Bubble Surface Research Articles

A Study on the Dilational Modulus Measurement of Polyacrylic Acid Films at Air-Water Interface by Pendant Bubble Tensiometry.

The dilational modulus (E) of polymer films has been commonly measured using the oscillating ring/bubble/drop methods with an external force, and often without specifying the state of the adsorbed film. This study explores an approach where E was determined from the relaxations of surface tension (ST) and surface area (SA) of natural perturbations, in which ST and SA were monitored using a pendant bubble tensiometer. The E of the adsorbed film of PAA (polyacrylic acid) was evaluated for aqueous solutions at CPAA = 5 × 10-4 g/cm3, [MW = 5, 25, and 250 (kDa)]. The E (=dγ/dlnA) was estimated from the surface dilational rate (dlnA/dt) and the rate of ST change (dγ/dt) of the bubble surface from the natural perturbation caused by minute variations in ambient temperature. The data revealed that (i) a considerable time is required to reach the equilibrium-ST (γeq) and to attain the saturated dilational modulus (Esat) of the adsorbed PAA film, (ii) both γeq and Esat of PAA solutions increase with MW of PAA, (iii) a lower MW solution requires a longer time to reach its γeq and Esat, and (iv) this approach is workable for evaluating the E of adsorbed polymer films.

Modified silica nanoparticles stabilized foam for enhanced oil recovery

Foam has been successfully used to improve mobility control in the process of enhanced oil recovery, yet the instability of foam limits its application. Modified nanoparticles with varying wettability were prepared by reacting 3-methacryloxypropyltrimethoxysilane (KH570) with spherical SiO2 nanoparticles in this study. Fourier transform infrared (FTIR) spectra and the measured contact angles were used to characterize the surface properties of the modified SiO2 particles, and the foam stabilization effects of wettability SiO2 were compared. Pore-scale visualization experiments were conducted using a 2D micromodel to identify the prevailing enhanced oil recovery (EOR) mechanisms of modified nano SiO2-Sodium alpha-olefin Sulfonate (AOS) foam flooding. The results indicate that modified SiO2 effectively improves foam stability by adsorbing on the bubble surface and forming a mesh-like structure. The optimum contact angle of the particles is approximately 60°, resulting in a significant increase in drainage half-life by 29.4% compared to foam stabilized only by AOS. Additionally, Foam stabilized by modified SiO2 demonstrates superior dynamic stability and deformation resistance. The modified SiO2 stabilized foam exhibits enhanced interfacial viscoelasticity and plugging and profile control performance, surpassing AOS foam in displacing more residual oil in dead-end pores. The oil recovery of the micro model was determined by ImageJ software. KH570@SiO2 (0.2wt%)-AOS (0.2wt%) foam flooding increased the recovery by 8.7% compared to AOS (0.2wt%) foam flooding.

Quantifying Contributions of Different Repulsion to Film Drainage Time during the Bubble-Solid Surface Attachment and Implications for the Flotation of Fine Particles.

The flotation recovery of fine particles faces serious challenges due to the lack of kinetic energy required for supporting their radial displacement and attachment with bubbles. Generally, the hydrodynamic resistance and repulsive disjoining pressure successively inhibit the liquid outflow intervening between the bubble and solid surfaces. To quantitatively characterize the influence of the main repulsion on film thinning time, experiments have been designed in three different aqueous systems. Bubble surface mobility closely associated with hydrodynamic resistance was determined by the rising bubble technique, and the DLVO theory was employed to confirm the evolution of electrostatic repulsion. The film drainage process was then measured based on the high-speed microscopic interferometry. Furthermore, the influence of the main repulsion on bubble-solid surface interactions was examined by flotation recovery. Results show that the earlier buildup of hydrodynamic force ran through the whole film thinning process, and under immobile conditions, the central region gradually became dominant in film thinning due to the very limited fluid flow at the thinnest rim position. Therefore, to achieve the identical film thickness (∼100 nm), the large hydrodynamic resistance could prolong the film thinning time by about 1 order of magnitude, compared with that induced by electrostatic repulsion, which accounts for the increased flotation recovery by 10% using mobile bubbles. This study not only enhances the understanding of how typical repulsive forces work in film drainage dynamics but also opens up an avenue for enhancing flotation and avoiding wasting resources by modulating bubble surface mobility and thus micro/nanoscale fluid flow.

