Plateau border suction

The pressure within the plateau border can be related to the pressure in the dispersed phase pd and the plateau border suction Pc through... 

In order to solve the balance equations, the velocities of the film and Plateau border drainage as well as the kinetics of the protein adsorption in the films are used. The velocity of drainage of Plateau borders, u, depends on the flow due to gravity and due to the gradient of Plateau border suction. By neglecting the latter one obtains ... 

Column Operation To assure intimate contact between the counterflowing interstitial streams, the volume fraction of liquid in the foam should be kept below about 10 percent—and the lower the better. Also, rather uniform bubble sizes are desirable. The foam bubbles will thus pack together as blunted polyhedra rather than as spheres, and the suction in the capillaries (Plateau borders) so formed vidll promote good liqiiid distribution and contact. To allow for this desirable deviation from sphericity, S = 6.3/d in the equations for enriching, stripping, and combined column operation [Lemhch, Chem. E/ig., 75(27), 95 (1968) 76(6), 5 (1969)]. Diameter d still refers to the sphere. 

Figure 3.28 Sketch of the plateau border in a surfactant foam. Due to the curvature (radius r) a suction effect in the direction of the arrows results.

Polyhedral gas cells produced on aging thin flat walls are produced with junction points of the interconnecting channels (plateau borders). Due to the interfacial curvature, the pressure is lower and the film is thicker in the plateau border. A capillary suction effect of the liquid occurs from the centre of the film to its periphery. 

To keep the foam stable (i.e., to prevent complete rupture of the film), this capillary suction effect must be prevented by an opposing disjoining pressure that acts between the parallel layers of the central flat film (see below). The generalised model for drainage involves the plateau borders forming a network through which the liquid flows due to gravity. 

The physical basis for the lamella number is that a combination of capillary suction in the Plateau borders and the influence of mechanical shear cause the oil-phase distortion and pinch off into droplets. This result is in accord with the observations of emulsification and imbibition by Lobo et al. (50), French et al. (54), and Schramm and Novosad (37). The mechanical shear may come from several sources, including the flow... 

For each film to be stable, it must be able to develop an internal, repulsive disjoiningpressureYl ) to counter-act the capillary suction acting at the film/Plateau border junction. At equilibrium, it can be readily shown from the above that... 

Lamella Number. A dimensionless parameter used to predict the likelihood that a combination of capillary suction in plateau borders and the influence of mechanical shear will cause an oil phase to become emulsified and imbibed into foam lamellae flowing in porous media (reference [19]). 

In Eq. (1), 1 is the time, q is the viscosity of the continuous phase, is the radius of the disk, and AP is the pressure difference causing the flow. The driving force AP is a net result of the suction pressure in the adjacent Plateau border channels and the disjoining pressure (17) in the films, and is given by AP = a jr — 77, where a is the surf ace tension and is the radius of curvature of the Plateau border channels. The coefficient Cf is a correction factor that accounts for the mobility of the film surfaces and is given by [42] ... 

P ne parallel films after dimple disappears. Drainage due to suction at plateau borders and disjoining pressure. 

A related phenomenon to asymmetric drainage in horizontal cylindrical foam films is that of the so-called marginal regeneration. This process occurs in vertical foam films subject to both capillary suction from the Plateau borders and gravity. It is manifest as an apparent turbulent motion on the margin of foam films where thin elements of film are drawn out of the Plateau border and thick elements are sucked... 

It should be clear then that asymmetric drainage of horizontal cylindrical films and marginal regeneration in vertical foam films, although often apparent, are not always exhibited. Liquid flow by capillary suction from the Plateau border is. 

Foam film thins due to plateau border capillary suction... 

In making comparison between p (y = 0) and we note that the former is a suction applied to entrapped drops by the walls of the Plateau borders with negative curvature. The critical capillary pressure measured by the FTT, is, on the other hand, the suction pressure in the aqueous phase surrounding a drop trapped in a film against a solid substrate (see description of the FTT in Chapter 2). In comparing with p (y = 0), we should note that rupture of the relevant pseudoemulsion film is supposed determined by the magnitude of the critical disjoining pressure at the... 

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