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Aarts, Act Annemarie; Ooms, G.

doi:10.1023/a:1004314014329

Cited by 78 publications

(33 citation statements)

References 4 publications

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“…The latter choice of solution is motivated by the fact that the peristaltic flow is essentially a non-linear (second order) effect [1], and adding a non-oscillatory term in the first order gives only trivial solution. Thus, we can add non-oscillatory terms, such as U 20 (r), V 20 (r), P 20 (r), D 20 (r), which do not cancel out in the solution after the time averaging over the period, only in the second and higher orders.…”

Section: The Modelmentioning

confidence: 99%

“…Repeating the analysis similar to the one from Ref. [1], we obtain the master equation for U 1 (r) and find its general solution as…”

Section: The Modelmentioning

confidence: 99%

“…The most recent and general study of stimulation of fluid flow in porous media via peristaltic mechanism is presented in Ref. [1], which we will use as a starting point in order to include non-Newtonian effects into the peristaltic model.…”

Section: Introductionmentioning

confidence: 99%

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Non-Newtonian effects in the peristaltic flow of a Maxwell fluid

Tsiklauri

Beresnev

2001

Phys. Rev. E

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We analyzed the effect of viscoelasticity on the dynamics of fluids in porous media by studying the flow of a Maxwell fluid in a circular tube, in which the flow is induced by a wave traveling on the tube wall. The present paper investigates phenomena brought about into the classic peristaltic mechanism by inclusion of non-Newtonian effects that are important, e.g., for hydrocarbons. This problem has numerous applications in various branches of science, including the stimulation of fluid flow in a porous media under the effect of elastic waves and studies of blood flow dynamics in living creatures. We have found that in the extreme non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the wave traveling on the tube wall.

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Section: The Modelmentioning

confidence: 99%

“…Repeating the analysis similar to the one from Ref. [1], we obtain the master equation for U 1 (r) and find its general solution as…”

Section: The Modelmentioning

confidence: 99%

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Non-Newtonian effects in the peristaltic flow of a Maxwell fluid

Tsiklauri

Beresnev

2001

Phys. Rev. E

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“…The speed of flow through a pore can be enhanced significantly by the application of ultrasound. 3,4 The mechanism is of obvious practical interest to the oil industry.…”

Section: Introductionmentioning

confidence: 99%

Long-range dynamic correlations in a compressible viscous fluid confined in a circular tube

Felderhof

2011

The Journal of Chemical Physics

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A set of simplified one-dimensional hydrodynamic equations proposed for the description of transient small amplitude flow of a compressible viscous fluid in a linear channel is tested by comparison with exact results for a circular tube obtained from the linearized Navier-Stokes equations. There is a qualitative agreement between the approximate and exact results, but for the simplified calculation the amplitude of the algebraic long-time tail is a factor of 2 too small.

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“…17 As the AWs travel along the field lines (due to the plasma frozen-in condition that is somewhat offset by a finite resistivity), the flow that derives from the AW perturbation might generate the magnetic field by the dynamo action. It is a well-known fact that flows, which have similar mathematical structure to Eq.…”

Section: Following Ref 11 We Fix the Values Of The Coefficients Asmentioning

confidence: 99%

Three dimensional magnetohydrodynamic simulation of linearly polarised Alfven wave dynamics in Arnold-Beltrami-Childress magnetic field

Tsiklauri

2014

Physics of Plasmas

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Previous studies (e.g., Malara et al., Astrophys. J. 533, 523 (2000)) considered small-amplitude Alfven wave (AW) packets in Arnold-Beltrami-Childress (ABC) magnetic field using WKB approximation. They draw a distinction between 2D AW dissipation via phase mixing and 3D AW dissipation via exponentially divergent magnetic field lines. In the former case, AW dissipation time scales as S 1=3 and in the latter as logðSÞ, where S is the Lundquist number. In this work, linearly polarised Alfven wave dynamics in ABC magnetic field via direct 3D magnetohydrodynamic (MHD) numerical simulation is studied for the first time. A Gaussian AW pulse with length-scale much shorter than ABC domain length and a harmonic AW with wavelength equal to ABC domain length are studied for four different resistivities. While it is found that AWs dissipate quickly in the ABC field, contrary to an expectation, it is found the AW perturbation energy increases in time. In the case of the harmonic AW, the perturbation energy growth is transient in time, attaining peaks in both velocity and magnetic perturbation energies within timescales much smaller than the resistive time. In the case of the Gaussian AW pulse, the velocity perturbation energy growth is still transient in time, attaining a peak within few resistive times, while magnetic perturbation energy continues to grow. It is also shown that the total magnetic energy decreases in time and this is governed by the resistive evolution of the background ABC magnetic field rather than AW damping. On contrary, when the background magnetic field is uniform, the total magnetic energy decrease is prescribed by AW damping, because there is no resistive evolution of the background. By considering runs with different amplitudes and by analysing the perturbation spectra, possible dynamo action by AW perturbation-induced peristaltic flow and inverse cascade of magnetic energy have been excluded. Therefore, the perturbation energy growth is attributed to a new instability. The growth rate appears to be dependent on the value of the resistivity and the spatial scale of the AW disturbance. Thus, when going beyond WKB approximation, AW damping, described by full MHD equations, does not guarantee decrease of perturbation energy. This has implications for the MHD wave plasma heating in exponentially divergent magnetic fields. V C 2014 AIP Publishing LLC.

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Cited by 78 publications

References 4 publications

Non-Newtonian effects in the peristaltic flow of a Maxwell fluid

Non-Newtonian effects in the peristaltic flow of a Maxwell fluid

Long-range dynamic correlations in a compressible viscous fluid confined in a circular tube

Three dimensional magnetohydrodynamic simulation of linearly polarised Alfven wave dynamics in Arnold-Beltrami-Childress magnetic field

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