Spectra of turbulence in dilute polymer solutions

Fouxon, A.; Лебедев, В. В.

doi:10.1063/1.1577563

Cited by 183 publications

(226 citation statements)

References 29 publications

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“…The existing theories of drag reduction all share the same conceptual feature: They interpret the resulting flow as a modified form of ordinary Newtonian shear flow turbulence, with its properties being determined by the balance between elastic and viscous stresses (11,15,16,30,31). Theoretical studies of the influence of polymers on turbulence in unbounded (30-32) flows, however, showed some qualitative differences from Newtonian turbulence; in one case (32), the measured power spectra more closely resembled those found in elastic turbulence than those in Newtonian flows.…”

Section: Elasto-inertial Turbulencementioning

confidence: 99%

Elasto-inertial turbulence

Samanta

Dubief

Holzner

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

200

326

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Turbulence is ubiquitous in nature yet even for the case of ordinary Newtonian fluids like water our understanding of this phenomenon is limited. Many liquids of practical importance however are more complicated (e.g. blood, polymer melts or paints), they exhibit elastic as well as viscous characteristics and the relation between stress and strain is nonlinear. We here demonstrate for a model system of such complex fluids that at high shear rates turbulence is not simply modified as previously believed but it is suppressed and replaced by a new type of disordered motion, elasto-inertial turbulence (EIT). EIT is found to occur at much lower Reynolds numbers than Newtonian turbulence and the dynamical properties differ significantly. In particular the drag is strongly reduced and the observed friction scaling resolves a longstanding puzzle in non-Newtonian fluid mechanics regarding the nature of the so-called maximum drag reduction asymptote. Theoretical considerations imply that EIT will arise in complex fluids if the extensional viscosity is sufficiently large

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Section: Elasto-inertial Turbulencementioning

confidence: 99%

Elasto-inertial turbulence

Samanta

Dubief

Holzner

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

200

326

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“…4 could exclude the possible temporally random but spatially smooth chaotic flow normally observed at very low Re, which requires E( f ) to decay faster than f −3 . 32,33 Hence, although it is not clear if the flow forced at V = 8 V p-p is turbulent or not, the flow forced at V = 20 V p-p should be turbulent, considering that there are multiscale eddies corresponding to the wide bandwidth from 1 to 300 Hz, where E( f ) has no sharp decrease, another typical feature of turbulence.…”

Section: Multiscale Eddiesmentioning

confidence: 99%

There can be turbulence in microfluidics at low Reynolds number

2014

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Turbulence is commonly viewed as a type of macroflow, where the Reynolds number (Re) has to be sufficiently high. In microfluidics, when Re is below or on the order of 1 and fast mixing is required, so far only chaotic flow has been reported to enhance mixing based on previous publications since turbulence is believed not to be possible to generate in such a low Re microflow. There is even a lack of velocimeter that can measure turbulence in microchannels. In this work, we report a direct observation of the existence of turbulence in microfluidics with Re on the order of 1 in a pressure driven flow under electrokinetic forcing using a novel velocimeter having ultrahigh spatiotemporal resolution. The work could provide a new method to control flow and transport phenomena in lab-on-a-chip and a new perspective on turbulence.

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“…Obviously, such behavior can not be observed in Newtonian liquids, where the flow should be laminar, so the chaotic flow is generated by the elastic instabilities of polymer solution. The dynamics of polymers and possible mechanisms, explaining the chaotic state were studied in the recent theoretical works [6,7,8]. It was proposed that elastic instabilities occur because of elongation of a single polymer in external flows.…”

mentioning

confidence: 99%

Polymer dynamics in chaotic flows with a strong shear component

Turitsyn

2007

J. Exp. Theor. Phys.

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We consider the internal dynamics of the polymer molecule which is injected in the chaotic flow with strong mean shear component. The flow geometry corresponds to the recent experiments on the elastic turbulence (Groisman, Steinberg 2000). The passive polymer in such flows experiences aperiodic tumbling. We present a detailed study of the statistical properties of such polymer dynamics. First we obtain the stationary probability distribution function of the polymer orientation. Secondly we find the distribution of the time periods between consequent events of tumbling, and finally we find the tails of the polymer size distribution.PACS numbers: 83.80. Rs,47.27.Nz Hydrodynamics and rheology of dilute polymer solutions has attracted much theoretical and experimental attention recently. Addition of small amount of polymers to ordinary liquid leads to crucial changes of liquid properties. One of the most famous effects of this type is the phenomenon of drag reduction. The addition of few parts per million of long-chain polymer molecules produces a dramatic reduction of the friction drag. Although this effect was first observed by Toms in 1949 [1], there is still no rigorous theory, explaining the phenomena. The qualitative description was proposed by Lumley [2,3], but no quantitative theory is available. Another spectacular phenomena, observed in dilute polymer solutions is the effect of elastic turbulence, discovered recently by Groisman and Steinberg [4,5]. In this experiment a chaotic fluid motion was observed in the system with small Reynolds number Re ≪ 1. Obviously, such behavior can not be observed in Newtonian liquids, where the flow should be laminar, so the chaotic flow is generated by the elastic instabilities of polymer solution. The dynamics of polymers and possible mechanisms, explaining the chaotic state were studied in the recent theoretical works [6,7,8]. It was proposed that elastic instabilities occur because of elongation of a single polymer in external flows. The analysis of the single polymer dynamics in chaotic flows, shows that the transition between two qualitatively different types of behavior of polymers can be observed in such system. This transition is called coil-stretch transition. It separates the dynamics in weak flows, where polymer molecules remain in coiled state most of the time, and strong flows, where the molecules become substantially elongated. The measure of the flow strength is given by the Weissenberg number which is the product of the characteristic velocity gradient and the polymer relaxation time. More precisely the Weissenberg number is defined as Wi = λτ , where λ is the largest Lyapunov exponent, associated with the flow, and τ is the relaxation time of the slowest polymer excitation mode. The coil-stretch transition occurs at Wi = 1. With the development of novel optical methods a number of high quality experimental observations focusing on resolving dynamics of individual polymers (DNA molecules) subjected to a non-homogeneous flow have been reported [9,10,11,1...

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Spectra of turbulence in dilute polymer solutions

Cited by 183 publications

References 29 publications

Elasto-inertial turbulence

Elasto-inertial turbulence

There can be turbulence in microfluidics at low Reynolds number

Polymer dynamics in chaotic flows with a strong shear component

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