Table 2: Theoretical methods for predicting .

ReferenceConceptRemarks

Kolar [29]Energy necessary to suspend particles equals the energy dissipated by the particle moving at its terminal velocity in a still fluidIn a turbulent fluid, the settling velocity of a particle is different from that in a still fluid.
Very simple model, unable to precisely predict
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 eddiesCannot 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 particlesAssumption 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 particlesParticle 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 eddiesCannot 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 energyThe 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 liquidThe ratio between and settling velocity allows predicting easily
Mersmann et al. [5]Power input dissipated by two phenomena: consumption of power to avoid settling and generating discharge flow for suspensionValues for 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