Researching of the Method of Separation of Fine-Grain Particles by Centrifugation in a Liquid Medium

Abstract

In this paper developed the analytical methods of research that used in industrial separation method for the technical rotor installation used for treating a suspension. In this work, the rotor is installed symmetrically to the bearings, on a flexible shaft, and rotates with the angular velocity. The rotor is a round disk on which the cups (tubes) with the suspension are hung symmetrically at a certain distance from the spinning axis. Tubes are rotatable around its horizontal axis. The rotor position is determined relative to a fixed coordinate system. The position of the sample suspension particle is determined relative to the moving coordinate system, coupled with a rotating cup (tube). Angular spin rate of rotor is high enough to ignore the suspension gravitation force, which is much smaller than the centrifugal force. In addition, the shape of the particle is spherical; particle mean free path is much larger than its size; suspension turbulence is absent (laminar mode); the interaction forces between the particles and the walls of the cup (tube) are absent; cup (tube) is quite narrow (diameter ≪ length); after settling of on the walls of the cup the particles stop their motion; the friction force between the cups and their axis of rotation are ignored; the friction force between the solid particle and the wall of the cup is also ignored. In contrast to other researcher’s papers, in which the particles are moving only in the cup axis, this paper explores the spatial motion of a suspension particle. Suspended containers are symmetrically arranged relative to each other; however, the mass of suspension in them may be different. The number of fine particles in them may not be equal, and the time of particle precipitation differs. All of these factors are the cause of imbalance in the rotor system. For practical use of mathematical model are offered the individual cases and their solutions, which are often encountered in practice. For individual cases, determined the conditions of stability of rotor system using the method of complex amplitudes.