Patterns of constrained particle settling in water mineral suspensions of different densities

The settling velocity of particles in mineral suspensions is a crucial parameter for calculating the design of various hydraulic devices and equipment used for mineral pulp benefication. In studies of gravity separation of heterogeneous particles by settling, the determination of mass settling velocity, the influence of suspension density on the process, and the applicability of classical hydrodynamics laws remain the least explored aspects. Often, free settling conditions are used for calculating hydraulic separation processes, but this introduces significant error in the velocity magnitude, as, in practice, the process occurs under constrained conditions. The purpose of this work was to analyze the patterns of constrained settling using the example of coal particle settling in fly ash suspensions from thermal power plants. The article employs an original method for calculating the characteristics of suspensions and the velocity of constrained settling depending on the density. Experimental data on the mass settling velocity of natural fly ash are presented, which indicate the order of velocities and give grounds for the velocity calculation. Given the fine particle size of the ash, the main focus was on the settling of fine coal in the ash. The analysis covered a database in which the characteristics of suspensions and the velocity of constrained coal settling were determined by varying the density of the ash suspension from 1.05 g/cm³ to 1.3 g/cm³ and the size of the settling coal from 0.01 mm to 4 mm. The database was analyzed using the Reynolds number and the applicability of Stokes' law and Lyashenko's law. It was found that the more dilute is the suspension, the smaller is the particle size that follows Stokes' law, and the smaller is the range of particle sizes that Stokes' law covers, and vice versa. For fine coal fractions of 0.001–0.1 mm, the numerical coefficient in Stokes' law decreases according to an inverse power law depending on the pulp density. The ratio of free to constrained settling velocities decreases according to a power law, similar to Lyashenko's law for porosity. The conducted research expands scientific understanding of the processes of constrained settling, facilitates engineering calculations when designing hydraulic devices, and optimizes their operational modes.