Expansion Of Three-phase Contact Line Research Articles

Effect of heterogeneity size on three-phase contact line formation kinetics

Flotation relies on the differences in surface wettability. Although solids with the same hydrophobicity are generally regarded as having the same capture probability, the heterogeneities found on particle surfaces could complicate bubble–solid interactions. For surfaces with the same hydrophobicity and different sizes of inclusions, the heterogeneity size is expected to affect bubble–solid interactions. In this work, Microelectromechanical system techniques were used to fabricate chemically heterogeneous samples with the same hydrophobicity on which discrete hydrophilic dots with different diameters were distributed. The collision and adhesion processes between free-rising bubbles and these chemically heterogeneous surfaces were studied using a high-speed video camera. For all surfaces, the time intervals between successive collisions and the bubble trajectories were similar before bubble rupture. In contrast, the time elapsed between maximum air bubble deformation and rupture varied, with the rupture time appearing random. Nevertheless, the terminal diameter and average expansion velocity after bubble rupture were negatively correlated with the hydrophilic dot diameter. Thus, for heterogeneous surface with discrete hydrophilic dots, the bouncing behaviour of air bubbles before rupture is independent of heterogeneity size, whereas the three-phase contact line expansion behaviour after rupture is related to heterogeneity size. These insights can provide guiding principles for improving the flotation.

Three-phase contact line expansion during air bubble attachment to hydrophobic solid surface – experiment and modeling

Three-phase contact line expansion during air bubble attachment to hydrophobic solid surface – experiment and modeling

Bubble-surface interactions with graphite in the presence of adsorbed carboxymethylcellulose.

The adsorption of carboxymethylcellulose (CMC), and the subsequent effect on bubble-surface interactions, has been studied for a graphite surface. CMC adsorbs on highly oriented pyrolytic graphite (HOPG) in specific patterns: when adsorbed from a solution of low concentration it forms stretched, isolated and sparsely distributed chains, while upon adsorption from a solution of higher concentration, it forms an interconnected network of multilayer features. The amount and topography of the adsorbed CMC affect the electrical properties as well as the wettability of the polymer-modified HOPG surface. Adsorption of CMC onto the HOPG surface causes the zeta potential to be more negative and the modified surface becomes more hydrophilic. This increase in both the absolute value of zeta potential and the surface hydrophilicity originates from the carboxymethyl groups of the CMC polymer. The effect of the adsorbed polymer layer on wetting film drainage and bubble-surface/particle attachment was determined using high speed video microscopy to monitor single bubble-surface collision, and single bubble Hallimond tube flotation experiments. The time of wetting film drainage and the time of three-phase contact line spreading gets significantly longer for polymer-modified HOPG surfaces, indicating that the film rupture and three-phase contact line expansion were inhibited by the presence of polymer. The effect of longer drainage times and slower dewetting correlated with reduced flotation recovery. The molecular kinetic (MK) model was used to quantify the effect of the polymer on dewetting dynamics, and showed an increase in the jump frequency for the polymer adsorbed at the higher concentration.

Description of the three-phase contact line expansion

Knowledge of bubble-particle interaction is important in many industrial processes such as in flotation. While the collision (first interaction sub-process) between bubbles and particles is influenced only by hydrodynamic forces, the bubble behaviour during the attachment (second sub-process) is influenced both by hydrodynamic and surface forces. This work is focused on the study of the three-phase contact (TPC) line expansion during bubble adhesion on hydrophobic surface and on its experimental and mathematical description. The experiments were carried out in pure water where mobile bubble surface is expected. The rising bubble was studied in dynamic arrangement, whereas the stationary bubble was analysed in static arrangement. The attachment process was recorded using a high-speed digital camera and evaluated using image analysis. The diameter of the expanding TPC line as well as the dynamic contact angle was determined. Two approaches - the hydrodynamic and the molecular-kinetic - were used for mathematical description of the TPC line expansion. According to our results, the hydrodynamic model is suitable for the description of the initial fast phase of the expansion. The molecular-kinetic model was assessed as appropriate for almost whole range of TPC expansion. Parameters of the model were evaluated and compared for both types of arrangement.

Effect of Adsorbed Polymers on Bubble−Particle Attachment

The influence of adsorbed dextrin-based polymers on the attachment of a rising air bubble to a talc surface has been investigated. Liquid film rupture and dynamic contact angle studies have highlighted the major role that adsorbed polymers can play in bubble-particle attachment. No direct link was established between the equilibrium contact angle of polymer-treated talc surfaces and talc flotation recovery. However, clear correlations were observed between the flotation recovery of polymer-treated talc and the measured wetting film rupture time and rate of dewetting for a bubble attaching to a talc basal plane surface treated with the polymers. The retardation of the three-phase contact line expansion caused by the adsorbed polymers was found to have the largest influence on the bubble-particle attachment. The effect of the morphology (coverage, distribution, and shape) of the adsorbed layer on the wetting film rupture and the motion of the receding water front is discussed.

