Deformation of a tethered polymer in uniform flow

Abstract

Static properties of a single polymer fixed at one end and subjected to a uniform flow field are investigated for several polymer models: the Gaussian chain, the freely jointed chain, and the FENE (Finitely Extensible Nonlinear Elastic) chain. By taking into account first the excluded-volume interaction and subsequently also the hydrodynamic interaction, the polymer models are gradually completed and the relevance of each effect for the polymer deformation can be identified. Results from computer simulations of these bead spring chains are compared with analytical calculations using either the conformational distribution function or blob models. To this end, in contrast to the blob model with non-draining blobs introduced for a tethered polymer by Brochard-Wyart, we here develop also a model with free-draining blobs. It turns out that a limited extensibility of the polymer – described by nonlinear spring forces in the model – leads to a flow velocity dependence of the end-to-end distance, segment density, etc. which agrees with the power law predictions of the blob model only for very long chains and in a narrow range of flow velocities. This result is important for comparison with recent experiments on DNA molecules which turn out to be still rather short in this respect. The relative importance of finite extensibility, the excluded-volume effect, and hydrodynamic interactions for polymers in flow is not fully understood at present. The simulation of reasonably long chains becomes possible even when fluctuating hydrodynamic interactions are taken into account without employing averaging procedures by introducing efficient numerical approximation schemes. At medium velocity of the uniform flow the polymer is partially uncoiled and simulations show that the effects of excluded-volume and hydrodynamic interactions are position-dependent. Both are stronger near the free end than near the tethered end of the polymer. A crossover from a nearly non-draining polymer at small flow velocities to a free-draining almost uncoiled chain at large velocities is found in the simulations. Accordingly, models assuming the polymer to be composed of either free- or non-draining subunits, like the two blob models, cannot correctly describe the extension and shape of a tethered polymer in flow, and simple power laws for the polymer extension, etc. cannot be expected.