Liquid surface depression and bubble generation by acoustic radiation

AbstractLiquid surfaces can be depressed by applying acoustic radiation force. The balance between the acoustic radiation force, surface tension force, and buoyant force sustains the stable dimple depression. Beyond a certain threshold, higher acoustic radiation force leads to instability and bubble formation. The bubble size is determined by the acoustic radiation force and the liquid surface tension. Effective management of bubble generation can be achieved by controlling acoustic radiation waves. A novel method for creating depression on liquid surfaces and generating bubbles is described, which requires neither gas supply nor direct contact with equipment.

Study on the thermal characteristics and heat-insulation ability of gel-stabilized foam used for preventing the spontaneous combustion of coal

Gel-stabilized foam serves a critical role in preventing spontaneous combustion of coal by impeding heat transfer from the coal-fire area to adjacent safe areas. To elucidate the thermal characteristics of gel-stabilized foam, the microstructure and heat-transfer characteristics were investigated. The results revealed that gel-stabilized foam was an accumulation system of many stable and closed bubbles, and there was a layer of gel structure on the bubble surface. This gel layer endows the bubbles with exceptional heat-insulation capability by effectively encapsulating air. To further analyze the relationship of heat-transfer characteristics and foam structure parameters, a theoretical thermal-conductivity model was established to revel the thermal characteristics of gel-stabilized foam. Moreover, the experimental tests were conducted to verify the accuracy of theoretical model, and found that the fitting errors were around 8 %, affirming the model's suitability for gel-stabilized foam. Notably, the theoretical model demonstrated that foam's thermal-conductivity was only monotonically related to foam expansion ratios in theory. In addition, the heat-insulation experiments indicated that the heat-transfer rate of foam depended not only on the thermal-conductivity but also on the foam's stability, both of which were affected by the expansion ratio. Hence, the effective heat-insulation time (EHT) was proposed to assess gel-stabilized foam's heat-insulation characteristics. The heat-insulation ability tests results showed that EHT values initially increased and then decreased with rising foam expansion ratios, primarily influenced by the volume of air encapsulated within the foam. Particularly noteworthy were the test results indicating that gel-stabilized foam with an expansion ratio of 10 times and a stacking thickness of at least 15 cm exhibited excellent heat-insulation capability against heat transfer from the spontaneous combustion zones. The research may provide a theoretical foundation and offer guidance for the prospective utilization of gel-stabilized foam in coal mines.

Experimental and theoretical study of single bubble formation at the nozzle in a liquid oxygen crossflow

In this paper, the condensation bubbles generated by the mixing and condensation of gaseous and liquid oxygen crossflow experimentally and theoretically. The mixing and condensation experiment of the bubbles was carried out, employing gaseous and liquid oxygen as working fluids in vertical tubes. Three successive flow patterns were observed: initial gas plume, condensation oscillation, and separation condensation. The corresponding characteristics include gas mass aggregation, bubble surface smoothness and wrinkling alternately, and bubble disappearance after separation and condensation. Then, a Nusselt number (Nu) heat transfer correlation formula is fitted with a corresponding fitting error in the range of −31% ∼ 35%. In addition, bubble force balance and conservation equations were employed to establish a mixing condensation bubble model suitable for gaseous and liquid oxygen in vertical tubes, and the error between theoretical and experimental results was in the range of −25% ∼ 20%. Furthermore, the effects of working conditions and forces on bubble condensation length has been analyzed. The results showed that increasing the liquid oxygen flow rate, reducing the gas oxygen volume flow rate, or appropriately reducing the gas inlet diameter led to reducing the bubble condensation length. It was shown that the bubble drag and shear lift forces affect the condensation length mostly.

