Probing the strain-rotation balance in non-Newtonian turbulence with inertial particles

It has long been thought that small amounts of polymer additives can alter the balance between strain and rotation in turbulent flow. Quantitative evidence for this idea, however, is scant, in part because measuring the velocity gradient in intense turbulence is very difficult. Here, we take a different approach to investigating this question, using the well-known preferential concentration effect of inertial particles in turbulence as a probe of the strain-rotation balance. By measuring the pair correlation function of weakly inertial particles in a turbulent water flow with varying concentrations of a high-molecular-weight polyacrylamide, we show that particle clustering is monotonically enhanced as the polymer concentration increases. Our results are consistent with the recently developed energy flux balance model for polymer turbulence, which demonstrates that the balance between strain and rotation is indeed modified by polymers and that this effect increases with the polymer concentration. Our results provide further support for the energy flux balance model as the proper description of polymer turbulence, and highlight the utility of inertial particle clustering as a probe for characterizing the small-scale dynamics of turbulence.

Figure 1

(a) The pair correlation function $g\left(r\right)$ as a function of $r/{\eta }^w$ for pure water and five different polymer concentrations. Note that, as mentioned in the text, we define $g\left(r\right)$ so that $g\left(r\right)=0$ for homogeneously distributed particles. At small scales, the peak of $g\left(r\right)$ increases monotonically with concentration. (b) The same data shown on logarithmic scales. For small $r$, we observe roughly power-law behavior, which we fit to determine scaling exponents. We performed these fits between $r/{\eta }^w=15$ and 60 for $\varphi =0$, 1, and 5 ppm and between $r/{\eta }^w=40$ and 100 for $\varphi =10$, 15, and 20 ppm, as highlighted by the bold curve segments.

Figure 2

Power-law scaling exponents $\xi$ extracted from fits to the data shown in Fig. 1 as a function of polymer concentration $\varphi$, plotted on both (a) linear axes and (b) logarithmic axes. Error bars are estimated by both considering the statistical uncertainties from the fits and from adjusting the ranges over which we fit. The data are consistent with a power-law dependence of $\xi$ on $\varphi$; fitting the data gives a scaling exponent of $0.77\pm 0.04$, as shown with the dashed line.