Understanding viscoelastic flow instabilities: Oldroyd-B and beyond
arXiv:2202.08305 · doi:10.1016/j.jnnfm.2022.104742
Abstract
The Oldroyd-B model has been used extensively to predict a host of instabilities in shearing flows of viscoelastic fluids, often realized experimentally using polymer solutions. The present review, written on the occasion of the birth centenary of James Oldroyd, provides an overview of instabilities found across major classes of shearing flows. These comprise (i) the canonical rectilinear shearing flows including plane Couette, plane and pipe Poiseuille flows; (ii) viscometric shearing flows with curved streamlines such as those in the Taylor-Couette, cone-and-plate and parallel-plate geometries; (iii) non-viscometric shearing flows with an underlying extensional flow topology such as the flow in a cross-slot device; and (iv) multilayer shearing flows. While the underlying focus in all these cases is on results obtained using the Oldroyd-B model, we also discuss their relation to the actual instability, and as to how the shortcomings of the Oldroyd-B model may be overcome by the use of more realistic constitutive models. All the three commonly used tools of stability analysis, viz., modal linear stability, nonmodal stability, and weakly nonlinear stability analyses are discussed, with supporting evidence from experiments and numerical simulations as appropriate. Despite only accounting for a shear-rate-independent viscosity and first normal stress coefficient, the Oldroyd-B model is able to qualitatively predict the majority of instabilities in the aforementioned shearing flows. The review also highlights, where appropriate, open questions in the area of viscoelastic stability.
arXiv commentInvited review article for the special issue of JNNFM commemorating the birth centenary of James Oldroyd
References in corpus (56)
- Elastic turbulence in a polymer solution flow
- Efficient Mixing at low Reynolds numbers using polymer additives
- High Reynolds number Taylor-Couette turbulence
- Rheology of giant micelles
- Elastic turbulence in curvilinear flows of polymer solutions
- Elasto-inertial turbulence
- A nonlinear elastic instability in channel flows at low Reynolds numbers
- Turbulent drag reduction by polymer additives: Fundamentals and recent advances
- Spectra of turbulence in dilute polymer solutions
- Chaotic flow and efficient mixing in a micro-channel with a polymer solution
- The lift-up effect: the linear mechanism behind transition and turbulence in shear flows
- Exceeding the asymptotic limit of polymer drag reduction
- On the mechanism of elasto-inertial turbulence
- Flow phase diagrams for concentration-coupled shear banding
- From bypass transition to flow control and data-driven turbulence modeling: An input-output viewpoint
- Active and hibernating turbulence in minimal channel flow of Newtonian and polymeric fluids
- Viscoelastic pipe flow is linearly unstable
- Interface instability in shear banding flow
- Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction
- Solitary vortex couples in viscoelastic Couette flow
- The center-mode instability of viscoelastic plane Poiseuille flow
- Elastic turbulence in shear banding wormlike micelles
- Critical-layer structures and mechanisms in elastoinertial turbulence
- Linear instability of planar shear banded flow
- Exact travelling wave solutions in viscoelastic channel flow
- Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows
- Early stages of the shear banding instability in wormlike micelles
- A continuous pathway between the elasto-inertial and elastic turbulent states in viscoelastic channel flow
- Dynamics of viscoelastic pipe flow in the maximum drag reduction limit
- Flow Resistance and Structures in Viscoelastic Channel Flows at Low Re
- Nonmodal amplification of stochastic disturbances in strongly elastic channel flows
- Linear instability of viscoelastic pipe flow
- Elastic Alfven waves in elastic turbulence
- A first coherent structure in elasto-inertial turbulence
- On the relation between viscoelastic and magnetohydrodynamic flows and their instabilities
- Linear instability of planar shear banded flow of both diffusive and non-diffusive Johnson-Segalman fluids
- Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers
- Nonlinear traveling waves as a framework for understanding turbulent drag reduction
- Self-sustained elastoinertial Tollmien-Schlichting waves
- Worst-case amplification of disturbances in inertialess Couette flow of viscoelastic fluids
- Frequency responses of streamwise-constant perturbations in channel flows of Oldroyd-B fluids
- Nonlinear dynamics of the viscoelastic Kolmogorov flow
- Coil-Stretch Transition and the Break Down of Continuum Models
- Magnetorotational-type instability in Couette-Taylor flow of a viscoelastic polymer liquid
- Analog of Astrophysical Magnetorotational Instability in a Couette-Taylor Flow of Polymer Fluids
- Subcritical instabilities in plane Poiseuille flow of an Oldroyd-B fluid
- Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows
- Perturbative expansions of the conformation tensor in viscoelastic flows
- Solitary coherent structures in viscoelastic shear flow: computation and mechanism
- Interplay of edge fracture and shear banding in complex fluids
- Elastic instability in stratified core annular flow
- Pattern formation in Hamiltonian systems with continuous spectra; a normal-form single-wave model
- Amplification of localized body forces in channel flows of viscoelastic fluids
- How does flow in a pipe become turbulent?
- Universal coherent structures of elastic turbulence in straight channel with viscoelastic fluid flow
- Well-conditioned ultraspherical and spectral integration methods for resolvent analysis of channel flows of Newtonian and viscoelastic fluids
Cited by in corpus (13)
- Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers
- Coherent structures in plane channel flow of dilute polymer solutions with vanishing inertia
- Inertial enhancement of the polymer diffusive instability
- Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number
- Characterizing elastic turbulence in the three-dimensional von Karman swirling flow using the Oldroyd-B model
- Flow rate-pressure drop relations for shear-thinning fluids in deformable configurations: theory and experiments
- Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows
- Elastic instability in a straight channel of viscoelastic flow without prearranged perturbations
- Viscoelastic fluid flow in a slowly varying planar contraction: the role of finite extensibility on the pressure drop
- On the large-Weissenberg-number scaling laws in viscoelastic pipe flows
- Nature of continuous spectra in wall-bounded shearing flows of FENE-P fluids
- Two-fluid kinetic theory for dilute polymer solutions
- Asymptotic-analysis-inspired boundary conditions aiming at eliminating polymer diffusive instability