Resolving hydrate inhibition mechanism: Interactions between kinetic hydrate inhibitors and CH4 bubble

The kinetic hydrate inhibitors (KHIs) are known to be both economical and eco-friendly in preventing hydrate blockages. To date, two main inhibition hypotheses of KHIs have been proposed, in which the dominant interactions are KHIs-crystals and KHIs-aqueous, respectively. However, both hypotheses experience challenges as contrary phenomena are frequently observed. Herein, we find the extensively generated CH4 bubble in hydrate exploitation or natural gas transportation can greatly promote hydrate nucleation, thus, a new inhibition mechanism is proposed based on the interaction of KHIs-CH4 bubble. Specifically, PVCaps (one typical KHI) can absorb on CH4 bubble surface to mitigate CH4 dissolution, which thus i) reduces the concentrations and accommodations of CH4 in aqueous, thereby mitigating the formation of hydrate embryo; ii) decreases CH4 transfer from bubble to embryo, thereby mitigating the growth of hydrate embryo. As both the formation and growth of hydrate embryos are inhibited, the hydrate nucleation requires longer induction time and larger critical nucleus. Moreover, this new mechanism has been found to be applicable to other KHIs, in which the interaction strengths of KHIs-CH4 bubble can successfully explain the experimental inhibition efficiencies of PEO < PVP < PVCap < VIMA. Thus, the interaction of KHIs-CH4 bubble can act as the key criterion in screening and designing effective KHIs.

Cavitation-induced pressure saturation: a mechanism governing bubble nucleation density in histotripsy

Objective. Histotripsy is a noninvasive focused ultrasound therapy that mechanically disintegrates tissue by acoustic cavitation clouds. In this study, we investigate a mechanism limiting the density of bubbles that can nucleate during a histotripsy pulse. In this mechanism, the pressure generated by the initial bubble expansion effectively negates the incident pressure in the vicinity of the bubble. From this effect, the immediately adjacent tissue is prevented from experiencing the transient tension to nucleate bubbles. Approach. A Keller–Miksis-type single-bubble model was employed to evaluate the dependency of this effect on ultrasound pressure amplitude and frequency, viscoelastic medium properties, bubble nucleus size, and transducer geometric focusing. This model was further combined with a spatial propagation model to predict the peak negative pressure field as a function of position from a cavitating bubble. Main results. The single-bubble model showed the peak negative pressure near the bubble surface is limited to the inertial cavitation threshold. The predicted bubble density increased with increasing frequency, tissue viscosity, and transducer focusing angle. The simulated results were consistent with the trends observed experimentally in prior studies, including changes in density with ultrasound frequency and transducer F-number. Significance. The efficacy of the therapy is dependent on several factors, including the density of bubbles nucleated within the cavitation cloud formed at the focus. These results provide insight into controlling the density of nucleated bubbles during histotripsy and the therapeutic efficacy.

Relation of bubble size, grade and recovery in the copper flotation systems

In recent years, studies have shown that bubble structure, which is affected by reagent types, dosages, and particle size, is closely related to flotation performance. In contrast to two-phase systems, there is very limited information regarding bubble size in three-phase systems. To this aim, we investigated the relationship between bubble size and flotation performance with two different copper ores. Firstly, the surface tension and bubble size measurements were carried out in two-phase systems with Methyl isobutyl carbinol, and Polypropylene glycol methyl ether. Then the bubble size measurements were performed in three-phase systems at laboratory and industrial scales. The results showed that surface tension decreased with higher frother amounts and higher pHs. Although remarkable decreases in bubble size were observed with increasing frother amount, a direct relationship between surface tension and bubble size was not observed. However, pH affected the behavior of the frother, resulting in smaller bubble sizes at pH 12 compared to pH 7. Similarly, the three-phase laboratory tests showed that higher amount of frother caused a reduction in the bubble size and the copper grade. Increasing the amount of collector also caused the bubble size and copper grade to decrease, but the frothers were more effective in bubble size reduction. Compared to the two-phase, in the three-phase study bubble size was notably bigger due to the presence of a collector and solid. In the plant scale, smaller bubble size and higher grade were obtained compared with the laboratory scale due to presence of cleaning circuit measurements. The froth phase properties were also affected by the ore types due to properties such as size and hydrophobicity of the various mineral species present.

A dual-layer flow field design capable of enhancing bubble self-pumping and its application in water electrolyzer

The conventional flow-field configurations such as parallel and serpentine flow fields in proton exchange membrane water electrolyzer have encountered serious bubble accumulation phenomena in channels, blocking the water delivery to the electrode and creating a large mass-transfer resistance. Therefore, we propose a dual-layer flow field design. Specifically, the degassing layer is tightly installed on the base layer, forming a dual-layer configuration, capable of enhancing the self-pumping effect (bubbles automatically detach from the outer surface of the electrode) due to the formation of capillary pressure difference between the upper and lower surfaces of bubbles. Firstly, we theoretically analyze the feasibility of this dual-layer design through numerical simulation. The results show that the bubbles in the channel will be sucked into the degassing layer from the base layer, thus creating more space for water supply to the electrodes, which is further verified by in-situ visualization. Finally, it is found that an introduction of the degassing layer significantly upgrades the cell performance (approximately 0.15 V at 5.0 A cm−2) compared with conventional single-layer design. Therefore, this study provides insights for future flow-field design in high-performance water electrolyzers.

