In the soap film experiment, there is a strong flow along the length of the channel, so I never saw particles stay within the field of view for more than twenty frames in a row. This made it impossible to get tracks of a duration anywhere near to what we got in the Faraday experiment.
In connection with the work on the Faraday experiment, we found a sensible way to look at relative diffusion without having two tracks that actually meet at a point in time. The limited lengths of the individual tracks are thus not a problem.
The high average velocity made me hit another barrier in the processing algorithm. The typical distance between neighbouring particles was low compared to the distance a particle could travel between two frames, so there was a large risk that the processing software would be unable to identify particles correctly.
Sampling a particle track on a single image is one solution to the latter problem. I increased the shutter time until the particles appeared as reasonably long, but not overlapping lines. For each of these lines, the two ends of the line indicates the position of a particle at two times separated by the shutter time. If we write the positions at the two ends of the line as and , and the shutter time as , then is the average velocity of the particle for the duration of exposure.
Since the average flow velocity is much larger than the turbulent variations in the flow velocity, I can use the direction of the average velocity to find out which end of the lines is the beginning and which is the end. - The velocity vectors are chosen so they point downstream.