Analytical method of calculating the settling velocity of particles in gravitational apparatuses (original) (raw)

Annotation The article presents an engineering method of calculating the settling velocity of particles in industrial apparatuses. The proposed method is based on the results of fundamental studies of various authors followed by statistical processing of the experimental results of investigation of settling velocity of particles depending on their size, shape, density and concentration in the fluid. The movement of solid particles in the fluid caused by gravity is the basis of many hydro-mechanical processes in the mineral and chemical processes, viz. hydraulic separation, classification of polydisperse suspensions, thickening, dewatering and other processes of particles separation. The velocity and trajectory of particles in the fluid are determined by the interaction of the volume and surface forces, including the drag force, which plays a major role in all calculations of hydrodynamic separation processes. The proposed method for calculating the settling velocity of particles in a suspension is based on fundamental studies of various authors [1, 2, 3, 4, 5], followed by statistical processing of the experimental results of investigation of solid particles settling depending on their size, shape, density and concentration in the fluid. Most technological processes occur in suspensions with a sufficiently high concentration of solid particles, thus the disturbances of the velocity field in the vicinity of the moving particle caused by the presence of neighboring particles cannot be neglected. If the volume fraction of particles is high enough and the thickness of the boundary layer of the fluid is greater than the distance between the particles, the law of the drag of a single particle cannot be applied to a multitude of particles. When the concentration of solid particles in a suspension is more than 5%, the settlement of particles is constrained and their final velocities cannot be calculated according to the laws of free fall. The results of the article are based on the conclusions obtained in work [1], which summarizes the studies on determining the velocities of the settlement of solid particles in the form of volume concentration functions. On the basis of the cell model with a free surface, a dependence was