Experimental study on flow boiling heat transfer performance of nanowire-printed substrates with porous-like structures

In this study, ZnO nanowires (NWs) were demonstrated to have considerable potential for heat transfer enhancement in flow boiling. Unlike the conventional NW fabrication method using metal-assisted chemical etching, we use the microcontact printing (µCP) method comprising solution-based growing methodologies to create ZnO NWs on different substrates, including bare Si-, Cu-, and Al-coated surfaces. This ZnO NW fabrication approach successfully overcomes the substrate limitation of typical NWs, such as Si- and Cu-NWs, which can be only formed on its intrinsic material following the high-cost fabrication approaches required by the metal catalyst. Additionally, a high pore-connected structure was observed on the interfacial area of the ZnO NWs, with the nanocore distribution area considerably enhanced by lengthening the NW length, beneficial to bubble nucleation and surface coolant supply during nucleate boiling. The length of the ZnO NW substrates is controllable by varying the growing period during the hydrothermal growth procedure. Further, the ZnO NW substrates reveal a remarkable enhancement in the flow boiling heat transfer regardless of the substrate variation, thereby exhibiting high variability in the substrate selection and potential of being used as the cooling approach for the thermal management of the high heat flux applications. We conducted a series of experiments related to the surface wettability, wicking, and bubble characteristics for different test substrates under saturated flow boiling conditions to explicitly determine the underlying mechanism in the heat transfer enhancement of the ZnO NWs.

A combined experimental and computational investigation of an inducer’s characteristics with gas-water two-phase flow

The objective of the paper is to investigate the internal flow characteristics inside the inducer under the gas-water condition using a combination of experiment and numerical simulations. Gas-water mixing is achieved by an annular gas mixing device and visualized by high-speed imaging technology. Meanwhile, the shear stress transport (SST) k- ω model coupled with the VOF model is applied to investigate the gas phase distribution. Numerically simulated inducer energy characteristics and internal gas-phase distribution are in good agreement with experimental data. The results show that the mixed gas-liquid flow inside the inducer exhibits three flow patterns: wavy flow, bubbly flow, and plug flow. For the wavy flow, a series of wavy structures on the blade surface and gas-pocket bubbles near the blade rim are observed. From wavy flow to bubbly flow, uniform bubble streams on the blade surface and spiraling strip bubbles near the edge of the blade are observed. For plug flow, bubble accumulation results in a bullet-shaped plug, and the strip-shaped bubbles near the blade rim are more obvious. In the same axial position of the inducer, the proportion of gas phase is increasing as the flow coefficient increases, thus affecting the inducer performance. The main frequency amplitude of the pressure pulsations gradually rise when the flow pattern changes from wavy to plug flow.

Flow visualization experiments of argon injection in a molten salt natural circulation loop

Off-gas systems are implemented in molten salt reactor designs to control the release of gaseous fission products. Two-phase flow in molten salt must be studied to understand how the system will behave in comparison to traditional working fluids like water. Flow visualization experiments and particle image velocimetry measurements were performed for three argon bubble sizes injected into a co-current stream of molten salt in a natural circulation loop facility. Similar bubble sizes were injected in experiments with water to compare the bubble shape, trajectory, and wake flow behavior of the fluids. The bubble region of interest was used to calculate the equivalent diameter and terminal velocity. Results for water showed a wobbling bubble surface and less stable bubble trajectory due to lower surface tension and viscosity compared with molten salt. Particle image velocimetry results demonstrated the increased viscosity of salt dampens turbulent fluctuations for the smaller bubble size. For a cap bubble, turbulent fluctuations were larger and longer lasting than in results for the wake flow of an argon cap bubble in water.

