Dynamical slowdown of polymers in laminar and random flows

Entropic characterization of the coil-stretch transition of polymers in random flows

Polymer molecules in a flow undergo a coil-stretch phase transition on an increase of the velocity gradients. Model-independent identification and characterization of the transition in a random flow has been lacking so far. Here we suggest to use the entropy of the extension statistics as a proper measure due to strong fluctuations around the transition. We measure experimentally the entropy as a function of the local Weisenberg number and show that it has a maximum, which identifies and quantifies the transition. We compare the new approach with the traditional one based on the theory using either linear Oldroyd-B or nonlinear finite extensible nonlinear elastic polymer models.

Effect of internal friction on the coil-stretch transition in turbulent flows

A polymer in a turbulent flow undergoes the coil-stretch transition when the Weissenberg number, i.e. the product of the Lyapunov exponent of the flow and the relaxation time of the polymer, surpasses a critical value. The effect of internal friction on the transition is studied by means of Brownian dynamics simulations of the elastic dumbbell model in a homogeneous and isotropic, incompressible, turbulent flow and analytical calculations for a stochastic velocity gradient. The results are explained by adapting the large deviations theory of Balkovsky et al. [Phys. Rev. Lett., 2000, 84, 4765] to an elastic dumbbell with internal viscosity. In turbulent flows, a distinctive feature of the probability distribution of polymer extensions is its power-law behaviour for extensions greater than the equilibrium length and smaller than the contour length. It is shown that although internal friction does not modify the critical Weissenberg number for the coil-stretch transition, it makes the slope of the probability distribution of the extension steeper, thus rendering the transition sharper. Internal friction therefore provides a possible explanation for the steepness of the distribution of polymer extensions observed in experiments at large Weissenberg numbers.

Stretching of single DNA molecules caused by accelerating flow on a microchip

DNA elongation induced by fluidic stress was investigated on a microfluidic chip composed of a large inlet pool and a narrow channel. Through single-DNA observation with fluorescence microscopy, the manner of stretching of individual T4 DNA molecules (166 kbp) was monitored near the area of accelerating flow with narrowing streamlines. The results showed that the DNA long-axis length increased in a sigmoidal manner depending on the magnitude of flow acceleration, or shear, along the DNA chain. To elucidate the physical mechanism of DNA elongation, we performed a theoretical study by adopting a model of a coarse-grained nonlinear elastic polymer chain elongated by shear stress due to acceleration flow along the chain direction.

Knots modify the coil-stretch transition in linear DNA polymers

We perform single-molecule DNA experiments to investigate the relaxation dynamics of knotted polymers and examine the steady-state behavior of knotted polymers in elongational fields. The occurrence of a knot reduces the relaxation time of a molecule and leads to a shift in the molecule's coil-stretch transition to larger strain rates. We measure chain extension and extension fluctuations as a function of strain rate for unknotted and knotted molecules. The curves for knotted molecules can be collapsed onto the unknotted curves by defining an effective Weissenberg number based on the measured knotted relaxation time in the low extension regime, or a relaxation time based on Rouse/Zimm scaling theories in the high extension regime. Because a knot reduces a molecule's relaxation time, we observe that knot untying near the coil-stretch transition can result in dramatic changes in the molecule's conformation. For example, a knotted molecule at a given strain rate can experience a stretch-coil transition, followed by a coil-stretch transition, after the knot partially or fully unties.

Polymer stretching in the inertial range of turbulence

We study the deformation of flexible polymers whose contour length lies in the inertial range of a homogeneous and isotropic turbulent flow. By using the elastic dumbbell model and a stochastic velocity field with nonsmooth spatial correlations, we obtain the probability density function of the extension as a function of the Weissenberg number and of the scaling exponent of the velocity structure functions. In a spatially rough flow, as in the inertial range of turbulence, the statistics of polymer stretching differs from that observed in laminar flows or in smooth chaotic flows. In particular, the probability distribution of polymer extensions decays as a stretched exponential, and the most probable extension grows as a power law of the Weissenberg number. Furthermore, the ability of the flow to stretch polymers weakens as the flow becomes rougher in space.

Impact of the Peterlin approximation on polymer dynamics in turbulent flows

We study the impact of the Peterlin approximation on the statistics of the end-to-end separation of polymers in a turbulent flow. The finitely extensible nonlinear elastic (FENE) model and the FENE model with the Peterlin approximation (FENE-P) are numerically integrated along a large number of Lagrangian trajectories resulting from a direct numerical simulation of three-dimensional homogeneous isotropic turbulence. Although the FENE-P model yields results in qualitative agreement with those of the FENE model, quantitative differences emerge. The steady-state probability of large extensions is overestimated by the FENE-P model. The alignment of polymers with the eigenvectors of the rate-of-strain tensor and with the direction of vorticity is weaker when the Peterlin approximation is used. At large Weissenberg numbers, the correlation times of both the extension and of the orientation of polymers are underestimated by the FENE-P model.

