Thin liquid film drainage mechanism for bubble − particle attachment interactions in the low-rank coal flotation in the presence of salt and surfactants

[Display omitted] •The flotation efficiency of low rank coal is improved when surfactant and salt ions coexist.•Salt ions can compress the double electric layer thickness and promote the attachment of surfactant on the coal surface.•A methodology to obtain the hydrophobic force constants for bubble-particle attachment interaction.•The mechanism of liquid film drainage and the calculation of additional energy for drainage. Bubble-particle interaction is a fundamental process in froth flotation, where the attachment of bubbles and particles is the crucial process in effective flotation. However, modeling bubble-particle attachment interaction is challenging. This is because advanced methods like AFM (Atomic Force Microscope) characterizations are difficult to quantify hydrophobic interactions reproducibly for air bubbles and non-spherical particles. This study presents a methodology to obtain the hydrophobic force constants for bubble-particle attachment interaction in the presence of salt (KCl) and surfactants (DTAC and SDS). The hydrophobic interaction constants of bubble-particle interactions were acquired from first principles with the Stefan − Reynolds theory and Glembotsky experimental device. The Stefan − Reynolds theory was successfully applied in the determination of the real hydrophobic constants for bubbles and particles interaction in DI water (deionized water). However, in the coexistence of salt and surfactants, the real hydrophobic constants for bubbles and particles interaction cannot be obtained while the fictive hydrophobic constants were acquired with a linear extrapolation method. The results showed that the addition of inorganic salt and surfactants compressed the electronic double layer’s thickness and presented a higher hydrophobic force constant, enhancing the interaction between a bubble and a low-rank coal particle. In addition, the evaluations of hydrophobic constants reveal that the hydrogen bond energy and salt ions destruction energy should be considered to the comprehension of attachment interaction mechanism and the hydrophobic force source for bubble − particle attachment interactions.