Effect of Rheology and Interfacial Rigidity on Liquid Recovery from Rising Froth

Abstract

A dimensionless correlation for the liquid overflow rate from a rising column of foam has been developed that expresses the ratio of liquid to gas superficial velocities as a function of Reynolds, Grashof, and Morton numbers. This correlation is developed using new and previously reported data. An empirical approach is made after noting that models that estimate the overflow rate by adding a gross upward velocity to conventional solutions of stationary foam drainage that take into account viscous losses only at the Plateau border walls are unsatisfactory. Relaxation of the assumption of rigid Plateau borders by allowing for finite surface shear viscosity does not improve such a mechanistic approach. However, an existing semiempirical drainage expression that takes into account losses at the vertices within the foam enables a much better prediction of the overflow rate, although the newly developed correlation gives superior predictions and requires no a priori knowledge of the drainage behavior of the foam. Experiments performed on a shear-thinning solution are also discussed.

Foam drainage

“…(18) over-predicated the liquid overflow rate by a factor up to approximately 4. In the next work the authors [40] attempted to clear the inconsistency between the calculated and experimental data using the Nguyen formula [23 •• ], which takes into account the influence of the surface viscosity on the surface mobility, but the relaxation of the assumption that the PBs are rigid does not materially improve the predictions of Eq. (18).…”

Remarks on the shear viscosity of surfaces stabilised with soluble surfactants

“…It has been shown theoretically [14] that the Gibbs elasticity of the interface and the surface diffusion coefficient may play an important role in determining drainage rate due to gradients in surface tension being present and it has previously been asserted [15] that the appearance of surface tension in a correlation for the overflow rate from a column of rising foam may be as a proxy for some other surface rheological property. Nguyen [2] stated "In particular, the rheological properties of adsorption layers, like surface elasticity, surface dilational, and shear viscosities are important for the investigation of liquid foams."…”

Dimensional Analysis of Particle and Liquid Dispersion in Draining Foam

“…a is the radius of Saffman's capillaries of circular section. In foam the sectional shape of the Plateau border pores is that formed by three mutually-contacting circles; these pores have a cross-sectional area of 0.162r 2 where r is the radius of the Plateau borders and may be estimated from the expression of Stevenson and Stevanov (2004):…”