R. Hogg

Flow properties of powders using four testers — measurement, comparison and assessment

Abstract The flow properties, i.e. cohesion and slope of the yield locus, of wheat flour and sugar were measured using four testers, namely, the triaxial cell, the direct shear cell, the Jenike shear cell and the rotational split-level (RSL) shear cell over a range of loading conditions. A statistical comparison was done at the 0.05 level of significance ( P ) to evaluate the performance of the four testers with respect to the yield loci. For wheat flour, the flow properties determined from the Jenike shear cell, the direct shear cell, the triaxial cell and the RSL shear cell experimental data were not significantly different. For sugar, however, the test results from the RSL shear cell were significantly different from the other three testers. Therefore, the four testers seemed appropriate for determining the flow properties of wheat flour and similar powders, whereas, the Jenike shear cell, the triaxial cell and the direct shear cell seemed appropriate for measuring flow properties of sugar and similar powders.

An experimental study of the flow of dry powders over inclined surfaces

Abstract The behavior of dry particulate solids during unconfirmed flow over inclined surfaces has been investigated. The motion of individual particles is found to depend strongly on the nature of the surface over which they flow. For smooth surfaces, flow occurs primarily by sliding at the surface, and little or no shear is introduced into the stream. In the case of highly roughened surfaces consisting of, for example, a stationary layer of the same particles, there appears to be no slip at the surface, and flow occurs entirely by shear within the flowing stream. Surfaces of intermediate roughness lead to flow in which both slip at the surface and shear within the bed contribute significantly. Velocity profiles have been measured experimentally under a variety of conditions, and the effects of such variables as roughness and inclination of the surface, depth of the flowing stream and particle size have been evaluated quantitatively. Empirical relationships have been obtained which describe the flow behavior in all cases studied.

Transverse mixing in rotating cylinders

Abstract The mixing of solid particles in the plane perpendicular to the axis of rotation of a simple drum mixer has been shown to occur as the result of a combination of diffusion and convection. It has been demonstrated that, to first approximation, it is necessary to consider diffusion in the radial direction only and convection in the angular direction only. On this basis, a simple model of the process has been developed, and expressions relating the rate of mixing to the filling of the drum and its speed of rotation have been presented. Comparison of these expressions with results obtained from a simple experimental system yields quite good agreement.

Breakage mechanisms and mill performance in ultrafine grinding

Abstract Comminution processes that involve a combination of discrete breakage events by particle fracture and continuous degradation through attrition are evaluated. A simplified model for mathematical description of the overall process is described, and process simulations are used to illustrate the effects of the different mechanisms on grinding kinetics and product size distributions. Application to fine grinding systems is discussed.

Axial transport of dry powders in horizontal rotating cylinders

Abstract A simple physical model describing the axial transport of dry particulate solids through horizontal, rotating cylinders has been investigated. Design equations are presented which relate particle hold-up in the cylinder to mass flow rate as a function of the cylinder dimension and speed of rotation. Both open-ended cylinders and cylinders with a central overflow discharge have been studied. An empirical expression has been obtained which describes the resistance to flow offered by the discharge plate as a function of the size of the discharge opening and the mass flow rate through the cylinder. Experimental verification of the physical model has been obtained on a laboratory scale for a variety of operating conditions.

Agglomeration models for process design and control

Abstract The basic population balance models for agglomeration processes are reviewed and procedures are described for extending their applicability to systems with size-dependent rate constants and to the formation and growth of porous agglomerates from rigid, solid particles. Simplified procedures for the further extension of the models to include simultaneous agglomerate growth and breakage are also described.

Friction factors for powder flow

Abstract A new method of determining factors which inhibit the flow of dry particulate solids on inclined surfaces has been developed. The net effect of forces which act to inhibit flow is approximated by a frictional model. Two coefficients of resistance to flow: between particles and a smooth surface and between particles themselves, are determined. The experimental technique developed makes use of the fact that material flowing on an inclined surface will accelerate if the net gravitational force on any element is larger than the net resistive force acting on the same element to inhibit flow. This condition is analyzed, using a simple hopper and chute arrangement, by measurement of the materials velocity at various chute lengths. Velocities are determined from observations of the free-flight trajectories of the particles as they leave the end of the chute. The coefficient of resistance to flow is then calculated from the appropriate equations of motion. Experimentally it is found that the coefficients are independent of particle velocity and the inclination of the surface.

Diffusive mixing in flowing powders

Abstract Experimental studies of the mixing of dry powders during flow over an inclined surface have been carried out. Analysis of the rates of mixing indicates that the process occurs through a diffusion mechanism in which the diffusion coefficient varies linearly with the rate of shear in the flowing material.

Axial mixing of particles in batch ball mills

Abstract An experimental study of the axial mixing of dry, powders in batch ball mills has been carried out. For a system of silicon carbide and garnet particles in a laboratory mill containing small plastic balls, the observed mixing is in good agreement with a simple diffusion model. Empirical expressions are presented which relate the diffusion coefficient to the ball and particle loading in the mill. The expressions seem to be valid over most of the practical range of operating conditions except when the filing of either particles or balls is very low. Under these conditions, segregation of balls and particles occurs, apparently leading to anomalous values of the diffusion coefficient.

Internal classification in tumbling grinding mills

Abstract Two basic kinds of internal classification in tumbling grinding mills are identified. These have been termed velocity classification and exit classification. Velocity classification occurs when mass transport through the mill leads to effective axial velocities which vary with particle size. Exit classification arises when particles of different sizes are selectively retained at the mill exit. The effects of these kinds of classification on the size distribution of the mill contents and products are illustrated by mill simulations. Experimental evidence for such effects is presented for mills ranging in diameter from 0.20 to 1.83 m.