Flutter in a quasi-one-dimensional model of a collapsible channel

Pihler-Puzović, Draga; Pedley, T. J.

doi:10.1098/rspa.2014.0015

Cited by 5 publications

(5 citation statements)

References 29 publications

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“…This study follows in the spirit of many previous studies of fluid flow in collapsible vessels and the associated onset of self-excited oscillations, pertinent to physiological phenomena, such as Korotkoff noises generated during sphygmomanometry, wheezing in the lungs and phonation in the vocal folds. Theoretical models for the onset of these self-excited oscillations span empirical lumped parameter models [1,3], reduced long-wavelength models [19,36,43,49,50] and full numerical computations in channels and tubes [17,[27][28][29]41]. Comprehensive literature reviews are available elsewhere [13,18].…”

Section: Introductionmentioning

confidence: 99%

Self-Excited Oscillations in a Collapsible Channel With Applications to Retinal Venous pulsation

Stewart¹,

Foss²

2019

ANZIAM J.

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We consider a theoretical model for the flow of Newtonian fluid through a long flexible-walled channel which is formed from four compliant and rigid compartments arranged alternately in series. We drive the flow using a fixed upstream flux and derive a spatially one-dimensional model using a flow profile assumption. The compliant compartments of the channel are assumed subject to a large external pressure, so the system admits a highly collapsed steady state. Using both a global (linear) stability eigensolver and fully nonlinear simulations, we show that these highly collapsed steady states admit a primary global oscillatory instability similar to observations in a single channel. We also show that in some regions of the parameter space the system admits a secondary mode of instability which can interact with the primary mode and lead to significant changes in the structure of the neutral stability curves. Finally, we apply the predictions of this model to the flow of blood through the central retinal vein and examine the conditions required for the onset of self-excited oscillation. We show that the neutral stability curve of the primary mode of instability discussed above agrees well with canine experimental measurements of the onset of retinal venous pulsation, although there is a large discrepancy in the oscillation frequency.

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Section: Introductionmentioning

confidence: 99%

Self-Excited Oscillations in a Collapsible Channel With Applications to Retinal Venous pulsation

Stewart¹,

Foss²

2019

ANZIAM J.

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“…Arterioles constitute ~1% of tissue volume ( Hansen-Smith et al 1998 ; Leung et al 1992 ), expanding by 10% (0.1% of tissue volume) with each cardiac cycle. Venules can constitute several percent of tissue volume, but because the intraluminal venous pressure is often below the tissue pressure, venules in the artery wall collapse, sustaining intermittent flow ( Pedley and Luo 1998 ; Piechnik et al 2001 ; Pihler-Puzovic and Pedley 2014 ). However, they do have the capacity to inflate as venular luminal pressure exceeds tissue pressure, suddenly increasing tissue volume by several percent ( Barendsen and van den Berg 1984 ).…”

Section: Discussionmentioning

confidence: 99%

Quest for the Vulnerable Atheroma: Carotid Stenosis and Diametric Strain—A Feasibility Study

Yuan

Stutzman

et al. 2016

Ultrasound in Medicine & Biology

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The Bernoulli effect may result in eruption of a vulnerable carotid atheroma, causing a stroke. We measured electrocardiography (ECG)-registered QRS intra-stenotic blood velocity and atheroma strain dynamics in carotid artery walls using ultrasonic tissue Doppler methods, providing displacement and time resolutions of 0.1 μm and 3.7 ms. Of 22 arteries, 1 had a peak systolic velocity (PSV) >280 cm/s, 4 had PSVs between 165 and 280 cm/s and 17 had PSVs <165 cm/s. Eight arteries with PSVs <65 cm/s and 4 of 9 with PSVs between 65 and 165 cm/s had normal systolic diametric expansion (0% and 7%) and corresponding systolic wall thinning. The remaining 10 arteries had abnormal systolic strain dynamics, 2 with diametric reduction (>−0.05 mm), 2 with extreme wall expansion (>0.1 mm), 2 with extreme wall thinning (>−0.1 mm) and 4 with combinations. Decreases in systolic diameter and/or extreme systolic arterial wall thickening may indicate imminent atheroma rupture.