Development and performance evaluation of chitosan-graft-poly (N-vinyl pyrrolidone) as a dual-function inhibitor for hydrate decomposition and reformation

In the process of drilling and producing natural gas hydrates, the hydrate is prone to decomposition, leading to wellbore instability and well control problems, and the natural gas produced by the decomposition is prone to form hydrate again in the low-temperature and high-pressure wellbore, creating flow obstacles. The existing inhibitors, however, fail to effectively inhibit the decomposition and reformation of hydrates. In this work, N-vinylpyrrolidone was used to modify chitosan, and an inhibitor namely DFHI with a dual function of inhibiting hydrate decomposition and reformation was developed. The inhibitory effects of DFHI were analyzed using the optimized experimental method for evaluating hydrate decomposition and reformation, and the mechanism was analyzed. The results showed that the memory effect of hydrate reformation gradually weakened or even disappeared with the rising ambient temperature during hydrate decomposition. The inhibitory performance of DFHI exhibited a positive correlation with its concentration. 0.5% DFHI resulted in a 74.7% delay in the decomposition time of methane hydrate, along with an extension of the induction time for both hydrate formation and reformation by 137.2% and 262.1%, respectively, significantly weakening the memory effect of hydrate reformation. The mechanism of DFHI inhibiting hydrate decomposition primarily involves surface adsorption on hydrates and thickening effects that retard mass and heat transfer processes. During the process of hydrate formation and reformation, DFHI molecules tend to aggregate at the surface of methane bubbles, hindering gas–water contact and diffusion, particularly when numerous micro-nano bubbles generated by hydrate dissolution are present; furthermore, the adsorption of DFHI molecules on the surface of hydrates delays their nucleation and growth.

Bubble size distribution and turbulence characterization in a bubbly flow in the presence of surfactant

This study aimed to quantify the less explored complex multiphase hydrodynamics of a bubble swarm in the presence of surfactant which is the key to flotation process widely used in the resources and environmental engineering applications.Experiments were conducted in a rectangular column (cross-section: 100 mm × 100 mm) in batch mode by varying the gas flux (0.02 to and 0.08 cm/s) in the presence of an anionic surfactant sodium dodecyl sulphate (5 to 15 ppm). High-speed imaging was then used to visualise the unsteady bubble plume dispersion behaviour and estimate the bubble size distribution (BSD) which showed a reduction in the mean bubble size with the increasing gas flux and surfactant concentration.Next, particle image velocimetry (PIV) was utilised to measure the instantaneous velocity field which was used to determine the turbulence characteristics. It was shown that the bubble plume contributes to significant anisotropy in the flow field which increased in the higher surfactant concentration and gas flux cases. The energy containing turbulence length scale was characterized by the integral length scale, which was observed to increase linearly with both the gas flux and surfactant concentration. Also, the local turbulence energy dissipation rate exhibited a strong linear correlation with the bubble surface area flux parameter. In the presence of surfactant, the turbulence energy spectrum of the system exhibited a less steep slope in the inertial subrange regime compared to the Kolmogorov −5/3 slope. The spectrum also showed a leftward shift indicating energy addition to the larger turbulence length scales which was reflected in the formation of large recirculation zones around the bubble plume.

Magnetically responsive manipulation of droplets and bubbles

AbstractDroplets and bubbles have a wide range of applications in industry, agriculture, and daily life, and their controllable manipulation is of significant scientific and technological importance. Versatile magnetically responsive manipulation strategies have been developed to achieve precise control over droplets and bubbles. To manipulate nonmagnetic droplets or bubbles with magnetic fields, the presence of magnetic medium is indispensable. Magnetic additives can be added to the surface or interior of droplets and bubbles, allowing for on‐demand manipulation by direct magnetic actuation. Alternatively, magnetically responsive elastomer substrates can be used to actuate droplets and bubbles by controlling the deformation of microstructures on the substrates through magnetic stimulation. Another strategy is based on untethered magnetic devices, which enables free mobility, facilitating versatile manipulation of droplets and bubbles in a flexible manner. This paper reviews the advances in magnetically responsive manipulation strategies from the perspective of droplets and bubbles. An overview of the different classes of magnetic medium, along with their respective corresponding droplet/bubble manipulation methods and principles, is first introduced. Then, the applications of droplet/bubble manipulation in biomedicine, microchemistry, and other fields are presented. Finally, the remaining challenges and future opportunities related to regulating droplet/bubble behavior using magnetic fields are discussed.

