The Spex mixer mills are widely used in the industry to synthesize a variety of materials. In the present study, the discrete element method (DEM) simulation technique is used to understand the motion of the grinding media and the effect of the size of the grinding media and the mill length on grinding. The simulations correspond to a grinding chamber with grinding media only. The total mass of grinding media in different numerical experiments with different grinding media sizes is kept constant. The average collision intensity per ball, which is defined as the product of the median of the contact force distribution and the number of collisions normalized to the number of grinding media, is used as the parameter to study the quantitative differences. The collision intensity distribution shows an optimum as a function of the grinding media diameter. Moreover, it was found that the collision intensity varies with the length of the grinding chamber.

The effect of the grinding chamber length and the grinding media diameter in a Spex 8000M mixer mill was reported earlier [1]. Now a modification of the grinding chamber shape was investigated. The results presented are based on DEM (discrete element method) simulations performed for the same mass of grinding media in all cases. It was found that the rounded end caps of the grinding chamber gave higher collisional intensities of the grinding media compared to the flat end caps. The collision intensity can be maximized by adjusting the roundness of the end caps. For end cap curvatures of R/3 and R/4 (R is the radius of the grinding chamber), along the horizontal axis results in the highest intensity collisions compared to other cases studied. The maximum increase in the grinding media collision intensity in modified end caps was observed to be about 75 % for one particular grinding media diameter. IntroductionGrinding is widely employed in many industries such as chemical, cement, pharmaceutical, and waste treatment. It is quite essential to understand the grinding media motion, uniform product stressing, and prevention of product accumulation at the corners where the grinding media cannot reach. A number of experiments need to be performed over a range of operating conditions in order to study this. On the other hand, modeling can be used as a cost-effective tool to predict process performance, scale up, and to develop a good strategy to optimize experiments. The discrete element method (DEM) was used earlier to predict -to good accuracy -the motion of grinding media [2] and the effect of rotational speeds, sample loading, the mill diameter, and the filling ratio of grinding media on the rate of grinding [3][4][5][6].The SPEX mixer/mill is widely used in several research applications and, particularly, in the mechano-chemical synthesis of advanced materials [7]. It is a vibratory mill that allows relatively rapid milling of small quantities of material. The motion of the grinding chamber of a SPEX mill follows complex 3D cycles. The center of the grinding chamber vibrates in two-dimensional mode with the same frequency (x 1) ) but different amplitudes (A x and A z ), and its slanted axis rotates with a certain amplitude (X) around the third direction. The movement of the rotation and vibration has different frequencies. Mathematically, the grinding chamber motion can be given by Prasad and Theuerkauf [1]:Prasad and Theuerkauf [1] used the DEM to simulate the motion of the grinding media and produced the optimum ball diameter for which the impact forces are higher.In this report, we present the results with modified grinding chamber end caps. The number of grinding balls is varied in different simulations to obtain an optimum grinding ball diameter, keeping the total mass of the grinding media constant. Commercial software, Particle Flow Coding (PFC 3D ), is used. No charge (material to be ground) was introduced in order to avoid the simulations from running for an indefinite number of hours and also because the ...