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.Comment: 7 pages, see also the preceding paper (http://arxiv.org/nlin.CD/0503028

Single polymer dynamics: coil-stretch transition in a random flow

By quantitative studies of statistics of polymer stretching in a random flow and of a flow field we demonstrate that the stretching of polymer molecules in a 3D random flow occurs rather sharply via the coil-stretch transition at the value of the criterion close to theoretically predicted.Comment: 4 pages, 5 figure

Dynamics of threads and polymers in turbulence: power-law distributions and synchronization

We study the behavior of threads and polymers in a turbulent flow. These objects have finite spatial extension, so the flow along them differs slightly. The corresponding drag forces produce a finite average stretching and the thread is stretched most of the time. Nevertheless, the probability of shrinking fluctuations is significant and is known to decay only as a power-law. We show that the exponent of the power law is a universal number independent of the statistics of the flow. For polymers the coil-stretch transition exists: the flow must have a sufficiently large Lyapunov exponent to overcome the elastic resistance and stretch the polymer from the coiled state it takes otherwise. The probability of shrinking from the stretched state above the transition again obeys a power law but with a non-universal exponent. We show that well above the transition the exponent becomes universal and derive the corresponding expression. Furthermore, we demonstrate synchronization: the end-to-end distances of threads or polymers above the transition are synchronized by the flow and become identical. Thus, the transition from Newtonian to non-Newtonian behavior in dilute polymer solutions can be seen as an ordering transition.Comment: 13 pages, version accepted to Journal of Statistical Mechanic

Stretching of polymers around the Kolmogorov scale in a turbulent shear flow

We present numerical studies of stretching of Hookean dumbbells in a turbulent Navier-Stokes flow with a linear mean profile, =Sy. In addition to the turbulence features beyond the viscous Kolmogorov scale \eta, the dynamics at the equilibrium extension of the dumbbells significantly below eta is well resolved. The variation of the constant shear rate S causes a change of the turbulent velocity fluctuations on all scales and thus of the intensity of local stretching rate of the advecting flow. The latter is measured by the maximum Lyapunov exponent lambda_1 which is found to increase as \lambda_1 ~ S^{3/2}, in agreement with a dimensional argument. The ensemble of up to 2 times 10^6 passively advected dumbbells is advanced by Brownian dynamics simulations in combination with a pseudospectral integration for the turbulent shear flow. Anisotropy of stretching is quantified by the statistics of the azimuthal angle $\phi$ which measures the alignment with the mean flow axis in the x-y shear plane, and the polar angle theta which determines the orientation with respect to the shear plane. The asymmetry of the probability density function (PDF) of phi increases with growing shear rate S. Furthermore, the PDF becomes increasingly peaked around mean flow direction (phi= 0). In contrast, the PDF of the polar angle theta is symmetric and less sensitive to changes of S.Comment: 16 pages, 14 Postscript figures (2 with reduced quality