# Macro-Micro-Coupled Simulations of Dilute Viscoelastic Fluids
## 4 Discussion  
In this work, we have considered multiscale simulations of dilute polymeric solutions under homogeneous and non-homogeneous flow conditions. At the microscale, Langevin equations describing the behavior of elastic dumbbells are solved using GPUs, which allows for massively parallel simulations. Considering dumbbell equations provides more accurate information on the stretch and orientation of polymer chains, as opposed to macroscopic constitutive equations. In this way, the stretching and orientation of dumbbells are captured in a similar manner in which an experimentalist will analyze fluid behavior using scattering techniques. Under viscometric conditions of simple shear and uniaxial extension, we showed that there is a significant difference between predictions from macroscopic and mesoscopic models. These differences are exacerbated under nonlinear flow conditions. In the linear regime, dumbbells are stretched and oriented in the direction of the flow, but the distribution of lengths remains Gaussian. In the nonlinear regime, Gaussianity is lost around the same time the overshoot in the shear stress is observed. Furthermore, the PDF of dumbbell orientation shows that'molecules' are more oriented with respect to the flow in the nonlinear regime compared with molecules in the linear regime. Under capillary thinning, we investigated the effects of the Deborah number, wavenumber, and maximum extensibility on the formation of satellite drops. As the elasticity of the fluid (\(De\)) is increased, the formation of satellite droplets is inhibited. This inhibition is related to a higher tensile stress in the filament prior to the formation of the droplets, represented by a larger expansion ratio. This, in turn, hinders the reorganization of the strands that would result in a lower expansion ratio in the middle of the jet, which is what ultimately leads to the formation of droplets. The finite extensibility plays a similar role. By increasing the extensibility, the polymer becomes more elastic, suppressing droplet formation. For less elastic materials, significant pinching can be observed where the bead and string meet, as one might expect from a viscous filament. The wavenumber of perturbation, although not a material feature, plays a significant role in filament evolution. The expansion ratio shows the same trends as elastic effects, where the main stretching is observed at the bridges. In addition, smaller droplets result in a higher level of stretching in other regions of the filament. The objective of this work is to further examine and reveal the power and utility of microscopic descriptions of macromolecules. One of the primary concerns in using micro-macro multiscale simulations is computational efficiency. In homogeneous flow fields, configurations are easy to follow around due to the absence of spatial resolution. We extended the simulation capabilities to an inhomogeneous flow field, namely one-dimensional capillary thinning. The symmetry and thin film assumptions resulted in the problem being reduced to one spatial dimension. This allowed the decoupling of the dumbbell stretching in two dimensions, which simplifies computational time and effort. The goal now is to consider more general flow fields. In order to extend the solver's capabilities to other types of flow, a more careful coupling of the micro and macro  
Figure 12: Effects of different FENE parameter. Other parameters are \(\beta=0.27\), \(Oh=0.04\), \(k=0.8\), and \(De=0.8\). approaches is required, with extra limitations arising from the use of GPUs. The results of this work show that coupling a GPU solver for the Langevin equations with an efficient macroscale solver for the flow field can lead to large-scale multiscale simulations in complex flow fields. Conceptualization, M.C. and P.A.V. ; Methodology, M.C. and P.A.V. ; Software, M.C. and P.A.V. ; Writing--original draft, M.C. and P.A.V. All authors have read and agreed to the published version of the manuscript.