Solute uptake through the walls of a pulsating channel

Waters, Sarah L.

doi:10.1017/s0022112000003396

Cited by 23 publications

(29 citation statements)

References 21 publications

(26 reference statements)

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“…4; the diamonds are equally spaced by 0.05 along the ∆ axis). We now briefly discuss the dynamics for the secondary system (14), (15). Since the tapering flow function F 1 appears explicitly in (14), we expect any exponential growth in F 1 to force exponential growth in G 1 (with a structure analogous to (24) with F replaced by G), and this is what we find.…”

Section: Resultssupporting

confidence: 57%

“…In particular, flow in pulsating pipes and channels has been used to model blood flow in coronary arteries [12] and transmyocardial revascularisation in heart tissue [15,16], whilst oscillating flow in a tapered channel has been used to model ventilation in the lung [4]. The present investigation, which considers flow in a slightly tapering channel with oscillating walls, was motivated at an early stage by the desire to model the motion of digestive juices in the upper part of the stomach, whose diameter tends to decrease as the lower part of the stomach is approached.…”

Section: Introductionmentioning

confidence: 99%

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Flow in a slowly tapering channel with oscillating walls

Rickett

Blyth

2014

Acta Mech

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The flow of a fluid in a channel with walls inclined at an angle to each other is investigated at arbitrary Reynolds number. The flow is driven by an oscillatory motion of the wall incorporating a timeperiodic displacement perpendicular to the channel centreline. The gap between the walls varies linearly with distance along the channel and is a prescribed periodic function of time. An approximate solution is constructed assuming that the angle of inclination of the walls is small. At leading order, the flow corresponds to that in a channel with parallel, vertically oscillating walls examined by Hall and Papageorgiou (J. Fluid Mech. 393:59-87, 1999). A careful study of the governing partial differential system for the first-order approximation controlling the tapering flow due to the wall inclination is conducted. It is found that as the Reynolds number is increased from zero the tapering flow loses symmetry and undergoes exponential growth in time. The loss of symmetry occurs at a lower Reynolds number than the symmetry breaking for the parallel-wall flow. A window of asymmetric, time-periodic solutions is found at higher Reynolds number, and these are reached via a quasiperiodic transient from a given set of initial conditions. Beyond this window, stability is again lost to exponentially growing solutions as the Reynolds number is increased.

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Section: Resultssupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Flow in a slowly tapering channel with oscillating walls

Rickett

Blyth

2014

Acta Mech

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“…For a comprehensive review we refer the reader to the monograph by Drazin & Riley (2006). Besides its inherent mathematical interest, self-similar solutions of extensional channels are being used to model a wide variety of multidisciplinar phenomena such as physiological blood flows or oxygen transport in cardiac systems (Waters, 2001). Special cases of self-similar extensional flows in channels and pipes have been studied by many authors in the past addressing particular geometries and boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Extensional channel flow revisited: a dynamical systems perspective

et al. 2017

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Extensional self-similar flows in a channel are explored numerically for arbitrary stretching–shrinking rates of the confining parallel walls. The present analysis embraces time integrations, and continuations of steady and periodic solutions unfolded in the parameter space. Previous studies focused on the analysis of branches of steady solutions for particular stretching–shrinking rates, although recent studies focused also on the dynamical aspects of the problems. We have adopted a dynamical systems perspective, analysing the instabilities and bifurcations the base state undergoes when increasing the Reynolds number. It has been found that the base state becomes unstable for small Reynolds numbers, and a transitional region including complex dynamics takes place at intermediate Reynolds numbers, depending on the wall acceleration values. The base flow instabilities are constitutive parts of different codimension-two bifurcations that control the dynamics in parameter space. For large Reynolds numbers, the restriction to self-similarity results in simple flows with no realistic behaviour, but the flows obtained in the transition region can be a valuable tool for the understanding of the dynamics of realistic Navier–Stokes solutions.

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“…Few studies in this field may include Secomb (1978), Hydon and Pedley (1993), Waters (2001) etc. Dispersion process through a channel forced by unsteady pressure gradient has been studied by Mazumder (2009), Mazumder and.…”

Section: Introductionmentioning

confidence: 99%

On Dispersion in Oscillatory Annular Flow Driven Jointly by Pressure Pulsation and Wall Oscillation

Roy

Saha

Debnath

2017

JAFM

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Longitudinal dispersion of solute released in an unsteady flow between two coaxial cylinders is re-examined in the presence of first order chemical kinetics in the bulk flow. The flow unsteadiness is caused by the oscillation of the outer tube around its axis as well as by a periodic pressure gradient. Unlike some previous works, the gap width of the annular tube is used as the typical length scale which is physically meaningful to a greater extent. In order to employ the method of moment, a finite difference implicit scheme has been adopted to solve the Aris integral moment equations arising from the unsteady convective diffusion equation for all time periods. The individual and combined effects of different velocity components resulting from steady and timedependent parts of the driving forces are examined and they are identified based on their functionality. In any flow situation, wall factor is found to have a larger contribution in velocity as well as in dispersion compared to the pressure factor. The behaviour of dispersion coefficient with the variation of radius ratio, bulk flow reaction parameter, and frequency parameters have been examined. Dispersion coefficient is found to diminish with the increase of the reaction-rate in the bulk flow, whereas the effect of the radius ratio on the dispersion coefficient is fixed by the form of the velocity distribution. The axial distributions of mean concentration are approximated using Hermite polynomial representation from the first four central moments for a range of different reaction-rate parameters. It has been found that, irrespective of the flow situation, the peak of the concentration distribution decreases with the increase in reaction rate parameter.

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Solute uptake through the walls of a pulsating channel

Cited by 23 publications

References 21 publications

Flow in a slowly tapering channel with oscillating walls

Flow in a slowly tapering channel with oscillating walls

Extensional channel flow revisited: a dynamical systems perspective

On Dispersion in Oscillatory Annular Flow Driven Jointly by Pressure Pulsation and Wall Oscillation

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