A PHENOMENOLOGICAL DESCRIPTION OF MIXING-SEGREGATION EFFECTS DURING SHEAR DEFORMATION OF PARTICULATE SOLIDS
Advancing the chemical engineering fundamentals
Particulate Systems (T2-3P)
Keywords: shear deformation, mixing, segregation, particulate solids
In our previous paper [1] we have suggested the experimental unit and method of segregation and mixing exploration during shear deformation of particulate solids.
In the present paper we are developing a phenomenological approach to the description of the segregation-mixing effects, observing by means of the conveyor shear cell [1]. As a result of investigation we are suggesting a mathematical simulation of the process of the nonuniform particles distribution in particulate solids undergoing shear deformation at low and moderate shear rates.
The mathematical description is based on the general mass transfer equation taking into account the fluxes of convection, segregation and mixing of particles, differing in size and density. The mixing kinetic equation is expressed on the basis of the analysis of chaotic transversal moments of particles in a restricted environment as follows
Jm=-0.5s bd (du/dy) sin((0.25 pi(d+s))/d) Ro (dc/dy) (1)
where: (du/dy) is the shear rate, s is the mean distance between particles, b is the geometrical parameter, Ro is the bulk density, c is the concentration of test particles, d is the mean particle diameter.
The segregation kinetic equation is formulated on the basis of the mechanism of hydromechanical segregation [2]. This mechanism is adopted here for the conditions of the low and moderate shear rates. The adaptation allowed us to describe the segregation flux in the following way.
Js=K (bd) (du/dy) c Ro Delta_M0 (2)
where Delta_M0 is the relative excess moment of gravity and frictional forces, acting on the test particles, K is the segregation coefficient.
It was found out that the segregation coefficient is the experimental constant, which doesn’t depend on shear rate and size of large and small spherical cohesionless nonelastic test particles. The method suggested for determination of the segregation coefficient by means of the conveyor shear cell is discussed in this paper.
The adequacy of the developed mathematical simulation of mixing-segregation dynamics is checked by comparison of experimental and calculated results. It is noteworthy, that the complex segregation-mixing process is forecasted by the method using only one experimental kinetic constant.
1. Dolgunin V., Borschev V. and Klimov A. The conveyor shear cell for determination of particle tendency to segregation and mixing. 4th European congress of chemical engineering, full text of papers in CD-ROM; Granada, Spain, 2003.
2. Dolgunin V.N. Segregation modeling of particle rapid gravity flow / V.N. Dolgunin, A.A. Ukolov // Powder Technology. – 1995. – N 83. – P.95 – 103.
See the full pdf manuscript of the abstract.
Presented Monday 17, 13:30 to 15:00, in session Particulate Systems (T2-3P).
