Rigorous non-linear models of elasto-plastic contact deformation are time-consuming in numerical calculations for the distinct element method (DEM) and quite often unnecessary to represent the actual contact deformation of common particulate systems. In this work a simple linear elasto-plastic and adhesive contact model for spherical particles is proposed. Plastic deformation of contacts during loading and elastic unloading, accompanied by adhesion are considered, for which the pull-off force increases with plastic deformation. Considering the collision of a spherical cohesive body with a rigid flat target, the critical sticking velocity and coefficient of restitution in the proposed model are found to be very similar to those of Thornton and Ning's model. Sensitivity analyses of the model parameters such as plastic, elastic, plastic-adhesive stiffnesses and pulloff force on work of compaction are carried out. It is found that by increasing the ratio of elastic to plastic stiffness, the plastic component of the total work increases and the elastic component decreases. By increasing the interface energy, the plastic work increases, but the elastic work does not change. The model can be used to efficiently represent the forcedisplacement of a wide range of particles, thus enabling fast numerical simulations of particle assemblies by the DEM.

In the early stages of development of a new Active Pharmaceutical Ingredient (API), insufficient material quantity is available for addressing processing issues, and it is highly desirable to be able to assess processability issues using the smallest possible powder sample quantity. A good example is milling of new active pharmaceutical ingredients. For particle breakage that is sensitive to strain rate, impact testing is the most appropriate method. However, there is no commercially available single particle impact tester for fine particulate solids. In contrast, dry powder dispersers, such as the Scirocco disperser of the Malvern Mastersizer 2000, are widely available, and can be used for this purpose, provided particle impact velocity is known. However, the distance within which the particles can accelerate before impacting on the bend is very short and different particle sizes accelerate to different velocities before impact. As the breakage is proportional to the square of impact velocity, the interpretation of breakage data is not straightforward and requires an analysis of particle velocity as a function of size, density and shape. We report our work using an integrated experimental and CFD modelling approach to 2 evaluate the suitability of this device as a grindability testing device, with the particle sizing being done immediately following dispersion by laser diffraction. Aspirin, sucrose and -lactose monohydrate are tested using narrow sieve cuts in order to minimise variations in impact velocity. The tests are carried out at eight different air nozzle pressures. As intuitively expected, smaller particles accelerate faster and impact the wall at a higher velocity compared to the larger particles. However, for a given velocity the extent of breakage of larger particles is larger. Using a numerical simulation based on CFD, the relationship between impact velocity and particle size and density has been established assuming a spherical shape, and using one-way coupling, as the particle concentration is very low. Taking account of these dependencies, a clear unification of the change in the specific surface area as a function of particle size, density and impact velocity is observed, and the slope of the fitted line gives a measure of grindability for each material. The trend of data obtained here matches the one obtained by single particle impact testing. Hence aerodynamic dispersion of solids by the Scirocco disperser can be used to evaluate the ease of grindability of different materials.

Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks Journal of Rheology 30, 949 (1986) Abstract. Rigorous models of elasto-plastic contact deformation are time-consuming in numerical calculations for the Distinct Element Method and quite often unnecessary to represent actual contact deformation of common particulate systems. In this work a simple linear elastic-plastic-adhesive contact model for spherical particles is proposed, whereby the loading cycle is a linear plastic deformation and the unloading is elastic with a higher stiffness compared to the plastic deformation. The adhesive behaviour is considered once the unloading contact force reaches the pull-off force, at which point the contact deforms with negative elastic-adhesive stiffness. In order to account for increase in adhesion due to plastic deformation, the pull-off force is evaluated using negative linear plastic-adhesive stiffness. The model is applied to compression of spherical particles with elastic-plastic-adhesive contacts for which sensitivity analyses of the model parameters on work of compaction are carried out. As the ratio of elastic to plastic stiffness is increased, the plastic component of the total work increases for a given strain and the elastic component decreases. Large stiffness ratio values imply particles undergoing larger plastic work for a given strain. By increasing interface energy, the plastic work increases for a given solid fraction, however the elastic work does not change. In this case, the maximum tensile force is increased therefore the work of adhesion is increased.;

Spiral jet milling is a size reduction process driven by the fluid energy of high velocity gas jets. Inter-particle and particle-wall interactions are responsible for size reduction. The process is energy intensive, but inefficient. The underlying mechanisms for size reduction in the mill are also not very well understood. The optimum grinding conditions are still currently found by trial and error experimentation. In this work, the Discrete Element Method coupled with Computational Fluid Dynamics is used to investigate the effects of different parameters on the particle collisional behaviour in a spiral jet mill. These include the particle concentration in the grinding chamber, the particle size, and the fluid power input. We report on our work analysing the efficiency of energy transfer and how it can be improved by changing the milling conditions and particle properties.