Polymers in linear shear flow: a numerical study

– We study the dynamics of a single polymer subject to thermal fluctuations in a linear shear flow. The polymer is modeled as a finitely extendable nonlinear elastic (FENE) dumbbell. Both orientation and elongation dynamics are investigated numerically as a function of the shear strength, by means of a new efficient integration algorithm. The results are in agreement with recent experiments. Introduction. – Nowadays, thanks to the development of effective experimental techniques, it is possible to follow the motion of a single macromolecule in a flow, either laminar or turbulent [1–8, 11–18]. This is of crucial importance for applications in polymer processing [19] and biophysics [1]. Dynamical properties of biomolecules have been explored in detail (see e.g. [1–5,11–14] for DNA and [15] for chromatin) and protein–macromolecule interactions have been studied [16–18]. The formulation of theoretical models (see e.g. [19]) able to reproduce qualitatively and quantitatively these measurements represents an important step towards the understanding of single-molecule biophysics. An extensive analysis of single polymer dynamics in simple flows has been conducted in a series of papers by Chu and coworkers, Larson and coworkers and Shaqfeh and coworkers (see [1–8] and references therein). Here we mention in particular two recent papers where the statistics of orientation and conformation of long-chain molecules in linear shear flows has been studied in great detail, with a direct comparison with numerical models [9,10]. An intrinsic difficulty is represented by the large number of degrees of freedom required to describe the polymer conformation, and thus its dynamics. Nonetheless, nontrivial aspects of polymer–fluid interactions may be accounted for and even explained at a semi-quantitative level by means of simple, few degrees of freedom models. One of the simplest, yet reliable, model is the finitely extendable nonlinear elastic dumbbell (FENE) [19]. The polymer is described by its end-to-end distance vector R and the microphysical properties are essentially dumped into two parameters: 1/γ, the longest elastic relaxation time of the macromolecule, and ζ, its friction coefficient with the surrounding solvent. Nonlinear elastic