Peristaltic transport of rheological fluid:model for movement of food bolus through esophagus

Fluid mechanical peristaltic transport through esophagus is studied in the paper. A mathematical model has been developed to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube lengths. The Ostwald-de Waele power law of a viscous fluid is considered here to depict the non-Newtonian behaviour of the fluid. The model is formulated and analyzed specifically to explore some important information concerning the movement of food bolus through esophagus. The analysis is carried out by using the lubrication theory. The study is particularly suitable for the cases where the Reynolds number is small. The esophagus is treated as a circular tube through which the transport of food bolus takes place by periodic contraction of the esophageal wall. Variation of different variables concerned with the transport phenomena such as pressure, flow velocities, particle trajectory, and reflux is investigated for a single wave as well as a train of periodic peristaltic waves. The locally variable pressure is seen to be highly sensitive to the flow index ＂n＂. The study clearly shows that continuous fluid transport for Newtonian/rheological fluids by wave train propagation is more effective than widely spaced single wave propagation in the case of peristaltic movement of food bolus in the esophagus.

Unsteady peristaltic transport of Maxwell fluid through finite length tube:application to oesophageal swallowing

This paper analytically investigates the unsteady peristaltic transport of the Maxwell fluid in a finite tube. The walls of the tube are subjected to the contraction waves that do not cross the stationary boundaries. The analysis is carried out by a long wavelength approximation in the non-dimensional form. The expressions for the axial and radial velocities are derived. The pressures across the wavelength and the tubelength are also estimated. The reflux phenomenon is discussed, which culminates into the determination of the reflux limit. Mathematical formulations are physically interpreted for the flow of masticated food materials such as bread and white eggs in the oesophagus. It is revealed that the Maxwell fluids are favorable to flow in the oesophagus as compared with the Newtonian fluids. This endorses the experimental finding of Takahashi et al. （Takahashi, T., Ogoshi, H., Miyamoto, K., and Yao, M. L. Viscoelastic properties of commercial plain yoghurts and trial foods for swallowing disorders. Rheology, 27, 169- 172 （1999））. It is further revealed that the relaxation time does not affect the shear stress and the reflux limit. It is found that the pressure peaks are identical in the integral case while different in the non-integral case.

Interaction between compressibility and particulate suspension on peristaltically driven flow in planar channel

The peristaltic pumping of a viscous compressible liquid mixed with rigid spherical particles of the same size in a channel is theoretically investigated. The momentum equations for the compressible flow are solved with a perturbation analysis. The analysis is carried out by duly accounting for the nonlinear convective acceleration terms for the fluid part on the wavy wall. The zeroth-order terms yield the Poiseuille flow, and the first-order terms give the Orr-Sommerfeld equation. The explicit expression for the net axial velocity is derived. The effects of the embedded parameters on the axial fluid velocity are studied through different engineering applications. The features of the flow characteristics are analyzed and discussed in detail. The obtained results are evaluated for various parameters associated with the blood flow in the blood vessels with diameters less than 5 500 μm, whereas the particle diameter has been taken to be 8 μm. This study provides a scope to evaluate the effect of the theory of two-phase flow characteristics with compressible fluid problems, and is helpful for understanding the role of engineering applications of pumping solid-fluid mixture by peristaltically driven motion.

DTM Simulation of Peristaltic Viscoelastic Biofluid Flow in Asymmetric Porous Media： A Digestive Transport Model

A biofluid dynamics mathematical model is developed to study peristaltic flow of non-Newtonian physiological liquid in a two-dimensional asymmetric channel containing porous media as a simulation of obstructed digestive （intestinal） transport. The fractional Oldroyd-B viscoelastic rheological model is utilized. The biophysical flow regime is constructed as a wave-like motion and porous medium is simulated with a modified Darcy-Brinkman model. This model is aimed at describing the diges- tive transport in intestinal tract containing deposits which induce impedance. A low Reynolds number approximation is em- ployed to eliminate inertial effects and the wavelength to diameter ratio is assumed to be large. The differential transform method （DTM）, a semi-computational technique is employed to obtain approximate analytical solutions to the boundary value problem. The influences of fractional （rheological material） parameters, relaxation time, retardation time, amplitude of the wave, and permeability parameter on peristaltic flow characteristics such as volumetric flow rate, pressure difference and wall friction force are computed. The present model is relevant to flow in diseased intestines.

Electro-magnetohydrodynamic Flow of Biofluid Induced by Peristaltic Wave： A Non-newtonian Model

This article aims to develop a mathematical model for peristaltic transport of magnetohydrodynamic flow of biofluids through a micro-channel with rhythmically contracting and expanding walls under the influence of an applied electric field. The couple stress fluid model is considered to represent the non-Newtonian characteristics ofbiofluids. The velocity slip condition at the channel walls is taken into account because of the hyclrophilic/hydrophobic interaction with negatively charged walls. The essential features of the electromagnetohydrodynamic flow of biofluid through micro-channels are clearly highlighted in the variations of the non-dimensional parameters of the physical quantities of interest such as the velocity, wall shear stress, pressure gradient, pressure rise per wave length, frictional force at the channel walls and the distribution of stream function. It reveals that the flow ofhiofluid is appreciably influenced by the sufficient strength of externally applied magnetic field and electro-osmotic parameter. The velocity slip condition reduces the frictional force at the channel wall. Moreover, the formation of the trapping bolus strongly depends on electro-osmotic parameter and magnetic field strength.

Series solution of a natural convection flow for a Carreau fluid in a vertical channel with peristalsis

An analysis has been achieved to study the natural convection of a non-Newtonian fluid （namely a Carreau fluid） in a vertical channel with rhythmically contracting walls. The Navier-Stokes and the energy equations are reduced to a system of non- linear PDE by using the long wavelength approximation. The optimal homotopy analysis method （OHAM） is introduced to obtain the exact solutions for velocity and temperature fields. The convergence of the obtained OHAM solution is discussed explicitly. Numerical calculations are carried out for the pressure rise and the features of the flow and temperature characteristics are analyzed by plotting graphs and discussed in detail.

Couple stress fluid flow in a rotating channel with peristalsis

This article describes a new model for obtaining closed-form semi-analytical solutions of peristaltic flow induced by sinusoidal wave trains propagating with constant speed on the walls of a two-dimensional rotating infinite channel. The channel rotates with a constant angular speed about the z-axis and is filled with couple stress fluid. The governing equations of the channel deformation and the flow rate inside the channel are derived using the lubrication theory approach. The resulting equations are solved, using the homotopy perturbation method（HPM）, for exact solutions to the longitudinal velocity distribution, pressure gradient, flow rate due to secondary velocity, and pressure rise per wavelength. The effect of various values of physical parameters, such as, Taylor＇s number and couple stress parameter, together with some interesting features of peristaltic flow are discussed through graphs. The trapping phenomenon is investigated for different values of parameters under consideration. It is shown that Taylor＇s number and the couple stress parameter have an increasing effect on the longitudinal velocity distribution till half of the channel, on the flow rate due to secondary velocity, and on the number of closed streamlines circulating the bolus.