The objective of this study is to explore the interrelated mechanisms governing foam drainage and stability by modeling the foam column kinetics, measuring the interfacial properties of the air-water interface and conducting forced drainage experiments. Studies on foams are usually divided into four length scales: (i) a gas-liquid interface (molecular scale), (ii) a liquid film (nanometer scale), (iii) a bubble (millimeter scale), and (iv) a foam (meter scale). Although much progress has been made in each length scale, the correlation between the different length scales remains poorly understood and quantified. The present study seeks to address this problem. In many industrial processes, such as froth flotation and foam fractionation, careful control of the foam or froth stability is required to optimize the process performance. Therefore, an understanding of the correlation between the different length scales is of paramount interest for industrial applications. The present study can be divided into three different parts: (1) foam column kinetics, (2) mechanisms governing foamability and foam stability, and (3) foam drainage in the presence of solid particles.
The first part models foam column kinetics to predict the evolution of foam growth, liquid fraction, the transport of liquid and gas in growing foams and foam collapse by analogy with chemical kinetics. First, a modeling framework was formulated to categorize the foam or froth growth models into zeroth, first and second order, according to the dependence of the foam collapse rate on the foam volume or height. Then, a novel kinetic model was developed based on the mass balance of gas and liquid in the foam column to simulate the foam column kinetics. Finally, the simulation results were compared with the reported experimental data. Good agreement between model predictions and published experimental results confirms the validity of the analogy between foam column kinetics and reaction kinetics.
Mechanisms governing the foamability and foam stability are crucial to understanding foam behaviors. The foamability and foam stability of surfactant blend and surfactant solutions in different electrolyte concentrations were examined to elucidate the different mechanisms that collectively determine foamability and foam stability. The foam growth kinetic model developed in the previous section was also applied here. First, the foamability of sodium dodecyl sulfate (SDS)-dodecanol (DOH) solutions was investigated to test the conventional theories that apply to a single surfactant of pre-critical micelle concentration (CMC). The remarkable decrease in the foamability of SDS solutions caused by the addition of DOH could not be easily explained by the theories of surface tension and surface viscoelasticity. Instead, alternative mechanisms were proposed. Second, findings regarding the foamability of SDS-DOH solutions were extended to froth flotation, that is, the effect of a nonpolar collector (diesel oil) on the foamability of frother solutions (methyl isobutyl carbinol, MIBC). The results showed that the presence of diesel oil, even in trace amounts (e.g., 2 ppm), could effectively decrease the foam growth rate by accelerating the foam collapse process. Two mechanisms were proposed to explain the antifoam effect of diesel oil: (i) the spreading of the diesel oil droplets at the liquid film interface and (ii) the molecular interactions between the diesel oil and the frother molecules. Finally, the rupture of standing aqueous foams stabilized by SDS-DOH and SDS-NaCl mixtures was examined to obtain different values of the surface viscoelasticity and surface potential to elucidate the roles of surface rheology and intermolecular forces in foam stability.
Foam drainage in the presence of solid particles is relevant to the field of froth flotation, where the wash water is commonly applied to the froth layer to improve the product’s grade. Forced drainage experiments were conducted to study the liquid flow within the foam stabilized by hexadecyltrimethylammonium bromide (CTAB) with glass beads. Two foam drainage models for aqueous foams were applied to simulate and interpret the experimental results. The simulation results showed that the presence of solid particles in foams increases the rigidity of the interfaces and the viscous losses in the channels (Plateau borders) of the foams, which consequently resulted in a decrease in the foam permeability.
In summary, the present study focuses on modeling foam column kinetics, the effects of interfacial properties on the foamability and foam stability of surfactant solutions, and the effect of solid particles on foam drainage. To further understand the mechanisms governing foamability and foam stability, the interplay and magnitude of these mechanisms on the different stages of foam life should be addressed in future studies.