The coarse-graining approach is one of the most important mod- eling methods in research of long-chain polymers such as DNA molecules. The dumbbell model is a simple but e±cient 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 °ow. In the elongational flow case, by analyzing the governing ordinary di®erential equations the contribution of the IV to the stress tensor is discussed for fluids subjected to a sudden elongational jerk. In the shear °ow 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 e®ect of internal viscosity.
Yang, Xiao-Dong and Melnik, Roderick V.N., "Accounting for the Effect of Internal Viscosity in Dumbbell Models for Polymeric Fluids and Relaxation of DNA" (2007). Mathematics Faculty Publications. 32.