content_image/364791.jpg
We note that below the predicted threshold, above which hydrodynamic interactions have significant affect on bulk properties, our measure has approximate (square) power-law scaling as expected for the variance given linear growth in amplitude, which is in turn is expected if polymer coils are independent. The approximate power-scaling occurs with a concave rounding versus the strictly linear curve predicted on a log-log plot. This round- ing (breaking of power-law scaling) suggests subtle polymer-polymer interactions even in quite dilute solutions; recent systematic and careful rheological studies have demonstrated [31] polymer-polymer interactions can exist for concentrations as low as 1% of the overlap concentration in elogational flows. 

The lack of true power-law scaling at low concentrations, the mild decrease in fluctua- tions above a threshold, and the correspondence of this observed threshold with the predicted threshold for hydrodynamic interactions in (hard) colloids and (soft) polymers indicate hy- drodynamic interactions are important in nominally dilute solutions and limit fluctuation growth. 

<img src='content_image/364791.jpg'>

