Peristaltic Flow of Viscoelastic Liquids
TL;DR: In this article, the authors investigated peristaltic pumping by means of an infinite train of waves travelling along the wall of a cylindrical tube, which is based on the general second-order integral constitutive equation for simple liquids.
Abstract: Peristaltic pumping is investigated, generated by means of an infinite train of waves travelling along the wall of a cylindrical tube. The theory is based on the general second order integral constitutive equation for viscoelastic (simple) liquids. Analytical and closed form solutions are presented for the first order and the stationary part of the second order flow field approximations with respect to the amplitude ratio. It turns out that the zero—shear viscosity η 0 and the complex viscosity η*(ω) are the only relevant fluid properties.
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TL;DR: The effect of a magnetic field on peristaltic transport of blood in a non-uniform two-dimensional channels has been investigated under zero Reynolds number with long wavelength approximation and it is found that the pressure rise decreases as the couple-stress fluid parameter @c increases and increases as the Hartmann number M increases.
248 citations
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: In this article, the effect of channel width, wave amplitude, phase shift, and mean pressure gradient on the streamline pattern and properties of peristaltic flow in two-dimensional channels with sinusoidal waves is analyzed.
Abstract: Peristaltic flow in two-dimensional channels with sinusoidal waves is analysed. Under the assumption of creeping motion, the problem is formulated using the boundary integral method for Stokes flow. The effect of channel width, wave amplitude, phase shift, and mean pressure gradient on the streamline pattern and the properties of the flow is considered. The results are discussed with reference to various physiological and engineering processes. It is suggested that under the quasi-steady approximation, peristaltic flow with a varying mean pressure gradient offers an efficient method for molecular-convective transport.
197 citations
TL;DR: The paper presents the transportation of viscoelastic fluid with fractional Maxwell model by peristalsis through a channel under long wavelength and low Reynolds number approximations.
191 citations
Cites background from "Peristaltic Flow of Viscoelastic Li..."
...Bohme and Friedrich [2] investigated the peristaltic flow of viscoelastic liquids....
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...Friedrich [13] has developed a model to determine the relaxation and retardation time with different fractional time derivatives in the stress-strain relation by using the Riemann–Liouville definition....
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TL;DR: In this article, a numerical method employing an upwind finite-difference technique is adopted for an investigation of peristaltic pumping in circular cylindrical tubes, and the influence of the magnitude of these quantities on the flow is investigated.
Abstract: A numerical method employing an upwind finite-difference technique is adopted for an investigation of peristaltic pumping in circular cylindrical tubes. such as some organs in the living body. Various peristaltic flows are calculated under conditions of finite wave amplitudes, finite wavelengths and finite Reynolds numbers, and the influence of the magnitude of these quantities on the flow is investigated. The fluid mechanics of peristaltic mixing and transport are studied in detail by analysing the reflux and the trapping phenomena. The mechanical efficiency of peristaltic pumping is also discussed, with reference to engineering and physiological applications. It is shown that quantitative differences are observed between the results obtained for flows in a circular cylindrical tube and a two-dimensional plane channel. However, for both cases the appearance of peristaltic reflux depends upon the Reynolds number and the wavenumber (mean tube radius/wavelength). Much greater peristaltic mixing and transport are realized in a circular tube than in a plane channel.
185 citations
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TL;DR: In this article, the authors investigated the effect of peristaltic wave propagation on the flow of fluid in a tube and showed that the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow and that the percentage of reflux flow can be very high.
Abstract: Pumping by means of an infinite train of peristaltic waves is investigated under conditions for which the relevant Reynolds number is small enough for inertial effects to be negligible and the wavelength to diameter ratio is large enough for the pressure to be considered uniform over the cross-section. Theoretical results are presented for both plane and axisymmetric geometries, and for amplitude ratios ranging from zero to full occlusion. For a given amplitude ratio, the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow. An experiment with a quasi-two-dimensional apparatus confirmed the theoretical values.Calculations of the detailed fluid motions reveal that under many conditions of operation the net time-mean flow is the algebraic difference between a forward time-mean flow in the core of the tube and a backward (‘reflux’) time-mean flow near the periphery. The percentage of reflux flow can be very high. This reflux phenomenon is probably of physiologic significance in the functioning of the ureter and the gastro-intestinal system. A second fluid-mechanical peculiarity with physiological implications is that of ‘trapping’: under certain conditions an internally circulating bolus of fluid, lying about the axis, is transported with the wave speed as though it were trapped by the wave.
1,298 citations
01 Sep 1968
TL;DR: In this paper, the authors investigated the effect of peristaltic wave propagation on the flow of fluid in the tube and showed that the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow, and that the percentage of reflux flow can be very high.
Abstract: : Pumping by means of an infinite train of peristaltic waves is investigated under conditions for which (1) the relevant Reynolds number is small enough for inertial effects to be negligible and (2) the wavelength-diameter ratio is large enough for the pressure to be considered uniform over the cross-section. Theoretical results are presented for both plane and axi-symmetric geometries, and for amplitude ratios ranging from zero to full occlusion. For a given amplitude ratio, the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow. An experiment with a quasi-two-dimensional apparatus confirmed the theoretical values. Calculations of the detailed fluid motions reveal that under many conditions of operation the net time-mean flow is the algebraic difference between a forward time-mean flow in the core of the tube and a backward ('reflux') time-mean flow near the periphery. The percentage of reflux flow can be very high. This reflux phenomenon is probably of physiologic significance in the functioning of the ureter and the gastro-intestinal system. A second fluid mechanical peculiarity with physiological implications is that of 'trapping': under certain conditions an internally-circulating bolus of fluid, lying about the axis, is transported with the wave speed as though it were trapped by the wave. (Author)
1,104 citations
TL;DR: In this paper, the peristaltic motion of a power law fluid in a tube, with a sinusoidal wave of small amplitude travelling down its wall, was modeled as a power series in terms of the amplitude of the wave.
Abstract: To understand theoretically the flow properties of physiological fluids, we have considered as a model the peristaltic motion of a power law fluid in a tube, with a sinusoidal wave of small amplitude travelling down its wall. The solution for the stream function is obtained as a power series in terms of the amplitude of the wave. The stream function and the velocity components are evaluated by solving numerically two point boundary value problems with a singular point at the origin. The influence of the applied pressure gradient along with non-Newtonian parameters on the streamlines and velocity profiles are discussed in detail.
157 citations
108 citations