Hydrodynamic theory of rising foam

There is a large body of literature that tries to model flotation based on froth properties with little or no experimental verification of the underlying features. These models adopt the so called channel-dominated theory of foam drainage. There is no experimental evidence to support this foam drainage theory. Instead the new, simple and experimentally validated foam drainage equation of Stevenson (2006a) [Stevenson, P. 2006a. Dimensional analysis of foam drainage. Chem. Eng. Sci. 61, 4503–4510] has been extended to describe the liquid flux and liquid profile in columns of pneumatic froth. The condition for the maximum value of gas rate for froth stability has been described and this shows that there is a maximum volumetric liquid fraction that a foam can exhibit. It is shown that the numerical calculations of liquid profile of Neethling et al. (2003a,b) [Neethling, S.J., Lee, H.T., Cilliers, J.J. 2003a. The recovery of liquid from flowing foams. J. Phys.: Cond. Matter 15, 1563–1576; Neethling, S.J., Lee, H.T., Cilliers, J.J. 2003b. Simple relationships for predicting the recovery of liquid from flowing foams and froths. Miner. Eng. 16, 1123–1130] are incorrect, and this may mean that all of their later simulations of the flotation process are similarly deficient. Instead a simple and accessible method of calculated liquid fraction profiles, both with and without added washwater is shown. In addition, a model for the effect of surface and internal bubble coalescence on the hydrodynamic condition of the froth is presented. It is recognised that the gas–liquid systems considered in the current work are dissimilar to practical mineralised flotation froths and these differences are discussed.