Mathematical model for determining the hydraulic characteristics of finely dispersed water mineral suspensions

Abstract

Hydraulic characteristics of polydisperse mineral suspensions such as viscosity, concentration, porosity, volume and weight content of solid and liquid phases are necessary to calculate the speed of free or constrained deposition and floating of particles of different composition and size. This speed is the basis for the calculation of hydraulic classifiers and separators for the enrichment of mineral pulps. Determination of hydraulic characteristics requires a lot of experimental measurements, taking into account the different composition of suspensions and operating modes of the devices. The known calculation formulas are empirical and semi-empirical. Theoretical formulas are known only for viscosity, but they are limited by the concentration of the solid phase within 2–5%. The aim of the work is to develop a mathematical model for determining hydraulic characteristics depending on only one measured indicator – the density of the suspension (the volume weight of the sample). This indicator is easily measured in practice, at processing plants it serves to monitor the operating mode of the devices. In this work we use a cellular model of a water suspension consisted of discrete particles, and classical definitions of hydraulic characteristics. Based on this, defining formulas were obtained, an algorithm and a program for calculating characteristics were developed. When using the program, the obtained database allows us to establish approximating dependences: for the weight content of the solid phase θ, porosity ε, concentration β, kinematic viscosity v, density of the suspension ρs in a wide range. These dependencies allow us to calculate the hydraulic characteristics for any zone of the apparatus and different modes using only one simple measurement of pulp density by the weight method. Based on this, for example, it is possible to calculate the speed of constrained deposition and floating of particles and to build a map of the distribution of speeds and the efficiency of gravitational separation of particles. The developed mathematical model, algorithm and calculation program can be used to evaluate the optimal mode, control the stability of the equipment and design new hydraulic devices.