Peristaltic flow in tubes.
01 Dec 1968-Bulletin of Mathematical Biology (Kluwer Academic Publishers)-Vol. 30, Iss: 4, pp 663-680
TL;DR: The study is concerned with the analysis of two flow domains of peristaltic motion in tubes where the wall disturbance wavelength is much larger than the average tube radius and the disturbance wavelength may be as small as the average radius.
About: This article is published in Bulletin of Mathematical Biology.The article was published on 1968-12-01. It has received 144 citations till now. The article focuses on the topics: Radius & Wavelength.
Citations
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TL;DR: The problem of peristaltic transport of blood in a uniform and non-uniform tube has been investigated, under zero Reynolds number and long wavelength approximation and it is found that, for a given flow rate, the pressure rise decreases as the viscosity of the peripheral layer decreases.
248 citations
TL;DR: In this paper, the peristaltic flow of nanofluids through a two-dimensional channel is analyzed based on the long wavelength and low Reynolds number approximations.
241 citations
Cites background from "Peristaltic flow in tubes."
...Since the experimental work of Latham [1], many investigations [2–4] dealing with peristaltic flow for different flow geometries and under various assumptions, have been presented by employing analytical, numerical and experimental approaches....
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...Barton and Raynor [3] studied the peristaltic motion in a circular tube by using the long wavelength approximation for intestinal flow....
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TL;DR: In this paper, it was shown that the peristaltic transport in a finite-length tube is inherently non-steady and the effect of the number of waves in the tube is independent of tube length.
Abstract: The classical lubrication-theory model of steady peristaltic transport of periodic sinusoidal waves in infinite-length tubes (Shapiro et al. 1969) is generalized to arbitrary wave shape and wavenumber in tubes of finite length. Whereas the classical model is steady in a frame of reference moving with the peristaltic waves, peristaltic transport in a finite-length tube is inherently non-steady. It may be shown, however, that pumping performance is independent of tube length if there exists an integral number of peristaltic waves in the tube. Three particularly interesting characteristics of non-steady peristalsis are described: (i) fluctuations in pressure and shear stress arise due to a non-integral number of waves in the finite-length tube; (ii) retrograde motion of fluid particles during peristaltic transport (reflux) has inherently different behaviour with single peristaltic waves as compared to multiple ‘train waves’, and (iii) finite tube length, the number of peristaltic waves and the degree of tube occlusion affect global pumping performance. We find that, whereas significant increases in pressure and shear stress result from the tube-to-wave length ratio being non-integral, global pumping performance is only slightly degraded by the existence of a non-integral number of waves in the tube during peristaltic transport. Furthermore, the extent of retrograde motion of fluid particles is much greater with single waves than with train waves. These results suggest that in the design and analysis of peristaltic pumps attention should be paid to the unsteady effects of finite tube length and to the differences between single and multiple peristaltic waves.
209 citations
TL;DR: The low Reynolds number flow of a Newtonian fluid in a circular cylindrical tube involving a series of traveling nodal constrictions, which is axisymmetric and infinitely sharp, is studied.
159 citations
TL;DR: In this paper, the peristaltic flow of Herschel-Bulkley fluid in an inclined tube is analyzed and the velocity distribution, the stream function and the volume flow rate are obtained.
Abstract: Peristaltic flow of Herschel–Bulkley fluid in an inclined tube is analyzed. The velocity distribution, the stream function and the volume flow rate are obtained. Also, when the yield stress ratio τ → 0 , and when the inclination parameter α = 0 and the fluid parameter n = 1 , the results agree with those of Jaffrin and Shapiro (Ann. Rev. Fluid Mech. 3 (1971) 13) for peristaltic transport of a Newtonian fluid in a horizontal tube. The effects of τ and n on the pressure drop and the mean flow are discussed through graphs. Furthermore, the results for the peristaltic transport of Bingham and power law fluids through a flexible tube are obtained and discussed. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study of the effects of Herschel–Bulkley fluid on the flow characteristics.
150 citations
References
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TL;DR: In this article, a model of the tail of a spermatozoon is discussed from a hydrodynamical point of view. The tail is assumed to be a flexible cylinder which is distorted by waves of lateral displacement propagated along its length, the resulting stress and motion in the surrounding fluid is analyzed mathematically.
Abstract: The action of the tail of a spermatozoon is discussed from the hydrodynamical point of view. The tail is assumed to be a flexible cylinder which is distorted by waves of lateral displacement propagated along its length. The resulting stress and motion in the surrounding fluid is analyzed mathematically. Waves propagated backwards along the tail give rise to a forward motion with velocity proportional to the square of the ratio of the amplitude of the waves to their length. The rate at which energy must be supplied to maintain the waves against the reaction of the surrounding fluid is calculated. Similar calculations for the case when waves of lateral displacement are propagated as spirals show that the body is propelled at twice the speed given it by waves of the same amplitude when the motion is confined to an axial plane. An externally applied torque is necessary to prevent the reaction of the fluid due to spiral waves from causing the cylinder to rotate. This is remarkable because the cylinder itself does not rotate. A working model of a spermatozoon was made in which spiral waves could travel down a thin rubber tube without rotating it. The torque just referred to was observed and was balanced by an eccentric weight. The performance of the model while swimming freely in glycerine was compared with the calculations. The calculated speed of the model was higher than was observed, but this discrepancy could be accounted for by the fact that the model has a body containing its motive power while the calculations refer to a disembodied tail.
335 citations
TL;DR: In this paper, a theoretical analysis of the propagation of pressure waves through liquid filled flexible tubes is presented, which shows the dependence of phase velocity and damping factor on the viscosity of the liquid, and on internal damping in the tube wall.
Abstract: A theoretical analysis of the propagation of pressure waves through liquid filled flexible tubes is presented. Expressions are derived which show the dependence of phase velocity and damping factor on the viscosity of the liquid, and on internal damping in the tube wall. The analysis is restricted to tubes with thin walls and to waves whose amplitude is infinitesimal and whose wavelength is large compared to the radius of the tube.
150 citations