arXiv subjects

Victor Steinberg

Publications and source records attributed to Victor Steinberg.

At least 19 recordsLinked to original sources

arXiv2024

Mechanism of stochastic resonance in viscoelastic channel flow

We have recently discovered stochastic resonance (SR) in chaotic inertia-less viscoelastic channel flow. SR appears just above a pure elastic instability at a critical Weissenberg number, $Wi_c=150$, of a transition regime. In this lower sub-region up to $Wi\sim 300$, only the streamwise velocity, $u$, exhibits a chaotic spectrum, $E_u$, while the spanwise velocity continues to exhibit white noise, verified by its flat spectrum, $E_w$, accompanied by weak intensity elastic waves. However, SR vanishes at the upper limit at $Wi\sim 300$, when $E_w$ becomes chaotic, indicating $Wi$ as the control parameter. Here we clarify the mechanism of SR emergence by validating the control parameters, namely $Wi$ and the rms velocity fluctuations, $u_{rms}$, measured at multiple channel locations, which determine the range of SR existence. Our experiments verify three key ingredients of the SR mechanism: chaotic $E_u$, white noise $E_w$, and weak elastic waves, which are consistent with three constituents of autonomous dynamical systems exhibiting SR.

physics.flu-dyn↗

arXiv2024

From laminar to chaotic flow via stochastic resonance in viscoelastic channel flow

Recent research indicates that low-inertia viscoelastic channel flow experiences supercritical non-normal mode elastic instability from laminar to sustained chaotic flow due to finite-size perturbations. The challenge of this study is to elucidate a realization of such a pathway when the intensity of the elastic wave is too low to amplify velocity fluctuations above the instability onset. The study identifies two subregions in the transition flow regime at Weissenberg number $Wi>Wi_c$, the instability onset. In the lower subregion at $Wi_c\leq Wi\leq 300$, we discover periodic spikes in the streamwise velocity time series $u(t)$ that appear in the chaotic power spectrum as low-frequency, high-intensity peaks resembling stochastic resonance (SR). In contrast, the spanwise velocity power spectrum, $E_w$, remains flat with low-intensity, noisy, and broad elastic wave peaks. The spikes significantly distort the probability density function of $u$, initiating and amplifying random streaks and wall-normal vorticity fluctuations. The SR appearance is similar to dynamical systems where chaotic attractor and limit cycle interact with external white noise. This similarity is confirmed by presenting a phase portrait in two subregions of the transition regime. In the upper subregion at $Wi>400$ the periodic spikes disappear and $E_w$ becomes chaotic with a large intensity elastic wave sufficient to self-organize and synchronize the streaks into cycles and to amplify the wall normal vorticity according to a recently proposed mechanism.

physics.flu-dyn↗

arXiv2023

Polymer stretching in laminar and random flows: entropic characterization

Polymers in nonuniform flows undergo strong deformation, which in the presence of persistent stretching can result in the coil-stretch transition. This phenomenon has been characterized by using the formalism of nonequilibrium statistical mechanics. In particular, the entropy of the polymer extension reaches a maximum at the transition. We extend the entropic characterization of the coil-stretch transition by studying the differential entropy of the polymer fractional extension in a set of laminar and random velocity fields that are benchmarks for the study of polymer stretching in flow. In the case of random velocity fields, a suitable description of the transition is obtained by considering the entropy of the logarithm of the extension instead of the entropy of the extension itself. Entropy emerges as an effective tool for capturing the coil-stretch transition and comparing its features in different flows.

cond-mat.soft↗

arXiv2022

Re-laminarization of elastic turbulence

We report frictional drag reduction and a complete flow re-laminarization of elastic turbulence (ET) at vanishing inertia in a viscoelastic channel flow past an obstacle. We show that intensity of observed elastic waves and wall-normal vorticity correlate well with the measured drag above the ET onset. Moreover, we find that the elastic wave frequency grows with Weissenberg number, and at sufficiently high frequency it causes decay of the elastic waves, resulting in ET attenuation and drag reduction. Thus, this allows us to substantiate a physical mechanism, involving interaction of elastic waves with wall-normal vorticity fluctuations, leading to the drag reduction and re-laminarization phenomena at low Reynolds number.

