Download files
Abstract
Particle mixing is a unit operation in many industrial applications such as pharmaceutical and chemical engineering processes. However, there is a lack of fundamental understanding of these operations due to difficulties in describing particle behaviour by governing equations. Thus, most manufacturers depend on trial-and-error efforts to design mixers that suite a certain operation. Here, a vertically-shafted cylindrical mixer is chosen as the subject of study. The method to be used for analysing particle behaviour in the mixer is the numerical simulations of particles, and is based on the Discrete Element Method (DEM). Previously, results obtained by simulations have been validated to some degree against the experimental results obtained by Positron-Emitting-Particle-Tracking (PEPT) method. Therefore, an extended version of the same software code is used here to further investigate mixing behaviour of spherical particles in the vertically-shafted cylindrical mixer.
Mixing behaviour of such a mixer is generally known to be affected by many variables. The variables considered here are of three types: operational variables, design variables and properties of mixtures. The operational variables considered are blade speed and loading pattern; design variables are rake angle and blade clearance; and properties of the mixtures are volume fraction, size ratio and density ratio.
In the first stage of the study, mixture quality is assessed by a conventional mixing index known as Lacey’s index to quantify effects of blade speed, blade clearance and rake angle. Such indexes are obtained by statistical analysis based on sampling methods, which suffer from uncertainties in the size and number of samples. Although, such issues are known for many decades, little has been done to address the issue. To address this issue, in the second stage of the study, a novel method is developed and used to evaluate the quality of mixtures at the particle-scale. In this method, mixture quality is defined as the variance of the particle fraction at the particle scale, and is obtained by using coordination number information, thus linking the mixture quality to the particle structure. It now depends on the particle contact condition, which is handled by specifying a maximum clearance between two particles. This particle-scale index is compared against two more methods of assessments: conventional mixing index and coordination number.
In the third stage, a simple blade-particle system is considered, where a blade is dragged horizontally through a particle bed. Here, the possibility of creating dynamically similar systems is investigated. In addition, the simple system is used to model the mixing behaviour in the vertically-shafted cylindrical mixer. If proven effective, the simple system offers an easy solution for analysis of complex blade-particle systems. Both these methods are import to address scale-up issues. In the final stage, mixing of fine particles in a cylindrical mixer is considered by introducing a cohesive force on pairs of contacting particles. Cohesive force is implemented by van der Waals force, which depends on the material-dependent Hamaker constant Ha. The cohesive force is artificially varied by varying Ha to investigate effect of particle size on mixing. A higher Ha value indicates a larger cohesive force or a smaller particle diameter, and vice versa. Results show that small rake angles are suitable for mixing of cohesive particles.