# Saturation of turbulent drag reduction in dilute polymer solutions

@article{Benzi2004SaturationOT, title={Saturation of turbulent drag reduction in dilute polymer solutions}, author={Roberto Benzi and Victor S L’vov and Itamar Procaccia and Vasil Tiberkevich}, journal={EPL}, year={2004}, volume={68}, pages={825-831} }

Drag reduction by polymers in turbulent wall-bounded flows exhibits universal and non-universal aspects. The universal maximal mean-velocity profile was explained in a recent theory. The saturation of this profile and the crossover back to the Newtonian plug are non-universal, depending on Reynolds number e, concentration of polymer cp and the degree of polymerization Np. We explain the mechanism of saturation stemming from the finiteness of extensibility of the polymers, predict its dependence…

## One Citation

### Drag reduction by polymers in wall bounded turbulence.

- PhysicsPhysical review letters
- 2004

The phenomenology of the "maximum drag reduction asymptote" is developed which is the maximum drag reduction attained by polymers in turbulent wall-bounded flows.

### Identification and calculation of the universal asymptote for drag reduction by polymers in wall bounded turbulence.

- PhysicsPhysical review letters
- 2005

This insight rationalizes the universality of the MDR and provides a maximum principle which allows an ab initio calculation of the parameters in this law without any viscoelastic experimental input.

### Maximum drag reduction asymptotes and the cross-over to the Newtonian plug

- EngineeringJournal of Fluid Mechanics
- 2006

We employ the full FENE-P model of the hydrodynamics of a dilute polymer solution to derive a theoretical approach to drag reduction in wall-bounded turbulence. We recapture the results of a recent…

### Turbulent drag reduction with polymer additive in rough pipes

- EngineeringJournal of Fluid Mechanics
- 2009

Friction factor of drag-reducing flow with presence of polymers in a rough pipe has been investigated based on the eddy diffusivity model, which shows that the ratio of effective viscosity caused by…

### Drag reduction by compressible bubbles.

- Engineering, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

It is shown that the dynamics of bubbles and their effect on the compressibility of the mixture can lead to a much higher drag reduction.

### Drag Reduction Characteristics of Micro-Fibrillated Cellulose Suspensions

- Engineering
- 2011

Drag reduction characteristics of micro-fibrillated cellulose (MFC) suspensions are evaluated in a fully developed turbulent pipe flow. Drag reduction is estimated from pressure drop measurements…

### Remarkable drag reduction in non-affine viscoelastic turbulent flows

- Engineering
- 2013

We carry out a direct numerical simulation (DNS) study which aims to reveal the mechanism of turbulence drag reduction (DR) in polymer diluted flows. The polymer chains are modeled as elastic…

### Phenomenology of wall-bounded Newtonian turbulence.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

The model offers an analytic description of the profiles of the mean velocity and the correlation functions of velocity fluctuations in the entire boundary region, from the viscous sublayer, through the buffer layer, and further into the log-law turbulent region.

### Tumbling, bending, stretching : particles in laminar and chaotic flows

- Physics
- 2017

Particles, when subjected into a flow, may display preferred orientations and a variety of deformations depending on their geometry and elasticity and the flow velocity field. Flows can conversely be…

### Simple analytical model for entire turbulent boundary layer over flat plane: from viscous and mixing layers to turbulent logarithmic region

- Physics, Engineering
- 2004

We discuss a simple analytical model of the turbulent boundary layer (TBL) over flat plane. The model offers an analytical description of the profiles of mean velocity and turbulent activity in the…

## References

SHOWING 1-8 OF 8 REFERENCES

### Drag reduction by polymers in wall bounded turbulence.

- PhysicsPhysical review letters
- 2004

The phenomenology of the "maximum drag reduction asymptote" is developed which is the maximum drag reduction attained by polymers in turbulent wall-bounded flows.

### Drag reduction by a linear viscosity profile.

- EngineeringPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

It is shown, using direct numerical simulations, that a linear viscosity profile indeed reduces the drag in agreement with the theory and in close correspondence with direct simulations of the FENE-P model at the same flow conditions.

### Drag reduction by polymers in turbulent channel flows: Energy redistribution between invariant empirical modes.

- Physics, EngineeringPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

There is an enhancement of theEnergy containing modes in the viscoelastic flow compared to the Newtonian one; drag reduction is seen in the energy containing modes rather than the dissipative modes, as proposed in some previous theories.

### Polymer stress tensor in turbulent shear flows.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

It is demonstrated that the influence of the polymers on the balance of energy and momentum can be accurately described by an effective polymer viscosity that is proportional to the cross-stream component of the elastic stress tensor.

### AIChE J

- 21, 625
- 1975

### Phys

- Rev. Lett, 89 088302-1
- 2002

### Phys

- Rev. Lett. 78, 239
- 1997

### in Proceedings of the International Congress of Rheology Amsterdam Vol 2

- 0.135-141
- 1949