Peristaltic transport in a tapered tube

Theoretical modeling of the resistance to gastric emptying and duodenogastric reflux due to pyloric motility alone, presuming antral and duodenal quiescence

A theoretical model of the pyloric channel, approximated as a two-dimensional tube with sinusoidal corrugation, is developed to estimate the degree of resistance offered by the pylorus to transpyloric flow (gastric emptying and duodenogastric reflux) in the viscous regime. Study indicates that the resistance of the channel depends on pressure gradient, flow behavior index and channel diameter. Flow is majorly determined by the extent of luminal opening; since they scale to fourth power of the diameter for Newtonian flow, with the exponent being higher for pseudoplastic and lesser in case of dilatants relative to Newtonian fluid. At zero pressure difference, across the channel, the closing pylorus drives the aborad propulsion of the contents at the intestinal end, and at the gastric end the flow is driven along the orad direction. While no transfer of contents occur at the centre of pylorus due to zero pressure gradients, it is essential to have a non-zero pressure difference to drive the flow through the channel. The extent of pressure difference is found to linearly relate to the transpyloric flow rate. The resistive function of the pyloric channel is observed at a higher occlusion where there is a development of higher pressure barrier that is sensitive to the flow behavior index, frequency, occlusion, and contraction length.

PERISTALTIC TRANSPORT OF A COUPLE STRESS FLUID: SOME APPLICATIONS TO HEMODYNAMICS

The paper deals with a theoretical investigation of the peristaltic transport of a couple stress fluid in a porous channel. The study is motivated toward investigating the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. The velocity, pressure gradient, stream function, and frictional force of blood are investigated, when the Reynolds number is small and the wavelength is large, by using appropriate analytical and numerical methods. Effects of different physical parameters reflecting porosity, Darcy number, couple stress parameter, as well as amplitude ratio on velocity profiles, pumping action and frictional force, streamlines pattern, and trapping of blood are studied with particular emphasis. The computational results are presented in graphical form. The results are found to be in good agreement with those reported by Shapiro et al.52 that was carried out for a non-porous channel without consideration of couple stress effect. The present study puts forward an important observation that for peristaltic transport of a couple stress fluid during free pumping, flow reversal can be considerably controlled by suitably adjusting the couple stress effect of the fluid/Darcy permeability of the channel. It is also possible to avoid the occurrence of trapping, by reducing the permeability.

PERISTALTIC TRANSPORT OF A MAXWELL FLUID IN A CHANNEL OF VARYING CROSS SECTION INDUCED BY ASYMMETRIC WAVES: APPLICATION TO EMBRYO TRANSPORT WITHIN UTERINE CAVITY

This is an attempt to analyze the peristaltic flow of a Maxwell fluid in a tapered channel. Peristaltic wave trains with different amplitudes and phases are considered to propagate along the two walls of the channel producing asymmetric wall movements. A perturbation technique is employed to solve the problem by giving due consideration to the non-linear convective acceleration terms in the analysis. The effects of the non-Newtonian parameters relaxation time, angle of inclination between channel walls, and phase difference on the mean flow velocity are analyzed. It is found that the mean axial velocity decreases with relaxation time, phase difference, and the angle between the channel walls. Moreover, the value of the mean axial velocity is found to be less with asymmetric waves as compared with symmetric waves.

PERISTALTIC TRANSPORT OF A PHYSIOLOGICAL FLUID IN AN ASYMMETRIC POROUS CHANNEL IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD

This paper deals with a theoretical investigation of the peristaltic transport of a physiological fluid in a porous asymmetric channel under the action of a magnetic field. The stream function, pressure gradient, and axial velocity are studied by using appropriate analytical and numerical techniques. Effects of different physical parameters such as permeability, phase difference, wave amplitude and magnetic parameter on the velocity, pumping characteristics, streamline pattern, and trapping are investigated with particular emphasis. The computational results are presented in graphical form. The results are found to be in perfect agreement with those of a previous study carried out for a nonporous channel in the absence of a magnetic field.

Peristaltic flow in a tapered channel: application to embryo transport within the uterine cavity

Cyclic uterine peristalsis plays a central role in assisting the transport of sperm to the fallopian tube and later in the conception process in transporting the embryo to a fundal site for implantation. Fulfillment of these essential events within the time limits of fertilization and implantation depends on concomitant intrauterine fluid motion induced by uterine wall motility. A model of wall-induced fluid flow within a finite tapered two-dimensional channel was developed to simulate intrauterine fluid flow pattern and transport phenomena due to symmetric and asymmetric wall displacements. The analysis showed that the transport phenomena are strongly dependent on the phase shift of wall displacement and the angle between the walls. The velocities, flow rates, pressure and the axial transport of massless particles are reduced to zero when contractions are completely out of phase. Cases of reflux and trapping in a tapered channel are discussed for the first time. The reflux phenomenon is most likely to occur when wall motility is asymmetric, especially when the angle between the walls increases, while trapping is enhanced as the asymmetric motility and the angle between the channel walls decrease. The relevance of the results to intrauterine fluid transport phenomena, embryo transfer and hydrosalpinx was explored.