physics.flu-dyn↗

arXiv2022

Elastic instability in a straight channel of viscoelastic flow without prearranged perturbations

We report experimental results on elastic instability in a viscoelastic channel shear flow due to only a natural non-smoothed inlet and small holes along the channel for pressure measurements. We show that non-normal mode instability results in elastic waves and chaotic flow self-organized into periodically cycled stream-wise streaks synchronized by elastic wave frequency. The chaotic flow persists above the transition with increasing $Wi$ further into elastic turbulence and drag reduction regimes. Thus, we resolve the recent puzzle whether strong prearranged perturbations are necessary to get an elastic instability in parallel shear viscoelastic flow. Moreover, flow resistance, velocity spectra decay, and elastic wave speed reveal the same scaling with Wi as obtained in the case of strong disturbances. The remarkable result is that all scaling behavior and streaks are found in the entire channel with small attenuation, in sharp contrast to the flow with strong prearranged perturbations.

physics.flu-dyn↗

arXiv2022

Splitting of localized disturbances in viscoelastic channel flow

We examine the response of an inertia-less viscoelastic channel flow to localized perturbations. A simplified model shows that the non-linear interaction between the velocity and elastic stress fields can split an initial pulsed disturbance into two separate pulses if the initial disturbance and the base elastic stress are sufficiently high. In accordance, we demonstrate that a transition to a pulse-splitting regime can be achieved experimentally. These results suggest a possible new direction for studying the elastic instability of viscoelastic channel flows at high elasticity through the growth of localized perturbations.

physics.flu-dyn↗

arXiv2021

Non-modal elastic instability and elastic waves in weakly perturbed channel flow

In this paper, we present experimental results and reveal that strong perturbations are not necessary for elastic instability to occur in straight-channel, inertialess, visco-elastic flows at high elasticity. We show that a non-normal mode bifurcation is followed by chaotic fluctuations, self-organized as stream-wise streaks, and elastic waves due to weak disturbances generated by a small cavity at the center of the top channel wall. The chaotic flow persists in the transition, elastic turbulence, and drag reduction regimes, in agreement with previous observations for the case of strong perturbations at the inlet. Furthermore, the elastic waves we observe propagate in the span-wise direction, which allows to confirm the elastic waves linear dispersion relation directly for the first time. In addition, the span-wise propagating elastic wave's velocity depends on $\mathrm{Wi}$ with the same scaling that was previously observed for stream-wise propagating waves, although their velocity magnitude is significantly smaller than what was previously observed for the stream-wise ones.

physics.flu-dyn↗

arXiv2021

A first coherent structure in elasto-inertial turbulence

Two dimensional channel flow simulations of FENE-P fluid in the elasto-inertial turbulence regime reveal distinct regimes ranging from chaos to a steady travelling wave which takes the form of an arrowhead structure. This coherent structure provides new insights in the polymer/flow interactions driving EIT, which are observed in a set of controlled numerical experiments and the study of transfer between elastic and turbulent kinetic energy.

physics.flu-dyn↗

arXiv2021

Perspectives on viscoelastic flow instabilities and elastic turbulence

Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with the hallmarks of turbulence -- even though the effective Reynolds numbers may be $O(1)$ or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences.

physics.flu-dyn↗

arXiv2020

Elastically driven Kelvin-Helmholtz-like instability in planar channel flow

Kelvin-Helmholtz instability (KHI) is widely spread in nature on scales from micrometer up to Galactic one. This instability refers to the growth of perturbation of an interface between two parallel streams of Newtonian fluids with different velocities and densities, destabilized by shear strain and stabilized by density stratification with the heavier fluid at the bottom. Here, we report the discovery of the purely elastic KH-like instability in planar straight channel flow of viscoelastic fluid, which is theoretically considered to be stable. However, despite the remarkable similarity to the Newtonian KHI temporal interface dynamics, the elastic KHI reveals qualitatively different instability mechanism. Indeed, the velocity difference across the interface strongly fluctuates and non-monotonically varies in time due to energy pumping by elastic waves, detected in the flow. A correlation of the elastic wave intensity and efficiency of the elastic KHI in different regimes suggests that the competition between the destabilizing factor of the elastic waves and the stabilizing effect of the elastic stress difference generated by the velocity difference at the interface is the novel instability mechanism of the elastic KHI.

