How hydrodynamic interactions alter polymer stretching in turbulence

Abstract

Hydrodynamic interactions (HI) between segments of a polymer have long been known to strongly affect polymer stretching in laminar viscometric flows. Yet the role of HI in fluctuating turbulent flows remains unclear. Using Brownian dynamics simulations, we examine the stretching dynamics of bead-spring chains with inter-bead HI, as they are transported in a homogeneous isotropic turbulent flow (within the ultra-dilute, one-way coupling regime). We find that HI-endowed chains exhibit a steeper coil-stretch transition as the elastic relaxation time is increased, i.e., HI cause less stretching of stiff polymers and more stretching of moderately to highly elastic polymers. The probability distribution function of the end-to-end extension is also modified, with HI significantly limiting the range of extensions over which a power-law range appears. On quantifying the repeated stretching and recoiling of chains by computing persistence time distributions, we find that HI delays migration between stretched and coiled states. These effects of HI, which are consistent with chains experiencing an effective conformation-dependent drag, are sensitive to the level of coarse-graining in the bead-spring model. Specifically, an HI-endowed dumbbell, which cannot form a physical coil, is unable to experience the hydrodynamic shielding effect of HI. Our results highlight the importance of incorporating an extension-dependent drag force in dumbbell-based simulations of turbulent polymer solutions. To develop and test such an augmented dumbbell model, we propose the use of a time-correlated Gaussian random flow, in which the turbulent stretching statistics are shown to be well-approximated.