# Turbulent dynamics of polymer solutions

@article{Balkovsky1999TurbulentDO, title={Turbulent dynamics of polymer solutions}, author={Balkovsky and Fouxon and Lebedev}, journal={Physical review letters}, year={1999}, volume={84 20}, pages={ 4765-8 } }

We study properties of dilute polymer solutions. The probability density function (PDF) of polymer end-to-end extensions R in turbulent flows is examined. We show that if the value of the Lyapunov exponent lambda is smaller than the inverse molecular relaxation time 1/tau then the PDF has a strong peak at the equilibrium size R0 and a power tail at R>>R0. This confirms and extends the results of J. L. Lumley [Symp. Math. 9, 315 (1972)]. There is no essential influence of polymers on the flow in…

## 82 Citations

### Turbulence of polymer solutions.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

The existence of a critical value of the Reynolds number is shown, which separates two different regimes of high-Reynolds-number turbulence in dilute polymer solutions, characterized by the strong back reaction of polymers on the flow.

### Polymer Transport in Random Flow

- Physics
- 2005

Abstract.The dynamics of polymers in a random smooth flow is investigated in the framework of the Hookean dumbbell model. The analytical expression of the time-dependent probability density function…

### Polymers in turbulence: stretching statistics and the role of extreme strain-rate fluctuations

- Physics
- 2023

Polymers in a turbulent ﬂow are stretched out by the ﬂuctuating velocity gradient and exhibit a broad distribution of extensions 𝑅 ; the stationary probability distribution function (p.d.f.) of 𝑅…

### Dynamical slowdown of polymers in laminar and random flows.

- Materials SciencePhysical review letters
- 2006

It is shown that a pronounced dynamical slowdown occurs in the vicinity of the coil-stretch transition, especially when the dependence on polymer conformation of the drag is accounted for, resulting in the observation of conformation hysteresis.

### Statistics of polymer extensions in turbulent channel flow.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

Direct numerical simulations of turbulent channel flow with passive Lagrangian polymers investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow.

### Polymer stretching in the inertial range of turbulence.

- PhysicsPhysical review. E
- 2016

In a spatially rough flow, the statistics of polymer stretching differs from that observed in laminar flows or in smooth chaotic flows, and the ability of the flow to stretch polymers weakens as the flow becomes rougher in space.

### Numerical Study of Polymers in Turbulent Channel Flow

- Physics
- 2010

The phenomenon of drag reduction by polymers in turbulent flow has beenstudied over the last 60 years. New insight have been recently gained by meansof numerical simulation of dilute polymer solution…

### Fluid acceleration in the bulk of turbulent dilute polymer solutions

- Physics
- 2008

We studied the effects of long-chain polymers on the small scales of turbulence by experimental measurements of Lagrangian accelerations in the bulk of turbulent flows of dilute polymer solutions.…

## References

SHOWING 1-10 OF 27 REFERENCES

### Mechanical models of dilute polymer solutions in strong flows

- Physics
- 1977

In strong flows, such as turbulence, it is suggested that randomly coiled macromolecules might become nearly fully extended. To investigate this extended state, four models are considered which show…

### Dynamic Properties of an Extended Polymer in Solution

- Physics
- 1999

Extended polymers are relevant in a variety of situations ranging from the classic coil-stretch problem to recent single molecule polymer experiments with DNA. We present theoretical calculations and…

### Polymer stretching by turbulence

- PhysicsPhysical review letters
- 2000

The stretching of a polymer chain by a large-scale chaotic flow is considered. The steady state which emerges as a balance of the turbulent stretching and anharmonic resistance of the chain is…

### The dynamics of partially extended single molecules of DNA

- PhysicsNature
- 1997

This work finds that the motion of the DNA can be described by linearly independent normal modes, and it is shown that the spectrum of relaxation times obeys a power law.

### Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients

- Physics
- 1974

Because the hydrodynamic interactions are reduced by stretching, a solute polymer coil should unwind abruptly when a certain critical value of the velocity gradient is reached. Depending on the…

### Drag reduction in turbulent flow by polymer additives

- Physics
- 1973

A brief survey is given of the drag reduction phenomenon, emphasizing the aspects which must be explained by any theory: onset, the existence of intrinsic drag reduction, the Newtonian plug,…

### Drag Reduction by Additives

- Physics
- 1969

An examination is made of the experimental evidence for the reduction of skin friction in dilute solutions of high molecular weight linear polymers below that of the solvent alone. Inferences are…

### Statistics of a passive scalar advected by a large-scale two-dimensional velocity field: Analytic solution.

- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995

The change of variables that allows one to map the matrix problem onto a scalar one is found and to prove the central limit theorem for the stretching rate statistics, valid for any finite correlation time of the velocity field.

### Small-Scale Turbulent Dynamo

- Physics
- 1999

Kinematic dynamo theory is presented here for turbulent conductive fluids. We describe how inhomogeneous magnetic fluctuations are generated below the viscous scale of turbulence where the spatial…

### Relaxation of a single DNA molecule observed by optical microscopy.

- BiologyScience
- 1994

A rescaling analysis showed that most of the relaxation curves had a universal shape and their characteristic times (lambda t) increased as lambda t approximately L 1.65 +/- 0.13, in qualitative agreement with the theoretical prediction of dynamical scaling.