This paper addresses the influence of hydrostatic pressure ($P_{hyd}$) on bubble diameter ($d_b$) and contact angle ($\theta$) of quartz in pure water versus collector solution (Flotigam^® EDA, ${\gamma }_{LG}$ = 57 mN/m) at 20 °C. The pressure range (0–300 kPa) applied against the bubbles’ walls mimics what may happen along the vertical axis of a hypothetical flotation column (HFC) that processes iron ore slurry via cationic reverse flotation of quartz. From the column’s bottom ($P_{hyd}\approx$ 300 kPa) to its top ($P_{hyd}\approx$ 0 kPa), a continuous relief of $P_{hyd}$ occurs steadily. Results indicate that a decrease of $P_{hyd}$ promotes a decrease of θ from 47° to 16° in pure water and from 61° to 42° in the presence of collector. Likewise, $d_b$ increases approximately 60% from the column’s bottom to its top and, consequently promoting an increase in bubble ascending velocity ($v_b$). Values of $v_b$ and $d_b$ were used to assess the bubble Eötvos number (Eo) and the Weber number (We) aiming at characterizing bubble hydrodynamics. It was found that inertial forces dominate surface forces (We > 1) as $d_b>$ 1.86 mm. This dominance constitutes a preliminary indication of a greater likelihood of coarse particles (diameter > 100 $\mathsf{\mu }$m) detaching from bubbles. This situation is typically found in the upper parts of the HFC addressed in this paper.

The principle of maximum entropy (PME) relies on information theory, Shannon entropy, and four constraints, namely the total probability and conservation laws of mass, momentum, and energy. This paper applies PME theory to an exactly accurate data set available in the literature to develop a model that relates the friction factor ($f$ ) to the entropy parameter ($M$ ). The proposed model exhibits fair adherence to the experimental data, and it was validated by multiphase flow pumping tests with concentrated iron ore slurry. Extending the use of the proposed model for multiphase flow, particularly mineral slurries, allows for the determination of apparent viscosity and Reynolds number without resorting to rheological measurement. The deviations between the $M$ parameter obtained from the proposed model and that reported in the literature were smaller than 5% for the iron ore slurry. It has been demonstrated that the PME is a particularly important tool for hydraulic systems, especially in multiphase flow such as that of mineral slurries containing a high content of solids.

The rheological characterization of mineral slurries is a complex task, especially in the presence of coarse particles with high specific gravity, such as hematite. In laboratory rotational rheometers (LRRs), entrance effects, particle settling, and Taylor vortices can jeopardize the accuracy of the results. This paper presents a new methodology for the rheological characterization of mineral slurries in tubular devices and the Principle of Maximum Entropy (PME) supports this new approach. Iron ore slurries were prepared at mass concentrations of 36.8% and 43.6% solids and subjected to rheological characterization in LRR and a pumping loop tubular device (PLTD). The results from LRR revealed shear-thickening behavior for the slurries; whereas the results from PLTD, associated with entropic equations for the friction factor and shear rate, revealed shear-thinning behavior (at low shear rates) and shear-thickening behavior (at high rates). The results from LRR plus PLTD were plotted in a single rheogram, and curve fitting was accomplished by the power law model (R2=0.995), indicating an overall shear-thickening behavior. PME proved to be capable of supporting the rheological characterization of mineral slurries at shear rates above 1500s–1 in PLTD, complementing the results obtained by LRR.