Lagrangian transport by peristalsis in a closed cavity

2016

Synchronized contractions of the muscles that push food contents over the gastrointestinal (GI) tract to facilitate normal digestion and the absorption of nutrients is known as peristalsis. This phenomenon depends upon the synchronization between the muscles, nerves and hormones in the digestive tract. Apart from that peristalsis is also involved in urine transport from kidney to bladder, bile transfers from gall bladder into the duodenum, the transport of spermatozoa, blood circulation in small blood vessels, the motion of chyme in the small intestine, the mechanical and neurological aspects of reflux, transport of lymph in the lymphatic vessels and in the vasomotion of small blood vessels such as arterioles, venules and capillaries. Applications of peristalsis in industry include the transport of high solids slurries, aggressive chemicals, noxious fluids (nuclear industries) and other materials which are transported by peristaltic pumps. Hose pumps, roller pumps, tube pumps, heartlung machines, finger pumps, blood pumps and dialysis machines operate according to the principle of peristalsis. The mechanism of peristalsis is studied extensively in past few decades because of its practical importance. Literature survey indicates that a number of theoretical and experimental studies have been carried out dealing with peristaltic motion in straight geometries. However, less attention is paid to the analysis of peristaltic motion in curved channel. Moreover, such studies further narrow down for non-isothermal case. In view of the above mentioned gaps in the literature, the aim of this thesis is mainly to investigate the peristaltic flow of non-Newtonian fluids in a curved channel under long wavelength and low Reynolds number assumptions. The effects of magnetic field and heat transfer on the flow are also investigated. All problems are solved in dimensionless form with the help of analytical (regular and singular perturbation techniques) and numerical methods (finite difference technique, BVP4C technique, Spectral Chebyschev Collocation technique). The thesis is organized in the following manner. Chapter one is based on the brief introduction of peristaltic flows. Some basic definitions, fundamental equations in curvilinear coordinates and review of existing literature on peristalsis involving viscous and non-Newtonian fluids is presented. The important dimensionless numbers are also defined. In chapter two, peristaltic motion of a viscoelastic Jeffrey fluid in a curved channel under the influence of radially-imposed magnetic field is investigated. The Jeffrey fluid model is a fairly simple linear model using a time derivative instead of a convected derivative as featured in the Oldroyd-B model. This model includes elastic and memory effects known to be exhibited by gastric fluids and also certain dilute polymer solutions. The problem is first normalized and then governing partial differential equations are reduced to a single linear ordinary differential equation in terms of a stream function under long wavelength and low Reynolds number approximations. Exact as well as asymptotic solutions of this equation are obtained. The graphs of velocity profile and pressure rise per wavelength are plotted. The streamlines are presented to discuss the trapping phenomenon. The contents of this chapter are submitted for publication in the journal "AIP Advances". Chapter three deals with the peristaltic motion of an Oldroyd-B fluid in a curved channel. The flow equation is derived under long wavelength and low Reynolds number assumptions. Matlab built-in routine bvp4c is utilized to solve this nonlinear ordinary differential equation. Numerical solution for axial velocity, pressure gradient, pressure rise per wavelength and stream function are obtained for various values of Weissenberg number. The interaction of curvature parameter with Weissenberg number is highlighted. This study is published in "Meccanica", 51 (2016) 87-98. Chapter four examines the peristaltic transport of an Oldroyd 4-constant fluid through a curved channel. The components of stress, based on the constitutive equation of an Oldroyd 4-constant fluid are obtained in curvilinear coordinates. The governing equation is formulated in a wave frame of reference. The present flow model subject to long wavelength and low Reynolds number involves viscoelastic features. Moreover, the governing equations under such approximations are nonlinear. The resulting nonlinear mathematical problem is solved numerically by a finite-difference method (FDM) with an iterative scheme. Special attention is given to the flow characteristics, pumping and trapping phenomena. A comparative study between curved and straight channels is also included. The contents of this chapter are currently under review in "Brazilian Society of Mechanical Sciences and Engineering". Chapter five looks at the peristaltic motion of an incompressible Carreau fluid in a curved channel. The Carreau fluid model is capable of robustly predicting shear thinning, shear thickening and relaxation effects. Numerical solution of governing boundary value problem is presented by using a finite-difference method (FDM) with an iterative scheme. The nonlinear boundary value problem (BVP) is also solved with an optimized spectral Chebyschev collocation method (SCCM). An excellent correlation is observed between the results obtained by both methods. Boundary layer formation at the channel walls is observed for large values of Weissenberg number and for strong shear-thinning fluid. The pumping and trapping phenomena are illustrated. The analysis presented in this chapter is * 3 2 3 3 1 12 *  = 0.0061 and  = 0.4.

