Stretching in turbulent fluid regimes
Fluids display non-Newtonian behavior when additional stress components are introduced, via moving particles or stretching components. I will begin by providing a brief overview of the interesting dynamics of active and polymeric fluids, followed by more recent work in the field of polymers in turbulent flow. In particular, we will see how the probability distribution function (pdf) of polymer length configuration develops a power-law tail with exponent over time, being a constant depending on the polymer Weissenberg number Wi. Through numerical simulations, we identify two distinct regimes, governed by and the value of the exponent: an evolving power-law regime for below approximately 3/4 and a rapid-stretching regime for more extensible polymers. The former displays a power-law configuration even at early times, with a power law exponent increasing to its stationary value. For polymers with Wi bigger than 3/4, a transient power law develops but gives way to the formation of a local peak in the pdf, subsequently dictating the form of the stationary pdf. These results are compared to and analyzed via a stochastic model (approximating turbulence).