Attachment behavior is a key component of flotation and has a decisive influence on flotation performance, and the experiment research on the attachment between mineral particles and bubbles still needs further research. In this work, a particle–bubble attachment apparatus and multiple target tracking software were developed. Coal particles were used as the subjects, and the effect of particle properties on the attachment performance was studied from the perspective of the particle group. The particle–bubble attachment experiments indicated that the collision position had an effect on the attachment efficiency, and the attachment efficiency decreased with an increase in the collision angle. The efficiency-weighted attachment angle was proposed to quantitatively describe the attachment performance of coal samples. The efficiency-weighted attachment angle of low-density coal samples was greater than that of high-density coal samples. For particles with different sizes, the efficiency-weighted attachment angle of fine particles was greater than that of coarse particles. Furthermore, SDS weakened the attachment performance between coal particles and bubbles via adsorption on the bubble, and the efficiency-weighted attachment angle decreased as the concentration of the SDS solution increased. CTAB adsorbed on coal particles and bubbles, and the efficiency-weighted attachment angle first increased and then decreased with increasing CTAB concentration.

Biodiesel was found to be a more effective collector on low-rank coal flotation than the common oily collectors (diesel and kerosene) in previous research. However, the micro-adsorption behavior of these collectors on the coal surface remains to be further explored. In the present work, the adsorption behavior of methyl laurate and dodecane, representing biodiesel and common oily collectors, was investigated using experimental and molecular dynamics (MD) simulation methods. The results of MD simulations showed that dodecane was difficult to diffuse on the surface of sub-bituminous coal and formed a spherical structure on the surface of sub-bituminous coal. Methyl laurate was adsorbed on the surface of coal via the head group (ester group), while the tail group (alkyl chain) was exposed to a liquid environment, forming a wider network structure on the coal surface. The above results, mainly attributed to methyl laurate, had a higher interaction with the sub-bituminous surface compared to dodecane. The self-diffusion coefficient results showed that the aggregate configurations of methyl laurate cause higher water mobility, which was more conducive to enhancing the hydrophobicity of the coal surface. The adhesion efficiency measurement and X-ray photoelectron spectrometer (XPS) analysis confirmed that methyl laurate could cover more oxygen-containing functional groups on the coal surface than dodecane, thus enhancing the hydrophobicity of coal. The results of simulations conformed to the experimental results.

To study the effects of different oxygen functional groups on the quality of flotation clean low-rank coal, two kinds of collectors with different oxygen-containing functional groups, methyl laurate, and dodecanol, were selected and their flotation behaviors were investigated. The Bulianta coal was the typical sub-bituminous coal in China, and the coal molecular model of which was constructed based on proximate analysis, ultimate analysis, ¹³C-NMR, and XPS. The chemical structure model of the coal molecule was optimized, and the periodic boundary condition was added via the method of molecular dynamics methods. The different combined systems formed by collectors, water, and a model surface of Bulianta coal have been studied using molecular dynamics simulation. The simulation results of dodecanol and methyl laurate on the surface of Bulianta coal show that dodecanol molecules are not evenly adsorbed on the surface of coal, and have higher adsorption capacity near carboxyl and hydroxyl groups, but less adsorption capacity near carbonyl and ether bonds. Methyl laurate can completely cover the oxygen-containing functional groups on the coal surface. Compared with dodecanol, methyl laurate can effectively improve the hydrophobicity of the Bulianta coal surface, which is consistent with the results of the XPS test and the flotation test.

The collision and adhesion behavior of particles and bubbles is the key to flotation. Many scholars have investigated the collision and adhesion law of regularly shaped and homogeneous particles (glass beads, glass fiber), but the particles in flotation cells are irregular and heterogeneous. Therefore, it is necessary to take actual coal samples as the research object. First, based on previous research, a particle–bubble collision and adhesion behavior measurement device was set up to study free falling coal particles with different surface properties colliding and adhering to a bubble (db = 1.0 mm). Then bituminous coal from Inner Mongolia was taken as the test object, and the collision and adhesion process of a large amount of coal particles was traced. The entire process is photographically recorded by a camera and analyzed frame by frame through a self-designed software. Finally, the relationship between collision angle and initial settlement position (initial), particle velocity (process), and adhesion efficiency (result) was studied by taking the collision angle as the cut-in point. It was found that both the distribution range of the initial settlement position and the particle central distribution interval are expanding outward with the increase of collision angle. The resistance layer has an important influence on the velocity of particles. The collision angle had an effect on adhesion efficiency and the adhesion efficiency of low-density particles was higher than that of high-density particles.

Low-rank ultrafine flotation clean coal typically yields filter cake moisture above 20% due to abundant oxygen-containing functional groups and strong surface hydrophilicity. Conventional polyacrylamide (PAM) flocculants are hydrophilic and improve dewatering only by altering cake porosity, not by reducing particle surface hydrophilicity, so they remove little adsorbed water. In this study, hydrophobically modified anionic polyacrylamides (HMAPAM) were synthesized by grafting lauryl acrylate onto APAM. FTIR, ¹H NMR, XPS, and SEM confirmed the grafting and progressive enrichment of hydrophobic alkyl chains on the surface. Moderate hydrophobic modification markedly improved solid–liquid separation. HMAPAM-D (APAM/LA = 4.5:0.5) achieved a settling velocity of 0.817 cm/s at 9 mg/L, 50.2% higher than APAM, and reduced filter cake moisture to 16.64% at 1 mg/L under 0.6 MPa versus 19.39% for unmodified APAM. Excessive modification (HMAPAM-E, 4:1) promoted intramolecular self-association, producing heterogeneous flocs and higher filtration resistance that degraded dewatering efficiency. The performance gain stems from hydrophobic association combined with adsorption bridging. These results clarify how hydrophobic group content controls flocculation and dewatering, informing the design of better flocculants for this type of coal slurry.

Clay-mineral interference severely limits the flotation of high-ash fine coal, making selective depression essential for improving the ash-recovery balance. Sodium silicate and starch were compared under identical direct-flotation conditions using an original kaolinite-containing high-ash fine-coal sample. Batch flotation, zeta-potential measurements, X-ray photoelectron spectroscopy (XPS), and density functional theory (DFT) calculations were combined to investigate their different interfacial effects. Flotation tests identified 2000 g/t as the dosage providing the best overall separation performance for both reagents. Compared with starch, sodium silicate produced lower clean-coal ash (10.84% vs 11.54%), higher combustible recovery (87.60% vs 84.80%), and a higher flotation perfection index (62.99% vs 59.23%), whereas excessive starch addition caused a marked recovery loss. Zeta- potential measurements showed that sodium silicate caused a pronounced negative shift for kaolinite, whereas starch produced a larger negative shift for coal. XPS further showed that starch markedly increased oxygen-containing carbon species, particularly C–O, on the coal surface, while sodium silicate caused comparatively limited modification. DFT calculations indicated that the starch model fragment (C6H12O6) formed multipoint hydrogen bonds with oxygen-containing coal functional groups. In contrast, the representative silicate species, Si(OH)4, interacted preferentially with kaolinite, particularly the hydroxylated (001) surface, while showing weaker interactions with the siloxane-terminated (001̅) surface. These results link molecular interactions with interfacial-property changes and flotation performance, providing mechanistic guidance for depressant selection and dosage optimization in high-ash fine-coal flotation.