In practice, grinding media mixed with heterogeneous ore particles, known as slurry, are continuously fed into the mill from one end and the fine final product is collected from the exit at the top of the mill. With a numerical analysis, the behavior of slurry and grinding media suspension is captured using multi-phase computational model. Media particles collisions with each other and walls are solved numerically using Discrete Element Methods (DEM), while single-phase and ore slurry (multi-phase) are simulated using Computational Fluid Dynamics (CFD), Smoothed-Particle Hydrodynamics (SPH), or Lattice Boltzmann (LB) over different design and operating conditions.

Using the aforementioned approaches, vertical mill is simulated to gain a fundamental knowledge of the dynamic behavior of grinding media and slurry. Grinding efficiency of ore particles is estimated using stress intensity generated by particle-particle collision, and particle-wall collision in the mill for different media properties. Numerical estimation of grinding and power consumption is compared with experimental data to further validate the parametric dependencies between operating and design variables. The validated numerical model is used to analyze the grinding efficiency of vertical mills with different scales and process conditions. However, as a first step, it is crucial to develop a comprehensive DEM model of the grinding media (no slurry) in a sealed environment, no in and out flows considered. The simulated results are analyzed in terms of velocity field, stress intensity profiles, flow pattern, kinetic energy and power consumption of the system.

The energy provided to the fine grinding operation is not fully utilized into ore grinding, only a fraction of that energy is utilized. The rotating shaft in the mill transfers the energy

Considering the physics involved this multi-phase system, the energy distribution can be quantified. The change in gravitational potential energy (Delta E_g) can be described as per the following equation, where, n is the number of grinding media particles; g is the gravitational force, and m_i, v_i is mass and velocity of particles. Similarly, the impact energy dissipation can be formulated using damping force (f_{dn}, f_{dt}) and contact velocity (v_{dn}, v_{dt}) of two colliding particles. The viscous energy dissipation between in fluid-fluid (Delta E_{ff}) or fluid-wall (Delta E_{fw}) interaction can be written.

As observed both qualitatively and quantitatively from the equations and Figure-{fig:kwade}, only a part of provided energy is used in the collision of grinding media. The collision of grinding media may lead to breakage of ore particles which further depends on three factors: {enumerate} Stress energy generated in the collision of two grinding media particles due to impact, shearing, or torsion. Collision frequency which defines the rate at which the grinding media is colliding with each other. The probability of ore getting stressed while the grinding media is colliding. {enumerate}

Considering all these factors, the ore will break if the resultant stress generated is more than the breakage energy of the ore. Later in this study, we will review the model used to predict the breakage rate of grinding media based on the factors mentioned here.The grinding of ore is a highly energy-intensive process. It is regarded as the largest energy consuming operation in mineral processing. Stirred milling technology is employed in mining processing to grind particles down to fine and ultra-fine particle sizes in a wide range of mining application. Stirred mills convert electric energy provided by a high torque motor to kinetic energy to the grinding media. The ore particle size reduction is resulted from the high collisions and attrition frequency, which provide sufficient energy for the breakage of ore trapped in between {Blecher1996}.

Stirred mills are capable of grinding to particle size as low as 5 microns at a higher power intensity in stirred mills compared to conventional comminution equipment such as ball mills and tower mills. Despite the high power intensity, the overall power consumption of high speed stirred mills is lower due to short retention times. The major challenge encountered in the process of ore grinding is the use use of large size grinding media, which significantly affects the grinding efficiency. In stirred media milling, a smaller grinding media size compared to a conventional ball mill makes high-speed movement possible, thus higher force on the ore particles trapped in media is applied. This is significant since as the particle size becomes smaller, the force needed to break the particles increases.

Different types of high speed stirred mills have been developed in the mining industries. This technology was originally intended for the size reduction process in the pigment industry yet it has spread to a wide range of application in other field such as pharmaceuticals, ceramic and chemical industries {Mannheim2011, Jayasundara2011}. Each type of the mineral has its unique physical property. Different types of the stirred media mill have been developed and applied for specific industrial processes. The main types of stirred mills used in the mining industry are the IsaMill, HIGMill, Stirred Media Detritor (SMD), Tower mill and VXPmill. The IsaMill is horizontally oriented, while the rest are vertical.

The stirrer type is also a differentiating factor; the IsaMill, HigMill and VXPmill employ discs, while the SMD uses pin agitators, and tower mill uses uses a helical agitator. Figure {fig:mill_type_specific_energy} compares the specific energy input and particle size reduction for different types of mills. Stirred mills have the highest specific energy input, but are the only mills that have the capability to grind particles below 5 microns. Although all stirred mills are similar in terms of their basic principle of operation, a large number of different stirrer designs are available in the industry, each providing different energy transfer efficiency.

A number of studies focusing on the effect of operating variables on grinding performance and efficiency in vertical stirred mills can be found in literature. On the other hand, effect of design parameters (or mill geometry) on mill performance, grinding efficiency, and slurry and grinding media dynamics have not yet been investigated in depth. The following subsections discuss research work conducted to examine the impacts of mill orientation, stirrer layout, amount of stirrer arms/blades, and stirrer spacing on the mill’s grinding efficiency and performance. Some innovative designs to enhance grinding efficiency are suggested and anticipated.

At a given agitation rate, the pin stirrer type has a higher energy density than the disc stirrer because it moves the grinding media mainly by displacement force rather than adhesion, which is characteristic for disk designs. In general, stirrers with a larger contacting surface provide the highest power density more uniform force distribution. Using discrete element method (DEM) approach, Radziszewski et. al. [42] evaluated the mill power density of different stirred mills using a new parameter, named shear volume, that was developed based on the assumption that the higher the shear volume of a given mill design, the more surface area will be in contact with the grinding media and slurry causing the machine to consume more energy.