The rate of constrained particles deposition in a wide range of suspension densities in the laminar-turbulent operating modes

Abstract

The rate of constrained fall of mineral particles in suspensions of different densities is necessary for calculating the design and operating modes of gravity concentrating equipment. During hydraulic classification and separation, a mixed, laminar-turbulent, flow regime is observed in real pulps. There are no theoretical velocity formulas for such a regime, and most of the known semi-experimental and experimental formulas have limited application. This article proposes a new method for comparing different formulas with each other in a wide range of suspension densities. The method uses an analytical calculation of the hydraulic characteristics of the medium - porosity, concentration and viscosity. What is new is that all these characteristics depend on only one indicator - the density of the suspension, which is easily determined in practice by weighing a pulp sample. In these calculations, the weighted average density of heterogeneous particles in suspension is used. A feature of the method is the approximation of the analyzed calculation formulas to the conditions of free fall in order to obtain only one control point and compare it with known experimental data. This method allows to set the limits of the application of formulas depending on the density of the suspension. The choice of a more precise formula is necessary for the design hydraulic devices for the classification and separation of mineral suspensions and finely ground composite raw materials. The application of this method for the most common formulas of Ergan and Todes-Rosenbaum is shown. It was found that the latter formula іs actually not suitable for dilute suspensions with a density below 1.65 g/cm3. A new linear equation for calculating the rate of constrained particles deposition is proposed, which provides high accuracy in a wide range of suspension densities. The resulting equation has a simple form and, together with an analytical calculation of the characteristics of the medium, forms a system of linear equations for calculating the rate of constrained particles deposition of any size and density in mineral pulps of different densities. The calculation of the velocity of constrained settling and the ascent of particles is the basis for the design of hydraulic classifiers and separators for mineral dressing. Such calculations are necessary for determining of hydraulic devices optimal modes and monitoring indicators during their operation.