Analysis and Modeling of an Experimental Device by Finite-Time Lyapunov Exponent Method

In this paper, we investigate the transport and mixing process of the batch mixers with two different configurations, the centered-blade and offset-blade mixers, by using a dynamical system approach. The 2-D velocity fields of the mixers measured using Particle Image Velocimetry (PIV) are used to identify the Lagrangian coherent structures (LCSs). The results show that the LCSs separate the physical space into two portions. In the case of the center-blade mixer the portion bounded inside the LCS experiences a relatively slow mixing relative to the portion outside of the LCS boundary. However, when the blade position is located near the wall, the LCS becomes more complicated but it still separates regions of fast mixing from a slower one. We develop a heuristic dynamical system model of our mixers to understand how the vorticity strength at the blade tips influences the variation of the LCSs. Finally, we define an appropriate notion of mixing to study the mixing rate of our mixing devices.