(238e) Mixing of Cohesive Material in Low Shear Mixers

Mixing is an indispensable unit operation in many industries such as pharmaceuticals, food, and agriculture. Obviously there is an eminent necessity to characterize and predict the process of mixing and the quality of the mixture. Serious effort has been made to describe the mixing process in last decades. In our study we focused on characterization of mixture quality and effect of cohesion of material on the mixing process. It was found that cohesion had effect on the time that is required to obtain the specified quality of mixture. Flow pattern within the tumbling drum changed from granular flow to avalanche flow as cohesion increased. In all blenders there are two main mechanism in which mixing can occur. Either the material is transported from one location to another as a rigid body or shear is applied to the system and the particle mix due to diffusion. Variation in material properties such has powder cohesion, particle size distribution, and internal angle of friction affect the flow property of the mixture changing the velocity profile with in the mixer. Understanding the influence of these properties on the flow patterns in blenders will help industry design optimal blenders to work with the finer nano-particles being produced today. It is theoretically possible to ascertain the velocity profile of a blender, from which then we can obtain strain, from it material property. In granular material there is no direct link between stress and strain. The use of the plastic potential theory will however provide the constitutive equation necessary to predict the velocity distribution within the granular material. This theory makes the connection between stress and deformation (or velocity gradient) by utilizing the concepts of Yield Function, Plastic Potential and Flow Rule. Under a normal stress, a well-compacted granular material will flow only when the shear stress attains a critical magnitude, or yield stress. In many cases once flow is initiated the material may be treated as a rigid-plastic material according to Mohr-Coulomb model. The component of stress of powder medium must obey the equations of equilibrium (motion). Therefore, the condition of critical state, Coulomb law of friction on the wall, and absence of stresses on the free boundary of powder medium constitute the boundary-value problem for equations of equilibrium. For a tumble blender the blending volume is the volume of the avalanching zone formed during the rotation of the blender. After the material avalanches down the free slope the rotation of the blender recycles this material to the top of the pile for the next avalanche. The size and frequency of these cascades has a significant effect on the blending effectiveness. In order to predict the shape and size of these avalanche we using the method of characteristics. Characteristics of the system of equations of equilibrium form the network of slip lines along which actual motion of powder occurs. Examination of the network of slip lines will allow the prediction of the mass of powder slumping down, which is actually involve in mixing. By incorporating the effects of powder cohesion, friction, and also change in powder density due to compaction of powder in the direction of rotation the quality of mixing for various materials can be assessed.