Fingerprint diagram of coarsening phenomena

We have proposed a procedure to identify and characterise key topological transformations of coarsening phenomena. The method is based on the linear expansion of the Navier–Stokes equations. As an example, we characterised a polymer foaming process which involves the formation of gas bubbles in a fluid (nucleation) and evolution of both liquid and gas until stabilization occurs. The file named XR_foaming shows micro-radiographs of the process (resolution 15 um). Similar micro-radiographs at 3 um resolution were recorded and normalised. We then calculated the difference between each image and its successor in order to highlight the structural changes (File Diff, 250 frames of 1000). We subsequently computed the optical flow from one difference image to the next one in the sequence obtaining an unique fingerprint of the fluid dynamics of a foam where the y axis is time (File: Fingerprint). This diagram provides a straightforward identification of events, their duration, and the time between them, as well as both general and local flow patterns and velocities.  

We'll provide freely the algorithm (Fortran) upon request and further details can be found in Verdejo et al. 2009, Phys.Chem. Chem.Phys., 11, 10860-10866. DOI: 10.1039/b913262g.