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“…The 2D analysis that follows was initiated by Pedley & Stephanoff (1985) but developed further by Guneratne & Pedley (2006), Kudenatti et al (2012) and Pihler-Puzović & Pedley (2013). The full 2D equations are derived and analysed elsewhere in this Symposium volume by Kudenatti et al (2015); here we merely give an outline and concentrate on the quasi-one dimensional, inviscid system that can be derived for wall displacements that are large compared with the boundary-layer thickness (Pedley & Stephanoff 1985;Pihler-Puzović & Pedley 2014).…”

Section: Rational 1d Modelsmentioning

confidence: 99%

Flow and oscillations in collapsible tubes: Physiological applications and low-dimensional models

Pedley

Pihler-Puzović

2015

Sadhana

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The motivation for this subject comes from physiology: Air-flow in the lungs, where flow limitation during forced expiration is a consequence of large-airway collapse, and wheezing, which is a manifestation of self-excited mechanical oscillations; Blood flow in veins, such as those of giraffes, in which the return of blood to the heart from the head must be accompanied by partial venous collapse, and in arteries, which exhibit self-excited oscillations (Korotkov sounds) when compressed by a blood-pressure cuff. Laboratory experiments are frequently conducted in a Starling resistor, a finite length of flexible tube, mounted between two rigid tubes and contained in a pressurised chamber. Steady conditions upstream and downstream give rise not only to steady flows, but also to a rich variety of self-excited oscillations, which theoreticians have been seeking to understand for at least five decades. Some of the observations have been reproduced in full Navier-Stokes computations for a two-dimensional model, but these do not provide physical understanding. We seek a self-consistent mathematical model for the oscillations. We concentrate first on 1D models, in which the key dependent variables are the cross-sectional area A and the cross-sectionally averaged velocity u and pressure p, all taken to be functions of longitudinal coordinate x and time t. The governing equations are those of conservation of mass and momentum and a tube law representing the elastic properties of the vessel. In the momentum equation, the viscous resistance term is conventionally modelled either as a linear function of fluid velocity, accurate at low Reynolds number, or with an ad hoc representation of the energy loss at flow separation. Even with such crude approximations, the predictions of 1D models agree quite well both with observations in the giraffe and with some of the 2D computations and 3D experiments. For a more rational model, we examine a 2D model problem, in which part of one wall of a parallel sided channel is replaced by a membrane under tension. One * For correspondence 891 892 T J Pedley and D Pihler-Puzović approach, for large Reynolds-number flow, and a long membrane, is to consider small deflections of the membrane and use interactive boundary-layer theory. This leads to interesting predictions, such as the impossibility of simultaneously prescribing the flow rate and the upstream pressure, but not to oscillations, except in cases where wall inertia is important (flutter). Another approach is to assume a parabolic velocity profile everywhere, leading to a rational choice for the inertia and viscous terms in the 1D momentum equation. If, further, the undisturbed membrane is taken to be flat, by a suitable choice of external pressure distribution, the system leads to an oscillatory instability even without wall inertia. Whether these oscillations have the same physics as those computed numerically at lower Reynolds number remains to be seen.

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Flutter in a quasi-one-dimensional model of a collapsible channel

Cited by 5 publications

References 29 publications

Self-Excited Oscillations in a Collapsible Channel With Applications to Retinal Venous pulsation

Self-Excited Oscillations in a Collapsible Channel With Applications to Retinal Venous pulsation

Quest for the Vulnerable Atheroma: Carotid Stenosis and Diametric Strain—A Feasibility Study

Flow and oscillations in collapsible tubes: Physiological applications and low-dimensional models

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