Mathematical and Computer Modelling, 2008

Peristalsis is defined as a wave of relaxation contraction imparted to the walls of a flexible conduit effecting the pumping of enclosed material. Intense research on peristalsis has been attempted and is still demanded due to its practical applications especially in physiology. Examples ...

Mathematical Problems in Engineering, 2003

This paper is devoted to the study of the two-dimensional flow of a Johnson-Segalman fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic travelling wave of large wavelength. Both analytical and numerical solutions are presented. The analysis for the analytical solution is carried out for small Weissenberg numbers. (A Weissenberg number is the ratio of the relaxation time of the fluid to a characteristic time associated with the flow.) Analytical solutions have been obtained for the stream function from which the relations of the velocity and the longitudinal pressure gradient have been derived. The expression of the pressure rise over a wavelength has also been determined. Numerical computations are performed and compared to the perturbation analysis. Several limiting situations with their implications can be examined from the presented analysis.

Physics Letters A, 2008

The effects of both magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel are studied analytically and numerically. The channel asymmetry is generated by propagation of waves on the channel walls travelling with different amplitudes, phases but with the same speed. The long wavelength and low Reynolds number assumptions are considered in obtaining solution for the flow. The flow is investigated in a wave frame of reference moving with velocity of the wave. Closed form expressions have been obtained for the stream function and the axial velocity component in fixed frame. The effects of phase difference, Knudsen number and magnetic field on the pumping characteristics and velocity field are discussed. Several known results of interest are found to follow as particular cases of the solution of the problem considered.

Journal of Fluid Mechanics, 1979

This analysis demonstrates theoretically that a lateral bending wave propagating along the walls of a two-dimensional channel filled with a viscous incompressible fluid will induce a mean flow. In addition to this ‘pure’ bending wave, another possible condition is investigated: that of the superposition of an area contraction wave propagating with the same speed as the lateral bending wave. This second condition, called complex wave motion, takes into account the slight occlusion which occurs naturally at the amplitude peaks when a finite amplitude bending wave propagates along the walls of a container. A perturbation solution is found which satisfies Navier—Stokes equations for the case in which wave amplitude/wavelength is ‘small’. However the wave amplitude is finite, in the sense that it is of the same order as the channel width. Under these conditions, the occlusion at the amplitude peaks is allowed to be of the same order as the channel width. For the case of a pure bending wa...

Physics of Fluids, 2016

We analyze the peristaltic motion of aqueous electrolytes altered by means of applied electric fields. Handling electrolytes in typical peristaltic channel material such as polyvinyl chloride and Teflon leads to the generation of a net surface charge on the channel walls, which attracts counter-ions and repels co-ions from the aqueous solution, thus leading to the formation of an electrical double layer-a region of net charges near the wall. We analyze the spatial distribution of pressure and wall shear stress for a continuous wave train and single pulse peristaltic wave in the presence of an electrical (electroosmotic) body force, which acts on the net charges in the electrical double layer. We then analyze the effect of the electroosmotic body force on the particle reflux as elucidated through the net displacement of neutrally buoyant particles in the flow as the peristaltic waves progress. The impact of combined electroosmosis and peristalsis on trapping of a fluid volume (e.g., bolus) inside the travelling wave is also discussed. The present analysis goes beyond the traditional analysis, which neglects the possibility of coupling the net pumping of fluids due to peristalsis and allows us to derive general expressions for the pressure drop and flow rate in order to set up a general framework for incorporating flow control and actuation by simultaneous peristalsis and application of electric fields to aqueous solutions. It is envisaged that the results presented here may act as a model for the design of lab-on-a-chip devices. Published by AIP Publishing.

