Theoretical Study of Superposition of Macro- and Microscale Mixing and its Influence on Mixing Kinetics and Mixture Quality

Abstract

The objective of this study was to build a model that describes evolution of the state of a mixture where microscale mixing (penetration of particles into the closest neighborhood of its position during a small period of time) is accompanied by macroscale mixing (periodical exchange of large parts of the mixture inside a mixing volume after a certain period of time). The mixing kinetics for segregation and nonsegregation mixtures, agitated by blades placed in a certain sequence inside the mixing volume, was modeled. The case of exchange by the halves of material was examined as well. Two variants of the exchange were examined: the parallel displacement and the symmetric turn. It is shown that there exist optimal parameters of the macroscale transitions providing the highest rate of mixing. The proposed model helps to achieve better understanding of the process and suggests some ideas to improve the design of the mixers.

Keywords:

• blade mixing
• degree of capture
• granular material
• macroscale mixing
• Markov chain
• mixing quality
• transition probability