Dynamics of generalized Gaussian polymeric structures in random layered flows

We develop a formalism for the dynamics of a flexible branched polymer with arbitrary topology in the presence of random flows. This is achieved by employing the generalized Gaussian structure (GGS) approach and the Matheron-de Marsily model for the random layered flow. The expression for the average square displacement (ASD) of the center of mass of the GGS is obtained in such flow. The averaging is done over both the thermal noise and the external random flow. Although the formalism is valid for branched polymers with various complex topologies, we mainly focus here on the dynamics of the flexible star and dendrimer. We analyze the effect of the topology (the number and length of branches for stars and the number of generations for dendrimers) on the dynamics under the influence of external flow, which is characterized by their root-mean-square velocity, persistence flow length, and flow exponent α. Our analysis shows two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The influence of the topology of the GGS is unraveled in the intermediate-time regime, while the long-time regime is only weakly dependent on the topology of the polymer. With the decrease in the value of α, the magnitude of the ASD decreases, while the temporal exponent of the ASD increases in both the time regimes. Also there is an increase in both the magnitude of the ASD and the crossover time (from the subdiffusive to the superdiffusive regime) with an increase in the total mass of the polymeric structure.

Extreme-value statistics of work done in stretching a polymer in a gradient flow

We analyze the statistics of work generated by a gradient flow to stretch a nonlinear polymer. We obtain the large deviation function (LDF) of the work in the full range of appropriate parameters by combining analytical and numerical tools. The LDF shows two distinct asymptotes: "near tails" are linear in work and dominated by coiled polymer configurations, while "far tails" are quadratic in work and correspond to preferentially fully stretched polymers. We find the extreme value statistics of work for several singular elastic potentials, as well as the mean and the dispersion of work near the coil-stretch transition. The dispersion shows a maximum at the transition.

Coil-stretch transition in an ensemble of polymers in isotropic turbulence

We study the statistical properties of ensembles of polymers in isotropic turbulence numerically in the one-way coupling regime. A linear polymer chain passively convected by turbulence is modeled by a line of beads, each of which is connected by a finitely extensible nonlinear elastic force and subject to Brownian motion. We find that when the Weissenberg number Wi(η)<1, the polymer chain has a coiled configuration, while for Wi(η)>10, it remains stretched for a much longer time than the typical time scale of the fluctuating turbulent velocity gradient. Various statistical quantities characterizing the ensemble of polymers, such as the mean, variance, autocorrelation time, and probability density function of the end-to-end vector distance, indicate that the coil-stretch transition occurs at Wi(η)=3-4. We also find that this trend is insensitive to the number of beads N(b) ( N(b)=20 or N(b)=2), provided that the parameters in the model with a small number of beads are properly generated from the one with a large number of beads (i.e., using the formula of Jin and Collins). Finally, the Wi(η) effects on the alignment of the end-to-end vector versus the principal axis of the rate of strain tensor and on the polymer elongation are examined from the viewpoint of local flow topology.

Coil-stretch Transition of DNA Molecules in Slit-like Confinement

We experimentally investigate the influence of slit-like confinement on the coil-stretch transition of single DNA molecules in a homogeneous planar elongational electric field. We observe a more gradual coil-stretch transition characterized by two distinct critical strain rates for DNA in confinement, different from the unconfined case where a single critical strain rate exists. We postulate that the change in the coil-stretch transition is due to a modified spring law in confinement. We develop a dumbbell model to extract an effective spring law by following the relaxation of an initially stretched DNA. We then use this spring law and kinetic theory modeling to predict the extension and fluctuations of DNA in planar elongational fields. The model predicts that a two-stage coil-stretch transition emerges in confinement, in accord with experimental observations.

Critical slowing down in polymer dynamics near the coil-stretch transition in elongation flow

We present experimental results on relaxation dynamics of lambda-DNA and T4 polymer molecules toward a steady state in elongation flow. Strong critical slowing down (similar to the well-known effect in continuous phase transitions) in polymer relaxation near the coil-stretch transition (CST) is quantitatively investigated and found to be in good accord with predictions. For polymers with a small number of Kuhn segments the maximum of the relaxation time vs the strain rate provides precise information about the location of the CST and serves as its criterion.

Critical dynamics of vesicle stretching transition in elongational flow

We present results on the stretching of single tubular vesicles in an elongation flow toward dumbbell shapes, and on their relaxation. A critical strain rate epsilonc exists; for strain rates epsilon<epsilonc, the vesicle remains tubular but fluctuates, though its steady state extension increases with the strain rate epsilon. Above epsilonc, first a shape transition to dumbbell occurs, and then high order shape modes become unstable, leading to a pearling state. We have quantitatively characterized the transition and found a scaling of epsilonc with the system parameters. A remarkable feature of vesicle tube behavior around the critical point is a slowdown of the vesicle relaxation to the final extended state in the vesicle stretching. Such feature is similar to that found in continuous phase transitions and to the critical effects recently observed for polymer molecules near the coil-stretch transition in elongation flow.

Drag enhancement with polymers

Drag on a cylinder can be enhanced in the presence of polymers. This enhancement is directly related to the interaction of the polymers with the flow around the obstacle. The presence of the polymers modifies the flow in the vicinity of the cylinder giving rise to a band of higher shear, large molecular elongations and large velocity fluctuations. The measured drag on the cylinder is directly related to the modification of the flow field by the presence of the polymers.