physics.flu-dyn↗

arXiv2020

Universal coherent structures of elastic turbulence in straight channel with viscoelastic fluid flow

In the present study, we investigated flow structures and properties of elastic turbulence in straight 2D channel viscoelastic fluid flow and tested earlier observations. We discovered self-organized cycling process of weakly unstable coherent structures (CSs) of co-existing streaks and stream-wise vortices, with the former being destroyed by Kelvin-Helmholtz-like instability resulting in chaotic structures. The sequence periodically repeats itself leading to stochastically steady state. This self-sustained process (SSP) remarkably resembles one investigated theoretically and experimentally for Newtonian turbulence in straight channel flow. The unexpected new ingredient is the observation of elastic waves, which finds to be critical for existence of CSs and SSP generation due to energy pumping from large to smaller scales preceding sharp power-law decay in elastic turbulence energy spectrum. The reported finding suggests the universality of CSs in transition to turbulence via self-organized cycling (SSP) in linearly stable plane shear flows of both elastic and Newtonian fluids.

physics.flu-dyn↗

arXiv2019

Stokes flow analogous to viscous electron current in graphene

Electron transport in two-dimensional conducting materials such as graphene, with dominant electron-electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the classical Ohm's law. The transport behavior of these materials is best described by low Reynolds number hydrodynamics, where the constitutive pressure-speed relation is Stoke's law. Here we report evidence of such vortices observed in a viscous flow of Newtonian fluid in a microfluidic device consisting of a rectangular cavity$-$analogous to the electronic system. We extend our experimental observations to elliptic cavities of different eccentricities, and validate them by numerically solving bi-harmonic equation obtained for the viscous flow with no-slip boundary conditions. We verify the existence of a predicted threshold at which vortices appear. Strikingly, we find that a two-dimensional theoretical model captures the essential features of three-dimensional Stokes flow in experiments.

physics.flu-dyn↗

arXiv2019

Elastic Alfven waves in elastic turbulence

Speed of sound waves in gases and liquids is governed by medium compressibility. There exists another type of non-dispersive waves which speed depends on stress instead of medium elasticity. A well-known example is the Alfven wave propagating, with a speed determined by a magnetic tension, in plasma permeated by a magnetic field. Later, an elastic analog of the Alfven waves has been predicted in a flow of dilute polymer solution, where elastic stress engendered by polymer stretching determines the elastic wave speed. Here, we present quantitative evidence of elastic Alfven waves observed in elastic turbulence of a viscoelastic creeping flow between two obstacles hindering a channel flow. The key finding in the experimental proof is a nonlinear dependence of the elastic wave speed $c_{\mathrm{el}}$ on Weissenberg number $\mathrm{Wi}$, which deviates from the prediction based on a model of linear polymer elasticity.

physics.flu-dyn↗

arXiv2018

Mixing layer instability and vorticity amplification in a creeping viscoelastic flow

We report quantitative evidence of mixing-layer elastic instability in a viscoelastic fluid flow between two widely spaced obstacles hindering a channel flow at $Re\ll1$ and $Wi\gg1$. Two mixing layers with nonuniform shear velocity profiles are formed in the region between the obstacles. The mixing-layer instability arises in the vicinity of an inflection point on the shear velocity profile with a steep variation in the elastic stress. The instability results in an intermittent appearance of small vortices in the mixing layers and an amplification of spatio-temporal averaged vorticity in the elastic turbulence regime. The latter is characterized through scaling of friction factor with $Wi$, and both pressure and velocity spectra. Furthermore, the observations reported provide improved understanding of the stability of the mixing layer in a viscoelastic fluid at large elasticity, i.e. $Wi\gg1$ and $Re\ll1$, and oppose the current view of suppression of vorticity solely by polymer additives.

