Understanding viscoelastic flow instabilities: Oldroyd-B and beyond

Castillo-Sánchez, Hugo A.; Jovanović, Mihailo R.; Kumar, Satish; Morozov, Alexander; Shankar, V.; Subramanian, Ganesh; Wilson, H.J.

doi:10.1016/j.jnnfm.2022.104742

Cited by 46 publications

(30 citation statements)

References 338 publications

(687 reference statements)

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“…(2021) and Castillo-Sanchez et al. (2022) for extensive discussions of this) although there had been some evidence of instability to finite-amplitude disturbances at low (Bertola et al. 2003; Pan et al.…”

Section: Introductionmentioning

confidence: 99%

Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number

Buza¹,

Beneitez²,

Page

et al. 2022

J. Fluid Mech.

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Using branch continuation in the FENE-P model, we show that finite-amplitude travelling waves borne out of the recently discovered linear instability of viscoelastic channel flow (Khalid et al., J. Fluid Mech., vol. 915, 2021, A43) are substantially subcritical reaching much lower Weissenberg ( $Wi$ ) numbers than on the neutral curve at a given Reynolds ( $Re$ ) number over $Re \in [0,3000]$ . The travelling waves on the lower branch are surprisingly weak indicating that viscoelastic channel flow is susceptible to (nonlinear) instability triggered by small finite-amplitude disturbances for $Wi$ and $Re$ well below the neutral curve. The critical $Wi$ for these waves to appear in a saddle node bifurcation decreases monotonically from, for example, $\approx 37$ at $Re=3000$ down to $\approx 7.5$ at $Re=0$ at the solvent-to-total-viscosity ratio $\beta =0.9$ . In this latter creeping flow limit, we also show that these waves exist at $Wi \lesssim 50$ for higher polymer concentrations, $\beta \in [0.5,0.97)$ , where there is no known linear instability. Our results therefore indicate that these travelling waves, found in simulations and named ‘arrowheads’ by Dubief et al. (Phys. Rev. Fluids, vol. 7, 2022, 073301), exist much more generally in $(Wi,Re, \beta )$ parameter space than their spawning neutral curve and, hence, can either directly, or indirectly through their instabilities, influence the dynamics seen far away from where the flow is linearly unstable. Possible connections to elastic and elasto-inertial turbulence are discussed.

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Section: Introductionmentioning

confidence: 99%

Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number

Buza¹,

Beneitez²,

Page

et al. 2022

J. Fluid Mech.

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“…As well known, the linearized Navier-Stokes equation (NSE) (or Orr-Sommerfeld equation) for Newtonian parallel shear flows is non-Hermitian and proved to be linearly stable towards the normal modes in the limit of Re → ∞ , where the Orr-Sommerfeld equation becomes Hermitian. However, at finite Re, it is prone to transient algebraic temporal growth of non-normal eigenmodes, whereas linear normal modes decay exponentially since the flow is linearly stable 8-10 .Theoretical and numerical simulation studies of the non-normal mode instability in viscoelastic channel and plane Couette flows at Wi ≫ 1 and Re ≪ 1 (and so El ≫ 1 , where El = Wi/Re is the elasticity number) consider only a linear transient stage of the non-normal mode elastic instability [11][12][13][14][15] . Then during the linear growth of the transient non-normal modes, transient coherent structures (CSs), namely stream-wise streaks and rolls, are generated.…”

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confidence: 99%

Universal properties of non-Hermitian viscoelastic channel flows

Steinberg

2023

Sci Rep

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An addition of long-chain, flexible polymers strongly affects laminar and turbulent Newtonian flows. In laminar inertia-less viscoelastic channel flow, the supercritical elastic instability of non-normal eigenmodes of non-Hermitian equations at finite-size perturbations leads to chaotic flow. Then three chaotic flow regimes: transition, elastic turbulence (ET), and drag reduction (DR), accompanied by elastic waves, are observed and characterized. Here we show that independently of external perturbation strength and structure, chaotic flows above the instability onset in transition, ET, and DR flow regimes reveal similar scaling of flow properties, universal scaling of elastic wave speed with Weissenberg number, Wi, defined the degree of polymer stretching, and the coherent structure of velocity fluctuations, self-organized into cycling self-sustained process, synchronized by elastic waves. These properties persist over the entire channel length above the instability threshold. It means that only an absolute instability exists in inertia-less viscoelastic channel flow, whereas a convective instability, is absent. This unexpected discovery is in sharp contrast with Newtonian flows, where both convective and absolute instabilities are always present in open flows. It occurs due to differences in nonlinear terms in an elastic stress equation, where except for the advective term, two key terms describing polymer stretching along the channel length are present.

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“…The past few years have seen a growing interest in understanding of pressure-driven channel flows of dilute polymer solutions (Castillo Sánchez et al. 2022; Datta et al. 2022).…”

Section: Introductionmentioning

confidence: 99%

“…The rich variety of flow states associated with different parts of the space ranges from drag-reduction and elasto-inertial turbulence (Dubief, Terrapon & Hof 2023) to purely elastic instabilities and turbulence (Steinberg 2021), making it a subject of interest for turbulence and flow-control researchers, polymer rheologists and physicists studying flows of complex fluids (Castillo Sánchez et al. 2022; Datta et al. 2022).…”

Section: Introductionmentioning

confidence: 99%

Linear stability analysis of purely elastic travelling-wave solutions in pressure-driven channel flows

Lellep

Linkmann²,

Morozov³

2023

J. Fluid Mech.

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Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a subcritical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded in sufficiently wide three-dimensional domains. Our work demonstrates that studies of purely elastic and elasto-inertial turbulence in straight channels require three-dimensional simulations, and no reliable conclusions can be drawn from studying strictly two-dimensional channel flows.

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Understanding viscoelastic flow instabilities: Oldroyd-B and beyond

Cited by 46 publications

References 338 publications

Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number

Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number

Universal properties of non-Hermitian viscoelastic channel flows

Linear stability analysis of purely elastic travelling-wave solutions in pressure-driven channel flows

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