Accounting for the effect of internal viscosity in dumbbell models for polymeric fluids and relaxation of DNA

The coarse-graining approach is one of the most important modeling methods in research of long-chain polymers such as DNA molecules. The dumbbell model is a simple but efficient way to describe the behavior of polymers in solutions. In this paper, the dumbbell model with internal viscosity (IV) for concentrated polymeric liquids is analyzed for the steady-state and time-dependent elongational flow and steady-state shear flow. In the elongational flow case, by analyzing the governing ordinary differential equations the contribution of the IV to the stress tensor is discussed for fluids subjected to a sudden elongational jerk. In the shear flow case, the governing stochastic differential equation of the finitely extensible nonlinear elastic dumbbell model is solved numerically. For this case, the extensions of DNA molecules for different shear rates are analyzed, and the comparison with the experimental data is carried out to estimate the contribution of the effect of internal viscosity.