Impact of grain boundary and surface diffusion on predicted fission gas bubble behavior and release in UO2 fuel

In this work, we quantify the impact of grain boundary (GB) and surface diffusion on fission gas bubble evolution and fission gas release in UO2 nuclear fuel using simulations with a hybrid phase field/cluster dynamics model. We begin with a comprehensive literature review of uranium vacancy and xenon atom diffusivity in UO2 through the bulk, along GBs, and along surfaces. In our model we represent fast GB and surface diffusion using a heterogeneous diffusivity that is a function of the order parameters that represent bubbles and grains. We find that the GB diffusivity directly impacts the rate of gas release via GB transport, and that the GB diffusivity is likely below 104 times the lower value from Olander and van Uffelen (2001). We also find that the surface diffusivity impacts bubble coalescence and mobility, and that the bubble surface diffusivity is likely below 10−4 times the value from Zhou and Olander (1984).

Effects of Aqueous Isotopic Substitution on the Adsorption Dynamics and Dilational Rheology of β-Lactoglobulin Layers at the Water/Air Interface.

The effect of the degree of isotopic substitution of the aqueous medium on the adsorption kinetics and the surface dilational rheological behavior at the water/air interface of the globular protein β-lactoglobulin was investigated. Aqueous solutions with fixed concentrations of 1 μM protein and 10 mM hydrogenous buffer with controlled pH 7 were prepared in H2O, D2O, and an isotopic mixture of 8.1% v/v D2O in H2O (called air contrast matched water, ACMW). Using a bubble shape analysis tensiometer, we obtained various experimental dependencies of the dilational viscoelasticity modulus E as a function of the dynamic surface pressure and of the frequency and amplitude of bubble surface area oscillations, either in the course of adsorption or after having reached a steady state. In general, the results revealed virtually no effect from substituting H2O by ACMW but distinct albeit relatively weak effects for intermediate adsorption times for D2O as the aqueous phase. In the final stage of adsorption, established after around 10 h, the equilibrium adsorption and the dilational rheological behavior of all protein layers under investigation are only very weakly affected by the presence of D2O. The obtained results help to design experimental protocols for protein adsorption studies, for example, by neutron reflectivity.

Study on Non-Spherical Deformation Velocity of a Single Cavitation Bubble

Cavitation bubbles commonly exist in shipbuilding engineering, ocean engineering, mechanical engineering, chemical industry, and aerospace. Asymmetric deformation of the bubble occurs near the boundary and then has strong destructiveness, such as high amplitude loading. Therefore, the research on non-spherical deformation is of great significance, and the objective of this paper is to investigate the non-spherical collapse dynamics of laser-induced cavitation bubbles when near different boundaries. In this study, experimental data, such as the bubble pulsation process and bubble surface velocity distribution, were obtained by high-speed camera techniques and full-field velocity calculations. Near the different boundaries, the results show that the bubbles appeared to have different collapse shapes, such as near-hemispherical, near-ellipsoidal, near-cone, and near-pea shapes, and the surface velocity distribution is extremely non-uniform. When the bubble near the free surface or rigid boundary collapses, the smaller the stand-off r is, the more obvious the repulsive effect of the free surface or the attractive effect of the rigid boundary is. As the stand-off r decreases, the larger the Bjerknes force and the bubble surface velocity difference and the more pronounced the non-spherical shape becomes.

Dynamics of particle attachment in a model stirred cell: A new technique to characterize and quantify particle floatability

Floatability evaluation is critical to predicting flotation results and designing a flotation flowsheet. Laboratory-scale flotation cells are commonly used to study particle floatability, but differences in cell design and governing hydrodynamics make extrapolation to industrial scale operations difficult. In this work, a new experimental approach based on particle attachment dynamics is proposed to evaluate particle floatability. This method allows precise control of hydrodynamic conditions, visualization of attachment processes, and direct observation of the bubble surfaces. It is therefore ideal for studying attachment dynamics as a function of collector concentration, particle size and concentration, and propeller speed. In addition, it opens the possibility for future studies of the packing density of the particles at the interface and their selective attachment. By evaluating the time-dependent surface coverage as a function of bubble residence time, we illustrate its ability to predict flotation kinetics within a flotation cell. This innovative technique provides a faster, more versatile means of studying particle floatability and attachment dynamics with practical implications for flotation cell optimization.