Peristaltic flow of blood under effect of a magnetic field in a non-uniform channels

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.

Non-steady peristaltic transport in finite-length tubes

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.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112087001939

A study of peristaltic flow

Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel

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.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112088002149

Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency

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.

D. Nikolakis

Papers

Peristaltic Flow of Viscoelastic Liquids