Resonance behavior of viscoelastic fluids in Poiseuille flow and application to flow enhancement

Andrienko, Yu. A.; Siginer, Dennis A.; Yanovsky, Yuri G.

doi:10.1016/s0020-7462(98)00090-0

Cited by 31 publications

(35 citation statements)

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“…The same behaviour may occur even in oscillatory flows of linear viscoelastic fluids [2] and, indeed, may be predicted from Eqn. (13) by plotting the modulus of U M /P * M againstω and taking the complex viscosity η * to be that of a single mode linear Maxwell fluid, for example.…”

Section: × 10supporting

confidence: 71%

“…The existence of a resonant frequency in oscillatory tube flow of viscoelastic fluids is well documented and may be present even for linear viscoelastic fluids. It is important to distinguish resonance from flow enhancement in pulsatile flows, however, where any increase in the time-averaged flow rate relative to its value at zero frequency is a non-linear viscoelastic effect [2], although this mechanism might be most effective near resonant frequencies.…”

Section: Discussionmentioning

confidence: 99%

“…The frequency ω r (say) where the maximum occurs may be viewed as a resonant frequency. The phenomena of resonant frequencies and flow enhancement in oscillatory pipe flow is well known in both the experimental and theoretical viscoelastic literature and further discussion of these may be found, for example, in [2,8,13,32,41,46]. A helpful review of earlier work is to be found in the article of Siginer [35].…”

Section: × 10mentioning

confidence: 99%

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On the high frequency oscillatory tube flow of healthy human blood

Moyers-González¹,

Owens²,

Fang³

2009

Journal of Non-Newtonian Fluid Mechanics

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In this paper pressure gradient vs. volume flow rate calculations over a wide range of oscillatory frequencies for oscillatory tube flow of healthy human blood are performed using the non-homogeneous hemorheological model of MoyersGonzalez et al. [25,26,27]. Results at low (2 Hz) oscillatory frequencies are shown to be in close conformity to the experimental data of Thurston [39] and the behaviour may be interpreted using a linear viscoelastic model. As the oscillatory frequencies increase a resonant frequency at which flow rate amplitude enhancement occurs is encountered. For frequencies greater than the resonant frequency the pressure gradient amplitude required to maintain a constant volume flow rate amplitude increases with the oscillatory frequency.For very high frequency oscillations we use a multiple time scales technique in conjunction with our non-homogeneous hemorheological model to solve for the leading order flow variables. It is found that the leading order expressions for the cell number density, average aggregate size and rr-component of elastic stress (i.e. that due to the red blood cells) are functions only of the radial component r. The O(1) elastic shear stress is shown to be zero, so that, for sufficiently large values of the oscillatory frequency, the red cell contribution to the total shear stress tends to zero. Using our multiple time scales method it is also shown that the model behaves in the very high frequency regime like a generalised linear viscoelastic fluid, having a radially dependent complex viscosity. This allows us to explain the computed results using asymptotic expressions for the in phase and π/2 out of phase components of the pressure gradient in a linear viscoelastic fluid. In particular, we may predict the apparent complex viscosity of human blood in very high frequency oscillatory tube flow.

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Section: × 10supporting

confidence: 71%

Section: Discussionmentioning

confidence: 99%

Section: × 10mentioning

confidence: 99%

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On the high frequency oscillatory tube flow of healthy human blood

Moyers-González¹,

Owens²,

Fang³

2009

Journal of Non-Newtonian Fluid Mechanics

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“…(r)e i!t (9) Using Equations (8) and (9) into Equations (5) and (6) we obtain the equation satisÿed by u ! as follows…”

Section: Viscoelastic Mhd Poiseuille Flowmentioning

confidence: 99%

“…Resonance phenomena of viscoelastic uids appear in polymer processing, the so-called draw resonance, see References [2][3][4][5][6][7]. In References [8][9][10] pulsating viscoelastic ows and their resonance behaviour have been studied.…”

Section: Introductionmentioning

confidence: 99%

Resonance behaviour of viscoelastic fluid in Poiseuille flow in the presence of a transversal magnetic field

Mohyuddin

Götz

2005

Numerical Methods in Fluids

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SUMMARYThe oscillatory ow of a viscoelastic uid in a circular pipe under the in uence of a transversal magnetic ÿeld is studied. Exact solutions for the axial velocity and ow rate are presented. The velocity enhancement and the resonance behaviour are analysed both numerically and asymptotically in the case of small pipe radii.Approximations for the resonance frequencies and the achievable velocity enhancements are derived.

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Quasi‐periodic electro‐osmotic flow of fractional viscoelastic fluids

Tian

Ding

2022

Math Methods in App Sciences

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In this work, we study the unsteady electro-osmotic flow of fractional viscoelastic fluids in micro-parallel channels, where the velocity slip effect on the walls is also considered. The analytical solution is obtained through solving the Cauchy momentum equation, together with the linearized Poisson-Boltzmann equation and the fractional Maxwell constitutive equation. The influences of the normalized electrokinetic width K, Deborah number De, slip length L and fractional derivative 𝛼 on the velocity and volume flow rate are discussed. The results demonstrate that the dimensionless parameters L, De and K all have a promoting effect on the electro-osmotic flow and resonance behavior of fractional Maxwell fluids. In addition, compared with the classical Maxwell fluid, the microstructure of the fractional Maxwell fluid weakens the resonance behavior.

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Resonance behavior of viscoelastic fluids in Poiseuille flow and application to flow enhancement

Cited by 31 publications

References 0 publications

On the high frequency oscillatory tube flow of healthy human blood

On the high frequency oscillatory tube flow of healthy human blood

Resonance behaviour of viscoelastic fluid in Poiseuille flow in the presence of a transversal magnetic field

Quasi‐periodic electro‐osmotic flow of fractional viscoelastic fluids

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