A Stokesian viscoelastic flow: Transition to oscillations and mixing

Thomases, Becca; Shelley, Michael; Thiffeault, Jean-Luc

doi:10.1016/j.physd.2011.06.011

Cited by 32 publications

(58 citation statements)

References 44 publications

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“…In our numerical results of simulations, the similar instabilities are also observed as the results reported in Ref. 17. However, it is particularly found that the ratio of the kinematical viscosity has an important influence on the transition of the elastic instabilities of viscoelastic fluids.…”

Section: Introductionsupporting

confidence: 89%

“…17, the Oldroyd-B flow with the polymer diffusion based on the random initial data was discussed using a pseudo-spectral method. They have observed the typical flow states with a single-quadrant dominating vortex, which may be stationary (in 90 of the 100 random trials) or cycle persistently from cell to cell (in 10 of the 100 random trials).…”

Section: The Transition States Of Elastic Instabilitiesmentioning

confidence: 99%

“…By the way, the non-isothermal viscoelastic flow is now also a hot topic of stability. [13][14][15] It's interesting that Thomases et al 16,17 have studied some instabilities of a 2D periodic extensional flow using a Oldroyd-B model including the stress diffusion. In present paper, we aim to use a mesoscopic method to investigate some possibility of factors for the elastic instability in a periodic extensional flow under low Reynolds number.…”

Section: Introductionmentioning

confidence: 99%

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Simulations of viscoelastic fluids using a coupled lattice Boltzmann method: Transition states of elastic instabilities

Ouyang

et al. 2017

AIP Advances

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Elastic instabilities could happen in viscoelastic flows as the Weissenberg number is enlarged, and this phenomenon makes the numerical simulation of viscoelastic fluids more difficult. In this study, we introduce a coupled lattice Boltzmann method to solve the equations of viscoelastic fluids, which has a great capability of simulating the high Weissenberg number problem. Different from some traditional methods, two kinds of distribution functions are defined respectively for the evolution of the momentum and stress tensor equations. We mainly aim to investigate some key factors of the symmetry-breaking transition induced by elastic instability of viscoelastic fluids using this numerical coupled lattice Boltzmann method. In the results, we firstly find that the ratio of kinematical viscosity has an important influence on the transition of the elastic instability; the transition between the single stationary and cycling dominant vortex can be controlled via changing the ratio of kinematical viscosity in a periodic extensional flow. Finally, we can also observe a new transition state of instability for the flow showing the banded structure at higher Weissenberg number.

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Section: Introductionsupporting

confidence: 89%

Section: The Transition States Of Elastic Instabilitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simulations of viscoelastic fluids using a coupled lattice Boltzmann method: Transition states of elastic instabilities

Ouyang

et al. 2017

AIP Advances

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“…The result of the transversely narrow and sharply peaked stress distribution is a dip in the velocity whose magnitude is independent of the stress diffusion. Such a dip in the velocity field has been observed experi-mentally [23,24] and provides a possible mechanism for the instabilities seen in numerical simulations [6,7,8,9,10,11]. Simply stated, the instability mechanism is due to the fact that at extensional points in the flow the vorticity is low.…”

Section: Introductionmentioning

confidence: 61%

“…However it is precisely at these points in the flow that interesting dynamics arise. Instabilities have been found in experiments at internal stagnation points [1,2,3,4,5], and related numerical instabilities are found in similar geometries [6,7,8,9,10,11]. It is unclear what is driving these instabilities, but it is reasonable to conjecture that they are related to the large polymer stresses and stress gradients which accumulate along the incoming and outgoing streamlines of these internal stagnation points.…”

Section: Introductionmentioning

confidence: 94%

Equilibrium circulation and stress distribution in viscoelastic creeping flow

Biello¹,

Thomases²

2016

Journal of Non-Newtonian Fluid Mechanics

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An analytic, asymptotic approximation of the nonlinear steady-state equations for viscoelastic creeping flow, modeled by the Oldroyd-B equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow stretches and aligns polymers along the outgoing streamlines of the stagnation point resulting in a stress-island, or birefringent strand. The polymer stress diffusion coefficient is used, both as an asymptotic parameter and a regularization parameter. The structure of the singular part of the polymer stress tensor is a Gaussian aligned with the incoming streamline of the stagnation point; a smoothed δ-distribution whose width is proportional to the square-root of the diffusion coefficient. The amplitude of the stress island scales with the Wiessenberg number, and although singular in the limit of vanishing diffusion, it is integrable in the cross stream direction due to its vanishing width; this yields a convergent secondary flow. The leading order velocity response to this stress island is constructed and shown to be independent of the diffusion coefficient in the limit. The secondary circulation counteracts the forced flow and has a vorticity jump at the location of the stress islands, essentially expelling the background vorticity from the location of the birefringent strands. The analytic solutions are shown to be in excellent quantitative agreement with full numerical simulations, and therefore, the analytic solutions elucidate the salient mechanisms of the flow response to viscoelasticity and the mechanism for instability.

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Fluid‐Structure Interactions: Research in the Courant Institute's Applied Mathematics Laboratory

Childress

Shelley

Zhang

2012

Comm Pure Appl Math

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The Applied Mathematics Laboratory is a research laboratory within the Mathematics Department of the Courant Institute. It was established to carry out physical experiments, modeling, and associated numerical studies in a variety of problems of interest to Courant faculty, postdocs, and graduate and undergraduate students. Most of the research to date has involved fluid mechanics, and we focus in this paper on the work that relates to the interaction of fluids with rigid, movable, or flexible bodies.

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A Stokesian viscoelastic flow: Transition to oscillations and mixing

Cited by 32 publications

References 44 publications

Simulations of viscoelastic fluids using a coupled lattice Boltzmann method: Transition states of elastic instabilities

Simulations of viscoelastic fluids using a coupled lattice Boltzmann method: Transition states of elastic instabilities

Equilibrium circulation and stress distribution in viscoelastic creeping flow

Fluid‐Structure Interactions: Research in the Courant Institute's Applied Mathematics Laboratory

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