Large-scale numerical investigation of solids mixing in a V-blender using the discrete element method

Abstract

Over the past few years, the discrete element method (DEM) has been used in models for the simulation of granular flows in various mixing applications. If these models have shown rather efficient, they have so far been applied to predict the behavior of small numbers of particles over limited spans of time. The objective of this work is to show that DEM-based models can be used to predict the flow behavior of large numbers of particles over large spans of time and, more particularly, mixing phenomena that take time to manifest in such systems. To this end, several large-scale DEM-based numerical investigations of the flow of monodisperse and bidisperse blends of up to 225 000 particles over a span of 120 s in a V-blender will be discussed using entities such as the particle velocity and granular temperature, the torque of the mixing system, RSD curves and mixing times.

Introduction

Granular mixing plays a major role in many industrial processes. Unfortunately, several industries (e.g. pharmaceutical, cosmetics, mining, food, energy, polymer and semiconductor) are confronted with significant problems when dealing with granular materials because of a lack of knowledge in this field. As a consequence, the manufacturing of quality products becomes difficult to achieve [1]. Typical problems arise from the difficulty of achieving homogenous mixtures or obtaining reliable powder flows. The complexity of such flows is due to the nature of the granular material, which may contain components of different shapes, sizes, surfaces and mechanical properties. Moreover, technologies available for blending operations include a wide variety of geometries (e.g. V-, bin, ribbon, double-cone blenders) with specific kinematics, which of course influences flow behavior.

In order to investigate the mixing mechanisms inherent to blending equipment, models based on the discrete element method (DEM) [2] have been developed over the past 10 years and shown to be rather efficient in catching the particle interactions and predicting the salient features of the flow [3]. In fact, it is now well accepted that DEM is a reliable tool for the investigation of solids mixing. There exists a fairly large body of recent work that has compared numerical results obtained with DEM to experimental data. As an illustration, Kuo et al. [4] simulated powder flow in a V-blender and compared their DEM velocity results to mean velocity data obtained using positron emission particle tracking (PEPT). They showed, in particular, that these results are in good agreement, which constitutes one of the few attempts at validating DEM numerical results with a direct non-intrusive measurement of the flow field. Similar validation work for single-blade blenders [5] has also led to compliant numerical and experimental results. As can be seen in the short summary of some of the DEM investigations of powder mixing found in the literature given in Table 1, one thing that most of these investigations have in common is that they have considered relatively small amounts of particles (∼ 10 000) in small lab scale units and flow simulations over small spans of time (a few seconds). The reason for this is the fact that DEM simulations are computationally intensive, even if parallel computers are used, the computational complexity varying linearly with the number of particles if the model is conveniently implemented [3]. In the context of solids mixing, there is definitely a need for simulations of large numbers of particles over large spans of time. In particular, such simulations would be more realistic since, for instance, typical industrial pharmaceutical blenders may involve more than 10¹⁰ particles. But more importantly, these simulations could shed light into the effect of particle size on the mixing mechanisms in typical blenders, and could provide guidelines for their scale-up. In addition, simulations over large spans of time could help gain insight into mixing phenomena that have been observed experimentally to manifest themselves very slowly. One example of such phenomena is the segregation of particles of two different sizes in a V-blender over as many as 200 revolutions, which results in mixing times of the order of minutes [16].

The objective of this work is to show that DEM-based models can be used to predict the flow behavior of large numbers of particles over large spans of time and, more particularly, mixing phenomena that take time to manifest in such systems. First, the DEM-based model will be presented and thoroughly discussed, such discussion being often times overlooked by authors. Several large-scale DEM-based numerical investigations of the flow of up to 225 000 3-mm and 6-mm particles over a span of 120 s in a 16-quart V-blender will be discussed next, using entities such as the particle velocity and granular temperature, the torque of the mixing system, RSD curves and mixing times. This type of blender was chosen because it is commonly used in the pharmaceutical industry and because of the availability of literature reports related to its mixing characteristics and efficiency. Let us also mention that none of these previous investigations has involved more than 20 000 particles and spans of time larger than 24 s. Finally, a few remarks will be made as regards the suitability of DEM for simulating the flow of particles in industrial blenders.