Space-time diagrams of mixing in the channel
Space-time plots illustrating mixing of polymer solutions in the curvilinear channel (see above) at different distances from the inlet (the distances are proportional to the number N). Efficient mixing is due to a random similar to the elastic turbulence. Brightness profile was captured 12.5 times per second along a single line across the channel near the middle of a half-ring (a horizontal line in the middle in the images above). Profiles taken in consecutive moments of time are plotted as horizontal lines from top to the bottom. The space time-plots show how the distribution of the fluorescent dye across the channel changes in time. They stretch over slightly more than the channel width, d = 3 mm, in space, and cover a time span of about 42 seconds. At the beginning (N = 8) the dye concentration profile is strongly influenced by the initial conditions. There are large homogeneous regions with maximal and zero dye concentration. The dependence on the entrance conditions fades gradually as the liquids flow downstream and get mixed (N = 24). Further downstream the space-time diagrams exhibit characteristic features at similar spatial scales, but are much more faded. That should correspond to an asymptotic regime, when the small scale structures are generated by the random flow and smeared by the molecular diffusion at equal rates. At the last point (N = 54) the non-homogeneity in the concentration is hardly seen.