(158c) Experimental Characterization of the Chaotic Dynamics of Cohesionless Particles in a V-Blender Using Radioactive Particle Tracking

Recently, there has been an increasing body of experimental work concerning the chaotic characteristics of granular flow in 2D blenders (e.g. Khakhar et al. 1999). There is in fact an interest in performing such investigations in the case of more complex 3D blenders because they represent an important proportion of the blenders found in the industry. However, the study of the flow behavior in such blenders with standard non-intrusive methods such as Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV) is intricate owing to their complex geometries and kinematics, and to the opaque nature of the granular material. As an alternative, a lot of effort has been made to improve existing non-intrusive experimental technologies based on radioactive particle tracking methods (RPT). In particular, these advances have paved the way to the investigation of particle dynamics over a wide span of applications. For example, RPT has been shown to reveal important characteristics of the solid phase dynamics in multiphase fluidization (e.g. Cassanello et al. 1995) as well as in bubble columns and rotary kilns. With this method, the position of a single radioactive tracer that has the same properties as those of the inert particles is recorded over time and generates a time series of the tracer position. By applying the ergodicity theorem, which states that a time average is equal to a population average, and by performing a specific time series analysis, important properties of the flow can be determined, including those related to its chaotic behavior.

Granular material in systems with time-periodic boundaries, such as in a V-blender, is known to exhibit a chaotic behavior. As a result of recent advances in the field of non-intrusive methods, the quantification of chaos in such systems has become more tractable, principally because they provide a reliable measure of the flow field with no perturbation. Indeed, in a recent paper (Doucet et al. 2005), RPT was successfully extended to the case of complex geometrical systems in order to make possible the study of 3D flows in irregularly bounded domains. This has enabled the application of this method for the investigation of mixing in complex 3D blenders, such as the V-blender, which was out of reach with previous RPT capabilities. This work presents an original experimental analysis of the time series obtained with this extended RPT technique and a single tracer in motion in a 16-qt V-blender. A special attention is given to the chaotic behavior of the flow by computing for instance a few properties of the attractor such as the maximum Lyapunov exponent and the fractal dimension. Finally, the evolution of mixing/segregation is derived from the time series. More generally, this work shows that it is possible to perform a thorough experimental analysis of the flow dynamics in a powder mixing system by means of a non-intrusive method such as RPT.

Cassanello M., Larachi F., Marie M.-N., Guy C. and Chaouki J., Experimental characterization of the solid phase chaotic dynamics in three-phase fluidization, Ind. Eng. Chem. Res., 34, 2971-2980, 1995.

Doucet J., Bertrand F. and Chaouki J., An extended radioactive particle tracking method for systems with irregular moving boundaries, submitted to Powder Technology, 2005.

Khakhar D.V., McCarthy J.J., Gilchrist J.F. and Ottino J.M., Chaotic mixing of granular materials in 2-d tumbling mixers, Chaos, 9, 193-205, 1999.