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The physical model of partition function of the enrichment process in a heavy liquid |
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The physical model of partition function of the enrichment process in a heavy liquid Authors: M. Brożek, A. Turno
The enrichment in a heavy suspension liquid is carried out in the conditions of turbulent motion. In order to provide a constant liquid density in the entire volume of the separator working chamber the medium should be kept in a continuous movement which prevents the medium solids from sedimentation. Such a regime of separation leads to the phenomenon of particles scattering into inappropriate products. The statistical character of the separation process is formulated numerically by the partition function, determining the probability when a particie of a given density finds its way to a given separation product. The mathematical form of the partition function was derived basing upon the laws of statistical physics and taking into account the external and internal forces acting upon the particle. It was assumed that the distribution of potential energy along the vertical axis of the chamber separator is in agreement with Boltzmann's distribution. The stable state of the system of particles of the lowest energy is constituted by the state in which all the particles of densities higher than the liquid density are placed on the chamber bottom whereas the particles of densities lower than the liquid density constitute a ftoating product. Any other state is the state of higher energy. The particles are transported into this state as a result of the liquid turbulent motion. The energy state higher than the basic state is connected with the phenomenon of particles dispersion. The return of particles to the basic state is enhanced by the gravity force and liquid uplift force whereas this return is hindered by inter-particle actions whose value is proportional to the volume concentration of grains in the separator chamber. Such assumptions result in obtaining the expressions for the partition function and ecart probable in which the particle geometrical properties occur openly as well as the volume concentration of particles in the separator chamber, depending upon process efficiency. The mathematical form of the separation function was verified empirically in an industrial experiment.
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2011