A new constitutive model for the analysis of semi-flexible polymers with internal viscosity

Abstract

The analysis of dynamics of semi-flexible polymers, such as DNA molecules, is an important multiscale problem with a wide range of applications in science and bioengineering. In this contribution, we show how accounting for internal viscosity in dumbbell-type models may render physically plausible results with minimal computational cost. We focus our attention on the cases of steady shear and extensional flows of polymeric solutions. First, the tensors with moments other than the second order moment are approximated. Then, the nonlinear algebraic equation for the second moment conformation tensor is solved. Finally, substituting the resulting conformation tensor into the Kramers equation of Hookean spring force, the constitutive equations for the model are obtained. The shear material properties are discussed in the context of different internal viscosities and our computational results are compared with the results of other methods applicable for high shear or extensional rates. © Springer-Verlag Berlin Heidelberg 2007.