Heterocoagulation between coal and quartz particles studied by the mineral heterocoagulation quantifying system

Insights into the Dispersion Mechanism of Microfine Coal Particles Modified with Naphthalene Sulfonate Formaldehyde Based on EDLVO Theory

“…The interaction between microfine coal particles was analyzed on the basis of EDLVO theory. − Therefore, the total interaction energy ( V T ) was demonstrated by the following equation V normalT = V normalW + V normalE + V normalH + V normalS where the van der Waals force action energy ( V w , J) was determined by the Hamaker constant and radius of particles, as performed in eq ; the electrostatic repulsion energy ( V E , J) could be calculated in eqs 5–7, which was mainly determined by the charge potential and radius of the particles; the hydrophobic interaction energy ( V H , J) was determined by the acid–base free energy and radius of particles, and it was performed using eqs 8–12; and the steric hindrance energy ( V S , J), which could be obtained from eqs 13 and , was usually influenced by thickness of the adsorption layer and dispersant property V normalW = prefix− false( A 11 − A 22 false) 2 R 12 H where A 11 and A 22 are the Hamaker constants of coal particles and water in a vacuum, which equaled to 6.1 × 10 –20 and 3.7 × 10 –20 J, respectively; , R is expressed as the median size of microfine coal particles in the slurry, m ; and H is denoted as the distance between coal particles, nm. V normalE = π ε ε 0 R φ 2 ( ln true[ 1 + exp nobreak0em.25em⁡ false( <...…”

“…The interaction between microfine coal particles was analyzed on the basis of EDLVO theory. − Therefore, the total interaction energy ( V T ) was demonstrated by the following equation where the van der Waals force action energy ( V w , J) was determined by the Hamaker constant and radius of particles, as performed in eq ; the electrostatic repulsion energy ( V E , J) could be calculated in eqs 5–7, which was mainly determined by the charge potential and radius of the particles; the hydrophobic interaction energy ( V H , J) was determined by the acid–base free energy and radius of particles, and it was performed using eqs 8–12; and the steric hindrance energy ( V S , J), which could be obtained from eqs 13 and , was usually influenced by thickness of the adsorption layer and dispersant property where A 11 and A 22 are the Hamaker constants of coal particles and water in a vacuum, which equaled to 6.1 × 10 –20 and 3.7 × 10 –20 J, respectively; , R is expressed as the median size of microfine coal particles in the slurry, m ; and H is denoted as the distance between coal particles, nm. Here, ε is the dielectric constant of water, equaling to 80 F/m, ε 0 is the permittivity of free space, equaling to 8.854 × 10 –12 C 2 ·m/J; φ (V) is the charge potential of the particle surface, which could be calculated by eq ; ζ is the ζ-potential of particles; χ is a constant of 5 × 10 –10 m; k is the reciprocal value of Debye length, which could be determined by eq ; e is the charge intensity, 1.602 × 10 –19 C; N A is the Avogadro constant, which equals to 6.023 × 10 23 mol –1 ; C is the concentration of the KCl solution, equaling to 1 × 10 –4 mol/L; z is the valence of ions; K is the Boltzmann constant, 1.38 × 10 –23 kg·s –2 ·K –1 ; and T is the absolute temperature for slurry preparation, 298 K. Here, h 0 , which could be calculated using eq , is the decay length; H 0 is the minimum equilibrium contact distance between coal particles, equaling to 2 × 10 –10 m; θ is the contact angle of the particle surface; V H 0 expresses the acid–base free energy per unit area and could be determined using eqs and ; γ and γ d are the surface tension of the solution and the polar component of surface tension, respectively; γ – and γ + are the surface tension of the polar component including electron-donating and proton-donating entities, respectively; the subscripts L and S represent the liquid and solid parts in the suspension, respectively; the values of γ L , γ L d , γ ...…”

Exploring the effect of sodium hexametaphosphate in coal slime flotation

“…where ε0 is the dielectric constant of the solution (for water ε0 = 80) (Oats et al, 2010), εa is the dielectric constant of free space (8.854 × 10 −12 C 2 mJ −1 ) (Yoon, 2000), and R1 and R2 are spherical. The radius of coal particles and kaolinite, and the values of R1 and R2, are 23.376 μm and 4.018 μm, respectively; φ1 and φ2 are the surface potentials of coal and kaolinite, respectively, in mV; H is the distance between spherical coal particles and kaolinite; and κ is the Debye length, and its calculation expression is (2) (Hu et al, 2019):…”

Effect of Surface Heterogeneities on Interactions between Air Bubbles and Heterogeneous Surfaces

“…However, when investigating bubble–solid interactions, the solid surface is often considered to be chemically homogeneous. Typically, surface heterogeneity originates from crystal defects on a nanoscale, which are caused by missing or misplaced atoms in the crystal lattice, or association between various components. , On the macroscale, defects created by incomplete liberation after crushing and grinding, the adsorption of flotation reagents, the non-uniform dissociation and oxidation of surface functional groups, , or slime on the mineral surface − always induce heterogeneous. In particular, for coal, which is an organic sedimentary rock composed of inorganic and organic substances, defect-free coal surfaces are difficult to be achieved.…”