Continuity theory and settling model for spheres falling in non-Newtonian one- and two-phase media

The particle settling is a basic phenomenon: however, it determines the design of many unit operations and machines of mineral processing. A new test device has been developed in order to measure the terminal settling velocity of large steel balls settling in fine particulate solids - water mixtures. The developed inductive sensor does not influence the motion of the ball and it can be applied for non-transparent and non-Newtonian fine suspensions. A new hypothesis, namely a continuity theory for coarse disperse systems is introduced here. According to this theory, if the particles of a fine suspension are so small that they fit into the laminar sub-layer around a settling coarse particle, the fine suspension can be treated as a continuum. If they do not fit, hindered settling dominates between the coarse and fine particles. It was also recognised that if a particle settles at a constant speed in any media that is in an equilibrium state, therefore, the “equilibrium mean surficial shear stress (τ_e)” and the “equilibrium mean surficial shear rate” have been introduced. The equilibrium mean surficial shear stress can be calculated initially, because it is simply the force of gravity minus the buoyant force over three times the total surface of the particle. Once τ_e is known, the equivalent Newtonian absolute viscosity can be determined and the terminal settling velocity of particles falling in non-Newtonian media can be calculated by the known procedures for Newtonian fluids.