physics.flu-dyn↗

arXiv2018

Drag enhancement and drag reduction in viscoelastic flow

Creeping flow of polymeric fluid without inertia exhibits elastic instabilities and elastic turbulence accompanied by drag enhancement due to elastic stress produced by flow-stretched polymers. However, in inertia-dominated flow at high $\mbox{Re}$ and low fluid elasticity $El$, a reduction in turbulent frictional drag is caused by an intricate competition between inertial and elastic stresses. Here, we explore the effect of inertia on the stability of viscoelastic flow in a broad range of control parameters $El$ and $(\mbox{Re}, \mbox{Wi})$. We present the stability diagram of observed flow regimes in $\mbox{Wi}-\mbox{Re}$ coordinates and find that instabilities' onsets show unexpectedly non-monotonic dependence on $El$. Further, three distinct regions in the diagram are identified based on $El$. Strikingly, for high elasticity fluids we discover a complete relaminarization of flow at Reynolds number of the order of unity, different from a well-known turbulent drag reduction. These counterintuitive effects may be explained by a finite polymer extensibility and a suppression of vorticity at high $\mbox{Wi}$. Our results call for further theoretical and numerical development to uncover the role of inertial effect on elastic turbulence in a viscoelastic flow.

physics.flu-dyn↗

arXiv2018

Precise measurements of torque in von Karman swirling flow driven by a bladed disk

Scrupulous measurements and detailed data analysis of the torque in a swirling turbulent flow driven by counter-rotating bladed disks reveals an apparent breaking of the law of similarity. Potentially, such breakdown could arise from several possible factors, including dependence on dimensionless numbers other that $Re$ or velocity coupling to other fields such as temperature. However, careful redesign and calibration of the experiment showed that this unexpected result was due to background errorscaused by minute misalignments which lead to a noisy and irreproducible torque signal at low rotation speeds and prevented correct background subtraction normally ascribed to frictional losses. An important lesson to be learnt is that multiple minute misalignments can nonlinearly couple to the torque signal and provide a dc offset that cannot be removed by averaging. That offset can cause the observed divergence of the friction coefficient C_f from its constant value observed in the turbulent regime. To minimize the friction and misalignments, we significantly modified the experimental setup and carried out the experiment with one bladed disk where the disk, torque meter and motor shaft axes can be aligned with significantly smaller error, close to the torque meter resolution. As a result we made precise measurements with high resolution and sensitivity of the small torques produced for low rotation speeds for several water-glycerin solutions of different viscosities and confirmed the similarity law in a wide range of Re in particular in low viscosity fluids.

physics.flu-dyn↗

arXiv2017

On the role of initial velocities in pair dispersion in a microfluidic chaotic flow

Chaotic flows drive mixing and efficient transport in fluids, as well as the associated beautiful complex patterns familiar to us from our every day life experience. Generating such flows at small scales where viscosity takes over is highly challenging from both the theoretical and engineering perspectives. This can be overcome by introducing a minuscule amount of long flexible polymers, resulting in a chaotic flow dubbed \textit{elastic turbulence}. At the basis of the theoretical frameworks for its study lie the assumptions of a spatially smooth and random-in-time velocity field. Previous measurements of elastic turbulence have been limited to two-dimensions. Using a novel three-dimensional particle tracking method, we conduct a microfluidic experiment, allowing us to explore elastic turbulence from the perspective of particles moving with the flow. Our findings show that the smoothness assumption breaks already at scales smaller than a tenth of the system size. Moreover, we provide conclusive experimental evidence that \textit{ballistic} separation prevails in the dynamics of pairs of tracers over long times and distances, exhibiting a memory of the initial separation velocities. The ballistic dispersion is universal, yet it has been overlooked so far in the context of small scales chaotic flows.

nlin.CD↗

arXiv2017

Elastic wake instabilities in a creeping flow between two obstacles

It is shown that a channel flow of a dilute polymer solution between two widely spaced cylinders hindering the flow is an important paradigm of an unbounded flow in the case in which the channel wall is located sufficiently far from the cylinders. The quantitative characterization of instabilities in a creeping viscoelastic channel flow between two widely spaced cylinders reveals two elastically driven transitions, which are associated with the breaking of time-reversal and mirror symmetries: Hopf and forward bifurcations described by two order parameters $\mbox{v}_{rms}$ and $\barω$, respectively. We suggest that a decrease of the normalized distance between the obstacles leads to a collapse of the two bifurcations into a codimension-2 point, a situation general for many non-equilibrium systems. However, the striking and unexpected result is the discovery of a mechanism of the vorticity growth via an increase of a vortex length at the preserved streamline curvature in a viscoelastic flow, which is in sharp contrast to the well-known suppression of the vorticity in a Newtonian flow by polymer additives.

physics.flu-dyn↗