Plateau border gravity drainage

The Plateau borders in a foam form a network into which liquid from the films collects, and from which liquid is drained away by gravity. This drainage process, which is important in foam beds used for mass transfer or separation, has been modeled by several groups, starting with Haas and Johnson (1967 see Gururaj et al. 1995 for a recent review). 

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. 

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 ... 

As mentioned in Section I, drainage of the continuous-phase liquid plays a crucial role in the decay of a standing foam. Two mechanisms are responsible for fluid flow in a foam. The capillary pressure drives flow in the films, whereas the flow in the Plateau border channels occurs due to gravity. We will discuss the flow in individual films and Plateau border channels and then formulate the bulk conservation equations. 

R)RdR, where the faetor 2 arises due to the fact that bubbles on both sides of the plane are considered. The total number of spheres per unit area intersected by the plane is then given as J 2NRF R)6R = 2NR and the flux of liquid due to gravity drainage through the Plateau border channels is ... 

The generalised model for drainage involves the plateau borders forming a network through which the liquid flows due to gravity. 

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... 

Plateau showed that the vertices of the neighboring pentagonal dodecahedrons form junction comer in which four borders join. As a result, four vertices closest to the reference one form a tetrahedron. This arrangement is similar to that of atoms in the nearest coordination sphere in the diamond crystal lattice. The borders and nodes form a united branched network along which the transfer of dispersion medium, including drainage under gravity, may take place. 

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