Purely pulsating flow of a viscoelastic fluid in a pipe revisited: The limit of large Womersley number

Fernández‐Feria, R.; Alaminos-Quesada, J.

doi:10.1016/j.jnnfm.2015.01.002

Cited by 6 publications

(4 citation statements)

References 19 publications

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“…Note that there is no imposed macroscopic velocity in the system, and for this reason it is better to explain all the mechanisms in terms of the elastic number E, instead of other dimensionless numbers such as (i) Deborah, (ii) Mach, (iii) Newtonian Womersley number, and (iv) vibratile Reynolds [32,33]. The wavelength vector b (Equation ( 26)) deals with the pulsating Womersley number related to the competition between the viscous and oscillatory mechanisms [32,33]:…”

Section: Scales Dimensionless Numbers and Device Mode Classification ...mentioning

confidence: 99%

“…The role of the elastic number is a vertical shift [31,32]. This primitive quantity β(ω) associated with the velocity field shows the scaling of its norm with the Womersley (Wo) [33][34][35][36][37][38] and elastic (E) number [31,32] is:…”

Section: Scales Dimensionless Numbers and Device Mode Classification ...mentioning

confidence: 99%

“…In Equation (33), {J 0 , Y 0 } are the classical special Bessel functions [3]. From the boundary conditions (Equations ( 19) and ( 20)), the constants C 1 (ω) and C 2 (ω) are calculated as follows:…”

Section: Complex Axial Velocitymentioning

confidence: 99%

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Fluctuating Flexoelectric Membranes in Asymmetric Viscoelastic Media: Power Spectrum through Mechanical Network and Transfer Function Models

Herrera‐Valencia

Rey

2023

Symmetry

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Flexoelectric liquid crystalline membranes immersed in asymmetric viscoelastic media is a material system model with physiological applications such as outer hair cells (OHCs), where membrane oscillations generate bulk flow. Motivated by this physiological process, here we extend our previous work by characterizing the force transmission output of our model in addition to viscoelastic fluid flow, since solid–fluid interactions are an essential feature of confined physiological flow and flow in immersed elastic structures. In this work, the rigidity of the confinement results in a passive force reception, while more complete solid–fluid interactions will be considered in the future. A significant contribution of this work is a new asymmetry linear viscoelastic electro-rheological model and the obtained implicit relation between force transmission and flow generation and how this relation is modulated by electric field frequency and the material properties of the device. Maximal force and flow are found at resonant frequencies of asymmetry viscoelastic bulk phases, flexoelectric and dispersion mechanisms through the elastic and Womersley numbers.

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Section: Scales Dimensionless Numbers and Device Mode Classification ...mentioning

confidence: 99%

Section: Scales Dimensionless Numbers and Device Mode Classification ...mentioning

confidence: 99%

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Fluctuating Flexoelectric Membranes in Asymmetric Viscoelastic Media: Power Spectrum through Mechanical Network and Transfer Function Models

Herrera‐Valencia

Rey

2023

Symmetry

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“…Since the blood flow is pulsatile, the problems become additionally complicated if the non-Newtonian character is taken into account [7][8][9]. Apart from the Reynolds number, an additional parameter is introduced for the pulsatile or oscillatory flows, the so-called Womersley number (expressing the ratio of the local pulsating force to the viscous one) [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Oscillatory Carreau flows in straight channels

2020

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The present paper studies the oscillatory flow of Carreau fluid in a channel at different Womersley and Carreau numbers. At high and low Womersley numbers, asymptotic expansions in small parameters, connected with the Womersley number, are developed. For the intermediate Womersley numbers, theoretical bounds for the velocity solution and its gradient, depending on the problem parameters, are proven and explicitly given. It is shown that the Carreau number changes the type of the flow velocity to be closer to the Newtonian velocity corresponding to low or high shear or to have a transitional character between both Newtonian velocities. Some numerical examples for the velocity at different Carreau and Womersley numbers are presented for illustration with respect to the similar Newtonian flow velocity.

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Wave Propagation in Submerged Pipe Conveying Fluid

Deng

Yang

2019

Acta Mech. Solida Sin.

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Purely pulsating flow of a viscoelastic fluid in a pipe revisited: The limit of large Womersley number

Cited by 6 publications

References 19 publications

Fluctuating Flexoelectric Membranes in Asymmetric Viscoelastic Media: Power Spectrum through Mechanical Network and Transfer Function Models

Fluctuating Flexoelectric Membranes in Asymmetric Viscoelastic Media: Power Spectrum through Mechanical Network and Transfer Function Models

Oscillatory Carreau flows in straight channels

Wave Propagation in Submerged Pipe Conveying Fluid

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