Quasionedimensional foam drainage
Grassia, P. and Cilliers, J.J. and Neethling, S.J. and VenturaMedina, Esther (2001) Quasionedimensional foam drainage. European Physical Journal E, 6 (4). pp. 325348. ISSN 12928941 (https://doi.org/10.1007/s1018900180473)
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Foam drainage is considered in a froth flotation cell. Air flow through the foam is described by a simple twodimensional deceleration flow, modelling the foam spilling over a weir. Foam microstructure is given in terms of the number of channels (Plateau borders) per unit area, which scales as the inverse square of bubble size. The Plateau border number density decreases with height in the foam, and also decreases horizontally as the weir is approached. Foam drainage equations, applicable in the dry foam limit, are described. These can be used to determine the average crosssectional area of a Plateau border, denoted A, as a function of position in the foam. Quasionedimensional solutions are available in which A only varies vertically, in spite of the twodimensional nature of the air flow and Plateau border number density fields. For such situations the liquid drainage relative to the air flow is purely vertical. The parametric behaviour of the system is investigated with respect to a number of dimensionless parameters: K (the strength of capillary suction relative to gravity), α (the deceleration of the air flow), and n and h (respectively, the horizontal and vertical variations of the Plateau border number density). The parameter K is small, implying the existence of boundary layer solutions: capillary suction is negligible except in thin layers near the bottom boundary. The boundary layer thickness (when converted back to dimensional variables) is independent of the height of the foam. The deceleration parameter α affects the Plateau border area on the top boundary: weaker decelerations give larger Plateau border areas at the surface. For weak decelerations, there is rapid convergence of the boundary layer solutions at the bottom onto ones with negligible capillary suction higher up. For strong decelerations, two branches of solutions for A are possible in the K = 0 limit: one is smooth, and the other has a distinct kink. The full system, with small but nonzero capillary suction, lies relatively close to the kinked solution branch, but convergence from the lower boundary layer onto this branch is distinctly slow. Variations in the Plateau border number density (nonzero n and h) increase individual Plateau border areas relative to the case of uniformly sized bubbles. For strong decelerations and negligible capillarity, solutions closely follow the kinked solution branch if bubble sizes are only slightly nonuniform. As the extent of nonuniformity increases, the Plateau border area reaches a maximum corresponding to no net upward velocity of foam liquid. In the case of vertical variation of number density, liquid content profiles and Plateau border area profiles cease to be simply proportional to one another. Plateau border areas match at the top of the foam independent of h, implying a considerable difference in liquid content for foams which exhibit different number density profiles.


Item type: Article ID code: 52228 Dates: DateEvent1 December 2001PublishedSubjects: Technology > Chemical engineering Department: Faculty of Engineering > Chemical and Process Engineering Depositing user: Pure Administrator Date deposited: 13 Mar 2015 15:19 Last modified: 08 Apr 2024 22:08 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/52228