epl draft Polymer rheology simulations at the meso- and macroscopic scale

We show that dissipative particle dynamics (DPD) can be extended to simulate polymer rheology at the same time at the fluctuating mesoscopic coarse grained polymer scale and at the macroscopic scale where flow instabilities occur. We model the visco-elasticity of polymer liquids by introducing a finite fraction of dumbbells in the standard DPD fluid. The stretching and tumbling statistics of these dumbbells is in agreement with what is known for isolated polymers in shear flows. At the same time, the model exhibits behaviour reminiscent of drag reduction in the turbulent state: as the polymer fraction increases, the onset of turbulence in plane Couette flow is pushed to higher Reynolds numbers. The method opens up the possibility to model nontrivial rheological conditions with ensuing coarse grained polymer statistics. Introduction. – The plethora of intriguing phenomena that can be observed in flows of complex fluids is attracting increasing attention among physicists. The study of polymer fluids and melts has since long occupied a central position within this field [1,2]. Typically, one is either interested in the response properties of polymeric fluids or the way they flow. The former set of problems concerns viscoelasticity of polymers and biomaterials, behaviour of single long flexible molecules in flows, etcetera [2–5]. The latter usually focuses on the differences between macroscopic flows of Newtonian and polymeric fluids in the same geometry. One such striking example is the recently discovered chaotic flows of dilute polymer solutions at very small Reynolds numbers – the so-called purely elastic turbulence [6, 7]. Another is the phenomenon of dragreduction – the observation that even minute amounts of polymer can significantly suppress Newtonian turbulence and hence reduce turbulent drag [8]. In this Letter we introduce a mesoscopic simulation method that is capable of addressing both classes of problems. Simulation methods of polymers essentially fall into two classes. On one hand there are many mesoscopic coarsegrained approaches that have mainly been developed to study the thermoand hydrodynamic properties of polymers in equilibrium and in weakly non-equilibrium situations such as an imposed small shear. Such results can, e.g., be compared with recent experimental results for the orientation statistics of single DNA molecules in solution [3, 4]. However, these models typically cannot be scaled up to simulate flow at macroscopic rheological scales. On the other hand, numerical studies of polymer rheology at macroscopically relevant scales are based almost exclusively on numerical implementations of continuum constitutive equations like the Oldroyd-B or FENEP models [1, 2]. By their very nature, these deterministic approaches only give the average behaviour, so they cannot give insight into the coupling between the macroscopic flow behaviour and the molecular properties. In this Letter, we for the first time bridge the gap between these two approaches and scales by introducing a coarse-grained Dissipative Particle Dynamics (DPD) model [9, 10] for viscoelastic flows. The model is powerful enough to exhibit both stretching and tumbling of polymers at mesoscopic scales, and proper flow behaviour at hydrodynamic scales like the dramatic polymer drag reduction of turbulence. Our approach holds an additional promise. Computational rheology still turns out to be a major challenge [11]. The main difficulty lies in the fact that the convective non-