Characterization of Minimum Impeller Speed for Suspension of Solids in Liquid at High Solid Concentration, Using Gamma-Ray Densitometry

Table 2

Theoretical methods for predicting 𝑁_JS.

Reference	Concept	Remarks
Kolar [29]	Energy necessary to suspend particles equals the energy dissipated by the particle moving at its terminal velocity in a still fluid	In a turbulent fluid, the settling velocity of a particle is different from that in a still fluid.; Very simple model, unable to precisely predict 𝑁JS; Assumptions are more likely similar to homogenous suspension rather than just-suspended conditions
Baldi et al. [13]	Particles are picked up and kept suspended by turbulent eddies	Cannot describe the effect of viscosity nor the effect of solid concentration.; Cannot describe why the impeller that creates mass circulations (PBT) is more effective for suspending particles than impeller which creates a lot of turbulence
Narayanan et al. [30]	Balance of vertical forces acting on particles	Assumption of no slip between solid and liquid and homogenous distribution of solid particles is questionable.; Proposed for very diluted solid concentrations
Subbarao and Taneja [31]	Balance of forces acting on particles	Particle settling velocity was estimated from a correlation for the porosity of a liquid fluidized bed as a function of liquid velocity
Ditl and Rieger [32]	Same concept as Baldi et al. [13], solid particles are picked up by different sizes of eddies	Cannot describe the effect of viscosity nor the effect of solid concentration; Cannot describe why the impeller that creates mass circulations (PBT) is more effective for suspending particles than impeller which creates a lot of turbulence
Musil and Vlk [33]	Balance between liquid and particle kinetic energy	The approach followed by them was rejected by Ditl and Rieger [34] because of mathematical mistakes
Ayazi Shamlou and Zolfagharian [14]	Proposed a model for estimation necessary conditions for incipient motion of solid particles based on average velocity of the liquid near the bottom of the vessel and forces acting on particles, like lift, drag, buoyancy, and weight resting at the bottom of the vessel	Model does not need any experimental adjustment, but the parameter describing solid arrangement is unknown
Molerus and Latzel [15, 35]	Solid suspension governed by two different mechanisms based on Archimedes number.; Region responsible for solid suspension is the wall boundary layer of the vessel	Requires accurate correlation for predicting shear rate at the boundary layer of the vessel
Wichterle [36]	Difference between the terminal settling velocity of particle and velocity of the liquid	The ratio between 𝑁JS and settling velocity allows predicting 𝑁JS easily
Mersmann et al. [5]	Power input dissipated by two phenomena: consumption of power to avoid settling and generating discharge flow for suspension	Values for 𝑁JS calculated by this method are highly underpredicted compared to experimental data.; This could be because the correlations for fluctuating velocity at the bottom of the vessel are not accurate