Liquid overflow from a column of rising aqueous froth

Abstract A model for predicting the overflow rate from a column of rising foam is presented. This model assumes that the Plateau borders have the cross-sectional geometry the same as the void between three mutually contacting cylinders. Another assumption is that the Plateau border walls are rigid. This theory is tested against experimental data for the overflow rate of a rising foam of water/glycerol mixtures stabilised with sodium dodecyl sulphate. The theory is seen to over-predict the observed overflow rate; this discrepancy is attributed to the fact that the Plateau border walls probably do not exhibit the property of rigidity. An empirical approach to predicting overflow rate that uses a Richardson and Zaki-type expression for the hindered rising of bubbles is seen to have far greater success than the mechanistic model. The applicability of experiments and theories for gas–liquid foams to mineralised froths is discussed.

[1]  Stephen J. Neethling,et al.  Solids motion in flowing froths , 2002 .

[2]  J. F. Richardson,et al.  FLUID-PARTICLE INTERACTIONS AND FLOW CHARACTERISTICS OF FLUIDIZED BEDS AND SETTLING SUSPENSIONS OF SPHERICAL PARTICLES , 1989 .

[3]  J. F. Richardson,et al.  Sedimentation and fluidisation: Part I , 1997 .

[4]  Kari Heiskanen,et al.  Visual technique for measuring bubble size in flotation machines , 2002 .

[5]  Robert Lemlich,et al.  A study of interstitial liquid flow in foam. Part I. Theoretical model and application to foam fractionation , 1965 .

[6]  P. J. Moss,et al.  Fluid Mechanics and Transfer Processes , 1985 .

[7]  Denis Weaire,et al.  The foam drainage equation , 1996 .

[8]  Howard A. Stone,et al.  Liquid Flow through Aqueous Foams: The Node-Dominated Foam Drainage Equation , 1999 .

[9]  I. R. Shreiber,et al.  Liquid flow in foams , 1988 .

[10]  H. Stone,et al.  Drainage of single Plateau borders: direct observation of rigid and mobile interfaces. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Stephen J. Neethling,et al.  The recovery of liquid from flowing foams , 2003 .

[12]  G. Wallis One Dimensional Two-Phase Flow , 1969 .

[13]  P. A. Haas,et al.  A Model and Experimental Results for Drainage of Solution between Foam Bubbles , 1967 .

[14]  D. Desai,et al.  Liquid overflow from vertical co-current foam columns , 1984 .

[15]  P. Saffman The lift on a small sphere in a slow shear flow , 1965, Journal of Fluid Mechanics.

[16]  David G. Thomas Transport characteristics of suspension: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles , 1965 .

[17]  A. Einstein Zur Theorie der Brownschen Bewegung , 1906 .

[18]  Stephen J. Neethling,et al.  A foam drainage equation generalized for all liquid contents , 2002 .

[19]  Ephraim M Sparrow,et al.  Longitudinal Laminar Flow Between Cylinders Arranged in Regular Array , 1959 .

[20]  Graeme J. Jameson,et al.  Short-time tracer dispersion in a two-dimensional rising froth , 2003 .

[21]  N. Cheng,et al.  Exponential formula for computing effective viscosity. , 2003 .

[22]  Jan J. Cilliers,et al.  A model to describe flotation performance based on physics of foams and froth image analysis , 2002 .

[23]  G. Jameson,et al.  The coexistence of the froth and liquid phases in a flotation column , 1992 .

[24]  Anh V. Nguyen Liquid drainage in single plateau borders of foam. , 2002, Journal of colloid and interface science.