A Continuum Theory of Rhelogical Phenomena

Weissenberg, K.

doi:10.1038/159310a0

Cited by 364 publications

(122 citation statements)

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“…If, for example, a vertical rotating rod is inserted in a beaker with a highly elastic polymer solution, the liquid starts to climb up on it, instead of being pushed outward by the centrifugal force. The reason of this "rod climbing" (Weissenberg effect) (7,8) is, that the rod rotation produces a shear flow, which stretches the polymer molecules around the rod in the azimuthal direction. These elongated molecules act as stretched rubber rings that push the liquid towards the rod ("hoop stress").…”

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confidence: 99%

Solitary Vortex Pairs in Viscoelastic Couette Flow

1997

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We report experimental discovery of a localized structure, which is of a new type for dissipative systems. It appears as a solitary vortex couple ("diwhirl") in Couette flow with highly elastic polymer solutions. A unique property of the diwhirls is that they are stationary, in contrast to the usual localized wave structures in both Hamiltonian and dissipative systems which are stabilized by wave dispersion. It is also a novel object in fluid dynamics -a couple of vortices that build a single entity somewhat similar to a magnetic dipole. The diwhirls arise as a result of a purely elastic instability through a hysteretic transition at negligible Reynolds numbers. It is suggested that the vortex flow is driven by the same forces that cause the Weissenberg effect. The diwhirls have a striking asymmetry between the inflow and outflow, which is also an essential feature of the suggested elastic instability mechanism.

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confidence: 99%

Solitary Vortex Pairs in Viscoelastic Couette Flow

1997

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“…Examples of such extreme behavior, often seemingly counterintuitive, include the well-known Weissenberg or rodclimbing effect [1], the Fano or open-siphon effect [2], the large vortex enhancement that is observed in sudden contraction-flow geometries [3], and the extreme offcenterline velocity overshoots that occur in smooth contraction flow [4]. In addition to such gross-flow manifestations of viscoelasticity, a growing body of evidence has shown that viscoelastic fluid flows may develop purely elastic flow instabilities [5].…”

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“…Under these conditions, the equations that need to be solved are those of conservation of mass r u 0 and of momentum ÿrp r 0 together with a suitable choice for the viscoelastic stress tensor . As already discussed, we use the UCM model [21], 1 2 D, where 1 is the upper-convected derivative and D is the strain rate tensor. Although a number of shortcomings exist with this model, most notably the unbounded nature of the steady extensional stresses above a critical strain rate and its inability to predict shear-thinning behavior, it is the simplest differential model of an elastic fluid that can capture qualitatively many features of highly elastic flows.…”

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confidence: 99%

Purely Elastic Flow Asymmetries

2007

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Using a numerical technique we demonstrate that the flow of the simplest differential viscoelastic fluid model (i.e., the upper-convected Maxwell model) goes through a bifurcation to a steady asymmetric state when flowing in a perfectly symmetric ''cross-slot'' geometry. We show that this asymmetry is purely elastic in nature and that the effect of inertia is a stabilizing one. Our results are in qualitative agreement with very recent experimental visualizations of a similar flow in the microfluidic apparatus of Arratia et al.

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“…This implies non-linear relationship between τ and the rate of deformation in a flow [3]. The non-linear mechanical properties of polymer solutions are well manifested in their large extensional viscosity at high rates of extension [4] and in the Weissenberg effect [5,3]. Degree of non-linearity in the mechanical properties is expressed by the Weissenberg number, W i = V λ/L, which is a product of characteristic rate of deformation and the relaxation time, λ.…”

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Elastic turbulence in a polymer solution flow

Groisman

Steinberg

2000

Nature

748

739

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Turbulence is one of the most fascinating phenomena in nature and one of the biggest challenges for modern physics. It is common knowledge that a flow of a simple, Newtonian fluid is likely to be turbulent, when velocity is high, viscosity is low and size of the tank is large [1,2]. Solutions of flexible longchain polymers are known as visco-elastic fluids [3]. In our experiments we show, that flow of a polymer solution with large enough elasticity can become quite irregular even at low velocity, high viscosity and in a small tank. The fluid motion is excited in a broad range of spatial and temporal scales. The flow resistance increases by a factor of about twenty. So, while the Reynolds number, Re, may be arbitrary low, the observed flow has all main features of developed turbulence, and can be compared to turbulent flow in a pipe at Re ≃ 10This elastic turbulence is accompanied by significant stretching of the polymer molecules, and the resulting increase of the elastic stresses can reach two orders of magnitude.Motion of simple, low molecular, Newtonian fluids is governed by the Navier-Stokes equation [1,2]. This equation has a non-linear term, which is inertial in its nature. The ratio between the non-linearity and viscous dissipation is given by the Reynolds number, Re = V L/ν,where V is velocity, L is characteristic size and ν is kinematic viscosity of the fluid. When Re is high, non-linear effects are strong and the flow is likely to be turbulent.So, turbulence is a paradigm for a strongly non-linear phenomenon [1,2].Solutions of flexible high molecular weight polymers differ from Newtonian fluids in many aspects [3]. The most striking elastic property of the polymer solutions is that stress does 1

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A Continuum Theory of Rhelogical Phenomena

Cited by 364 publications

References 1 publication

Solitary Vortex Pairs in Viscoelastic Couette Flow

Solitary Vortex Pairs in Viscoelastic Couette Flow

Purely Elastic Flow Asymmetries

Elastic turbulence in a polymer solution flow

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