A measure of mixing from Lagrangian tracking and its application to granular and fluid flow systems

Abstract

This work concerns the development of two new indices that are extensive enough to be used to assess the mixing efficiency of both granular and fluid flow systems. They are based on the theory of principal component analysis and the concept of mixing in the weak and strong sense, and can be obtained from tracer trajectories (Lagrangian tracking) either numerically through computer simulation or experimentally by means of nonintrusive methods. It is explained how these measures, which in a way bridge the gap between global mixing properties and the local viewpoint of dynamical systems and chaotic theory, can provide the main mixing directions in a flow system and upper bounds for the mixing curves and mixing times. Two solid mixing cases and one fluid mixing case are presented to illustrate the wealth of detail provided by these two measures.