Plateau borders profiles

Study of Foam Liquid Distribution and Plateau Border Profiles... 

Study of foam liquid distribution and Plateau border profiles 375... 

If the condition for polyhedricity R/r 1 is not fulfilled, the radius of curvature and the area of the cross-section become dependent on the co-ordinates along the length of the Plateau border. Analytical dependence of the radius of curvature on the co-ordinates (the border profile) at different foam expansion ratio is not found. 

The simplest model of a border profile is a cylinder, the bottom of which is a slit between three adjoining cylinders (cylindrical model of a Plateau border). The cylindrical border profile is realised at the initial and final stage of drainage. 

Fig. 6.20. Profile of Plateau borders in the drainage process of a foam in a centrifugal field.

Eor the Plateau border we have z > / , 11 -> 0, o -> o = const., and both Equations 5.150 and 5.151 rednce to Eqnation 5.101 with AP = P. The macroscopic contact angle, a, is defined as the angle at which the extrapolated meniscns, obeying Equation 5.101, meets the extrapolated film snrface (see the dashed line in Fignre 5.16). The real surface, shown by solid line in Figure 5.16, differs from this extrapolated (idealized) profile, because of the interactions between the two film snrfaces, which is taken into acconnt in Eqnation 5.150, but not in Eqnation 5.101. To compensate for the difference between the real and idealized system, the line and transversal tensions are ascribed to the contact line in the macroscopic approach. In particnlar, the line tension makes up for the differences in snrface tension and running slope angle ... 

In conclusion, it should be noted that the width of the transition region between a thin liquid film and Plateau border is usually very small — below 1 pm. That is why the optical measurements of the meniscus profile give information about the thickness of the Plateau border in the region r > (Figure 5.16). Then, if the data are processed by means of the Laplace equation (Equation 5.101), one determines the contact angle, a, as discussed above. Despite that it is a purely macroscopic quantity, a characterizes the magnitude of the surface forces inside the thin liquid film, as implied by Equation 5.148. This has been pointed out by Derjaguin and Princen and Mason. ... 

At the place where the film contacts the bulk liquid, a curved surface profile (sometimes called a Plateau border) is present. For a plane vertical film this is sketched in Fig. 1.3. In a thick film this profile is smooth, but in a thin film, where the interaction forces become perceptible, a discontinuity emerges that can be measured as a so-called contact angle" (e.g., from a Fresnel diffraction pattern" of visible light). A similar phenomenon can be observed in small circular... 

There is no flow in the Plateau border charmels (i.e., m = 0) throughout the foam. This happens when the gradient in the capillary pressure balances gravity, that is, when pg = —9/9z(experimental measurements [63,64] of the pressure in a draining foam indicate that after a sufficiently long time, the pressure profile becomes linear with a slope equal to pg. 

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