Time of gas–solid–liquid three-phase contact expansion in flotation

The elementary step of gas–solid–liquid three-phase contact (TPC) expansion in bubble–particle attachment is theoretically and experimentally investigated. The TPC expansion is theoretically described using the extended molecular-kinetic theory [Nguyen, A.V., Stechemesser, H., Zobel, G., Schulze, H.J., 1997a. Order of three-phase (solid–liquid–gas) contact line as probed by simulation of three-phase contact line expansion on small hydrophobic spheres. J. Colloid Interface Sci., 187: 547–550.], which involves the effect of three-phase contact line tension on the TPC expansion with a small wetting radius. A theoretical model for the time of the TPC expansion is proposed and compared with the experimental data. Our data shows that the TPC expansion kinetics in flotation is strongly controlled by line tension, along with particle hydrophobicity. This is consistent with the results of the earlier investigation of the line tension effect on flotation by Scheludko et al. [Scheludko, A., Toshev, B., Bogadiev, B., 1976. Attachment of particles to a liquid surface (Capillary theory of flotation). J. Chem. Soc., Faraday Trans. 1, 72: 2815–2828.]. The line tension obtained in this paper is close to the reported data for similar systems [Li, D., Neumann, A.W., 1990. Determination of line tension from the drop size dependence of contact angles. Colloids Surfaces, 43: 195–206; Duncan, D., Li, D., Gaydos, J., Neumann, A.W., 1995. Correlation of line tension and solid–liquid interfacial tension from the measurements of the drop size dependence of contact angles. J. Colloid Interface Sci., 169: 256–261.] and depends on the interfacial energies of the solid–liquid and gas–liquid interfaces. TPC expansion is an important elementary step in particle-bubble attachment and has to be taken into consideration in modelling and predicting the probability of particle-bubble attachment in flotation.

On modelling of bubble–particle attachment probability in flotation

We have developed the theoretical basis for experimental determination of bubble–particle attachment probability in single-bubble flotation experiments. We use these experimentally determined data to simulate the dependence of induction time on particle size. Using these simulated results, we verify the bubble–particle attachment probability prediction developed on the basis of sliding time and induction time (the Sutherland approach). We have calculated the induction times of fine quartz particles of different diameters less than 80 μm and different hydrophobicity, collected by single bubbles with diameters of 0.75 mm, 1.2 mm and 2.0 mm. The simulation reported in this present paper shows that the calculated induction times increase with decreasing particle size, except for particles of strong hydrophobicity (advancing water contact angle of 65° and 88°) collected by the small bubbles with a diameter of 0.75 mm. These results for induction time indicate that extant attachment probability models, based on sliding time and induction time, cannot adequately describe the elementary steps in the bubble–particle attachment microprocess in flotation. A detailed analysis of induction time, as originally defined and measured by Sven-Nilsson and others was performed. The necessity of the elementary step `rupture of liquid film and formation of three-phase contact of a critical radius (TPC nuclei)' in bubble–particle attachment has been demonstrated. It is suggested that attachment probability can be adequately described by the product of the probabilities of three elementary steps: (1) thinning of intervening liquid film to a critical film thickness; (2) rupture of intervening liquid film and formation of TPC nuclei; (3) expansion of three-phase contact line from the critical radius to form a stable wetting perimeter. The attachment probability model developed according to the Sutherland approach describes only the first elementary step. The poor response of fine particle flotation may be attributed to the decreasing probability of the second elementary step. A more detailed investigation of these elementary steps is required for understanding the attachment microprocess in flotation.

Elementary steps in particle—bubble attachment

Elementary steps in particle—bubble attachment interaction are critically analysed. Three elementary steps are of great importance: (1) thinning of the intervening liquid film to a thickness of film rupture (critical thickness); (2) rupture of the intervening liquid film and formation of a three-phase contact nucleus (a hole of a critical wetting radius); and (3) expansion of three-phase contact line from the critical radius to form a stable wetting perimeter. Some preliminary theoretical and experimental results are presented.

Expansion of three-phase contact line after rupture of thin non-symmetrical liquid films

Expansion of three-phase contact line after rupture of thin non-symmetrical liquid films

Expansion of three-phase contact line after rupture of thin non-symmetrical films

Expansion of three-phase contact line after rupture of thin non-symmetrical films

Expansion of three-phase contact line after rupture of thin non-symmetrical liquid films

One of the important stages in the process of interaction between a particle and a gas bubble in the liquid phase is the expansion of three-phase contact perimeter immediately after rupture of the thin liquid film. The rate of expansion for the system flat quartz surface/liquid dodecylamine hydrochloride solution is determined by use of a high-speed camera. The results were discussed on the basis of a theory on hydrodynamics of thin liquid films.