Shannon entropy for local and global description of mixing by Lagrangian particle tracking

If 100 dice cannot be cast simultaneously, one single die can be cast 100 times. On the basis of this simple principle, the experimental technique of positron emission particle tracking has been used to develop and implement a new methodology for quantifying the local and global mixing characteristics within a mechanically agitated fluid batch system. This Lagrangian technique uses a single positron-emitting particle as flow follower. Using a high data acquisition rate, such a tracer is continuously tracked in 3D space and time to accurately determine its trajectory over a considerable period of time. By partitioning its long trajectory, the single particle tracer can be regarded as thousands of simultaneously tracked particles which are instantaneously, locally and non-invasively injected in the mixing system at varying feed positions. A large amount of PEPT data were collected for impeller rotational speeds ranging from 100 to 500 rpm which allowed new statistical tools derived from information theory, such as Shannon entropy and uncertainty, to be implemented in the data analysis. Thus, measurements of entropy mixing indices were obtained as a function of position, time and impeller speed. The method also allowed the determination of characteristic time parameters including the macroscale mixing time which agreed very well with correlations of the dimensionless mixing time available in the mixing literature. Detailed local information is provided on minimum mixing time positions for feed and withdrawal of material, which can be used to optimise the design or operation of stirred batch mixing systems.