all the continuous phase is contained in the Plateau borders, and the surfactant tiuns the film surfaces immobile as a result of surface-tension gradients. Hydrodynamic interaction between the films and the Plateau borders is considered to be crucial. This model, believed to be more realistic for common sur factant-stabilized emulsions and foams, draws on the work of Mysels et al. (109) on the dynamics of a planar, vertical soap film being pulled out of, or pushed into, a bulk solution via an intervening Plateau border. An important result of their analysis is commonly referred to as FrankeTs law, which relates the film thickness, 2h., to the pulling velocity, U, and may be written in the form ... 

This section begins with a qualitative description of thin liquid PU films. This initial investigation had five goals in mind to confirm that stable, vertically-oriented, thin liquid films could be prepared using mixtures of ingredients designed to model a PU foam, to study the hydrodynamic phenomena in the films, to compare the physical behaviour of these films to the behaviour of the more common aqueous soap films, to observe specific surfactant effects on the properties of these films, and to extrapolate conclusions about the behaviour of these films to operational PU foam. 

A vertical soap film can be in mechanical equilibrium only if the force of gravity acting on each film element is balanced by a gradient in the surface tension on both surfaces. Calculate the necessary surface tension gradient for a film with a thickness of 100 nm, given a soap solution density of 1 g cm (g = 980 cm s ). 

This is akin to a vertical radiator heating a room. Warm air near the radiator starts rising and generates turbulent flows. Similar turbulent flows exist in a soap film near the lateral walls. These flows close the loop at the center (Figure 8.15). Thus, there is a net redistribution of liquid from the central portion of the film toward the bottom. The physical law s involved are rather complex. For more details, the reader is encouraged to consult the book by Mysels, Shinoda, and Frankel/ ... 

The two conditions, (a) and (b), are satisfied by most fluids. For a soap film, however, it is possible that (b) will only be satisfied approximately. For example consider the equilibrium of a section of a vertical soap film of thickness t, width /, and height h (Fig. 1.8). Let the surface tension at the bottom of the section of film be ao and that at height h, ah. The vertical force at the top of the film is 2/(7, the factor of 2 arises because the film has two surfaces. This force balances the force at the bottom of the film, 2/ao, plus the weight of the film mg, where m is the mass of the film. If p is the density of the fluid in the film then m = tlhp. For equilibrium. 

Fig. 1.8 Forces acting on a vertical rectangular soap film.

Fig. 1.18(a) Interference of light produced by a vertical soap film after withdrawal from a bath of soap solution, (b) The film sometime later, (c) The final equilibrium film. 

Table 2.1 is taken from Lawrence s book Soap Films. It contains a descriptive indication of the colours produced by the interference of white light. The white light is incident normally on a vertical soap film of refractive index jti = 1.41. The Table also contains the thickness of soap film associated with each colour of film. For an incident beam which has an angle of refraction 6, an additional factor of cos 6 is required, Eq. (2.26), in order to obtain the thickness of the film from its colour in Table 2.1. Thick soap films will produce overlap of different orders of interference for the different spectral colours. The film will consequently appear increasingly white as the correlation between the interference produced by different colours decreases to zero.

Interference colours produced by a vertical soap film, shortly after formation, using white light... 

As we have seen in the previous example of the vertical soap film (Figure 2.10), thick film surfaces can be curved. However, as the films lose water (drainage), they progressively flatten due to interactions between the sinfaces. 

The forces acting on a hemispherical section of a soap bubble are the film tension force, lirrof, pulling vertically downwards (Fig. 1.13), and the force due to the excess pressure, p, acting vertically upwards on the hemispherical section of bubble, irr p. The weight of the hemispherical shell of fluid can be neglected compared with either of these forces. As the hemispherical section is in equilibrium these two forces must balance, thus... 

The usual soap bubbles observed in white light show bright interference colors. Their thickness ranges from 0.1 to 10 pm, and they are called "thick" films. When such thick films placed in vertical frames, their thickness varies. This variation can be easily calculated for insoluble surfactants, where Tg 0 and c = 0. In this case n= r RT(see (2.11)) with (2.17) gives that ... 

A situation when a bubble is rising in a normal fluid is illustrated in Figure 4.23b with the motion of thinner zones of soap fluid in a vertical soap fluid frame. It is possible to create zones of different two-dimensional density touching the film with pure soap surfactants. The locally increased soap concentration causes the surrounding film to stretch rapidly characterized by a smaller surface tension. This process creates a thinner zone with a constant thickness hi, which could be as small as that of the black films (4.5 nm or 30 nm) or to the silvery white (-100 nm). The limit between the zone of area S and the film is sharply defined with the width of the rim comparable to the film thickness /Zj. If this thin zone is created near the bottom of the frame and surrounded by thicker fluid, it will experience a buoyant force ... 

It is obvious that these considerations would apply also if the ring, while it is withdrawn, would be oblique or vertical, instead of horizontal, and that they would apply in the same way when the wire, instead of being curved circularly, would be folded in an arbitrary polygon. Always there would be formed, by the same causes, a film between it and the surface of the liquid if thus we immerse in soap water or glyceric liquid one of our frames, itsiron wires will be, as they leave the liquid, attached to it by films, as indeed experiment shows. 

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