# How Slurry Transport inside a Tumbling Grinding Mills

The transport of slurry within the ball mill depends on the peripheral velocity and porosity of the ball charge. Residence time distribution and mill hold up are often used as indicators of the mode of transport. In this work, the transport problem is tackled via direct simulation of the three dimensional motion of the ball charge.

## The Numerical Method

The multibody collision problem as is the case in ball mills is best suited to analysis by the discrete element method (DEM). DEM is a numerical scheme for simulating the motion of discrete but interacting bodies. At the outset, the entire mill is divided into sections or boxes; each section is a cube whose dimension is slightly greater than the diameter of the largest ball. From this point the computation is done in two separate ways. where Fi, is the force acting on the ball, Mk is the moment about the kth coordinate axis, Li is the perpendicular distance from the line of action of the force to the centroid of the ball, and the X,Y,Z-coordinates are denoted by 1, 2, 3 respectively.

## Analysis of Porosity in the Ball Charge

The fluid flow or the transport problem in the ball mill is intimately related to the porous structure of the ball charge. It is clear that if the voids in the bell bed are filled by the material being ground then the slurry will add to the pool formed beneath the ball bed. The pool height will increase till it reaches the discharge opening height. ### Motion of Balls through the Porous Bed

The transport of slurry through the ball-bed in tumbling mills depends on the distribution of voids inside the charge and the speed of the mill. When balls of different sizes are present in the mill, then there is a tendency for the balls to move at different speeds along the axial direction. Ideally, balls would not move in the axial direction if they are of one size.   ### Holdup Computations

The discrete element analysis gives sufficiently detailed knowledge of the porous ball charge bed. The next step is to model the flow of water and mineral ore particles of different sizes through the mill i.e., the mass transport of the slurry and solids in the mill. This requires a knowledge of the mill hold-up, slurry velocity and composition, and the residence time distribution. As a first step, mill holdup which is one of the key parameters involved in the transport study is estimated.   ## Discussion

The characteristics of the slurry flow inside the mill are difficult to measure. For example, the variation in slurry concentration within the mill due to the non uniform rate of settling of particles of different sizes by itself complicates the situation. It is proposed to tackle this problem by decoupling the ball motion problem and the fluid flow problem. The ball motion problem as shown here can be precisely done by DEM approach; what is needed is a fluid flow model.  where: dP/dy is the presure gradient, Sv is the shape factor, µ is the viscosity, and ε is the bed porosity. The important parameter in the above equation is the bed porosity that is obtained by DEM simulation. The computational results based on this approach found to be unrealistic. 