John Dodds

The porosity and contact points in multicomponent random sphere packings calculated by a simple statistical geometric model

Abstract The structure of a random packing of spheres with different sizes is reduced to an amenable system composed of known subunits by making one simplifying assumption: that all spheres touch their neighbors. A simple theory involving statistics and geometry is presented by which the frequency distribution of these subunits can be calculated from the sphere size distribution and hence the structure of the packing can be determined. Results are presented for the porosities of binary and ternary sphere packings which bear a qualitative similarity to previously published experimental results. After defining the coordination numbers which are involved in multicomponent packings, results are presented for the contacts in such a packing. These results give more detail and a more comprehensive description of the structure of these packings than is possible to obtain by experiment. The model is proposed as providing a general idealized framework for the description and further investigation of multicomponent packings.

Particle morphology: from visualisation to measurement

The main steps of characterisation of particle morphology by image analysis, i.e., visualisation, image treatment, shape quantification, for routine use in powder technology are reviewed and illustrated by examples. Macroscale and mesoscale bidimensional descriptors are presented, depending upon the desired level of detail. Elements for a quantification of the 3D shape are given, stressing out the special case of faceted particles. The difficulties of comparing the size measurements by image analysis with those obtained by other methods (laser diffraction granulometers, sieving) are discussed.

Determination of the wettability of powders by the Washburn capillary rise method with bed preparation by a centrifugal packing technique.

The Washburn capillary rise method is a standard technique for determining the wettability of powders expressed as a contact angle. The method requires the preparation of two identical beds of powder. One of these beds is used to follow the capillary rise with a perfectly wetting liquid (contact angle = 0) giving access to a bed structure parameter. The other bed is used with the liquid of interest (contact angle not = 0) and the capillary rise data is analysed using the previously determined structure parameter to obtain the contact angle. In the experiments reported here we have used a centrifugal packing technique to prepare beds of powder. This gives reproducible packings and also allows a certain degree of control of the bed porosity. In addition the air permeability of the beds is also determined prior to the capillary rise experiments. The results show that the value of the contact angle of a powder determined by the Washburn method depends on the porosity of the powder bed, and that the structure parameter can be determined from the air permeability using the Kozeny-Carman expression.

Wet granulation: the effect of shear on granule properties

This paper presents a study of the wet granulation of fine cosmetic particles using a high-shear mixer granulator on a given particle and binder system. The shear effect on granule properties is highlighted. The granules formed under different impeller speeds are divided into size classes and further examined in terms of porosity, friability and binder content. The main result of this study is that, depending on operating conditions, the granulation of a fine powder with a given binding liquid can result in the formation of granules of very different characteristics in terms of size, porosity and friability. Mechanical energy brought to the granulation system is as important as the physicochemical characteristics of the powder-binder pair.

Approximate calculation of breakage parameters from batch grinding tests

Abstract A mathematical treatment, based largely on the work of Kapur, has been developed to obtain breakage and selection matrices from batch grinding tests which are valid for the initial period of the process. The method is illustrated using experimental results for the grinding of hydrargillite and carbon in a laboratory scale stirred bead mill for 15 min and it is shown that this restriction still allows application of the method to continuous grinding processes in the mill. The breakage and selection functions determined by the method are shown to give a good representation of the grinding kinetics and to lead to a normalized breakage function.

Prediction of the product size distribution in associations of stirred bead mills

Abstract In order to determine the operating conditions leading to a product with a given particle size distribution, a study has been made of the influence of the operating parameters (stirrer speed, solids concentration, beads diameter) on the particle size distribution of the product obtained in wet fine grinding in a stirred bead mill. Combination of the results of this study with a flow model through the mill leads to a model of the continuous grinding process. This model suggests that the spreading of the particle size distribution could be reduced either in multiplying the number of mills associated in series, nor in multiplying the number of passages through the same mill. Experiments made with the same overall residence time confirm this assumption.

Identification of the fragmentation mechanisms in wet-phase fine grinding in a stirred bead mill

Abstract Breakage and selection functions for wet-phase grinding of carbon in a stirred bead mill have been determined by a method based on Kapurs first-order approximate solution. This allows calculation of curves of B ij = F( x i x j ) which are used to characterise the fragmentation mechanisms in terms of either abrasion or fragmentation. Comparison of the mechanisms identified in this way, with observation of the fragments produced under different grinding conditions by means of a scanning electron microscope coupled with image analysis confirms the validity of these conclusions.

Properties of disordered sphere packings I. Geometric structure: Statistical model, numerical simulations and experimental results

Abstract This paper presents a study of the characterisation of topological disorder in packings and the resulting effects on the mechanical and electrical properties of binary packings of spheres. It is shown that the contacts between spheres as predicted by an idealised statistical model are different from those found by computer simulations and from experimental results. These differences depend on the assumptions used in the model and the method of packing, sphere by sphere in computer simulations and collectively in experiments. The consequences of these differences are interpreted in terms of cooperative effects and local arching in real packings. Finally, we give a range of 4.75 to 6 for the mean co-ordination number for the stability of sphere packings under gravity. The minimum value of 4.75 is determined by an analysis of local arching and the maximum value of 6 by the stability of a single sphere.

Talc grinding in an opposed air jet mill: start-up, product quality and production rate optimization

We present a study of talc grinding in an Alpine 100 AFG opposed air jet mill with an inline laser granulometer. The conditions for steady state operation have been determined from continuous grinding experiments and show that overloading occurs above a critical value of feed rate classifier resulting in unstable product size distribution. For each rotation speed of the classifier, there is an optimum feed rate, which gives the finest product, thus fixing a maximum reduction ratio. A linear relation exists between this ratio and the rotation speed of the classifier. The use of liquid grinding aids have been studied and showed they can result in an increase in the production rate but can also lead to a coarser product.

Validation of a model of a stirred bead mill by comparing results obtained in batch and continuous mode grinding

In this paper we present a generalization of the asymptotic solution of the batch grinding equation proposed by Kapur in 1970. It is shown how this can be combined with the residence time distribution to give the particle size distribution of the product of a continuous grinding process. The residence time distribution in a stirred bead mill has been determined by tracer experiments and used to propose a flow model of the mill. The results of batch grinding experiments of hydragillite are combined with this flow model to successfully predict the product size distribution in continuous grinding experiments.