Communications in Nonlinear Science and Numerical Simulation, 2010

Of concern in this paper is an investigation of peristaltic transport of a physiological fluid in an asymmetric channel under long wave length and low-Reynolds number assumptions. The flow is assumed to be incompressible, viscous electrically conducting micropolar fluid and the effect of induced magnetic field is taken into account. Exact analytical solutions obtained for the axial velocity, microrotation component, stream line pattern, magnetic force function, axial induced magnetic field as well as the current distribution across the channel. The flow phenomena for the pumping characteristics, trapping and reflux are also investigated. The results presented reveal that the velocity decreases with the increase of magnetic field as well as the coupling parameter. Moreover the trapping fluid can be eliminated by the application of an external magnetic field. Thus the study bears the promise of important applications in physiological systems.

International Journal of Engineering Science, 1999

This paper is devoted to the analytical study of the two-dimensional¯ow of a power-law¯uid with a peripheral layer. The analysis is carried out by using wavelength approximations. The solution has been obtained in the form of a stream function from which the shape of the interface has been determined. The relation between the¯ow-rate and the pressure dierence for one wavelength has been derived. This is used to determine the maximum pressure and the maximum¯ow-rate. The expressions for the eciency of pumping, the trapping limit and the re¯ux limit have also been determined. The computational results indicate that the¯ow is increased when the value of the¯ow behaviour index is raised or the viscosity of the outer layer is increased. The study reveals that in the case of physiological¯ows where the viscosity of the peripheral layer is usually less than that of the core layer, a thinner peripheral layer is responsible for a greater¯ow-rate.

IOSR Journal of Mathematics, 2016

Peristaltic pumping is a form of the fluid transport in a flexible tube caused by a progressive wave of contraction or expansion from a region of lower pressure to higher pressure. Peristalsis is one of the major mechanisms for fluid in many biological systems. It is an automatic and vital process that moves food through the digestive tract, urine from the kidneys through the ureters into the bladder, and bile from the gall bladder into the duodenum and transport of blood through the artery with mild stenosis. In addition, the mechanism of peristalsis is applied in the design of biomechanical instruments in chas heart-lung machine. In many biomechanical devices such as small blood vessels, the tube wall is not rigid. The tissne region of the blood vessel is modelled as a permeable layer. In view of this it will interesting to study peristaltic pulsatile flow of a viscous fluid in a tube with permeable boundary. In this paper, we study the effect of the pulsatile flow on the peristaltic pumping of a Newtonian fluid in an axi symmetric cylindrical tube with permeable wall is investigated The analytical solution of this problem is given as on asymptotic expansion in the Womersly number  which characterize the unsteadyness effect in the wave frame. The pumping characteristics are discussed.

International Journal of Applied and Computational Mathematics

In this paper we have investigated the effect of slip velocity on peristaltic transport of a physiological fluid through a porous non-uniform channel under the long wave length and low-Reynolds number assumptions. We analyzed the flow characteristics of incompressible, viscous, electrically conducting micropolar fluid (a non-Newtonian fluid model). The analytical expressions for the axial velocity, microrotation component, stream function as well as the pressure gradient are obtained. The flow phenomena for the pumping characteristics, trapping and reflux are furthermore investigated. The results presented here reveal that the central line velocity decreases with the increase of magnetic field strength as well as the slip parameter. Again the velocity increases with the increase of porous permeability parameter. Moreover the trapping fluid can be eliminated with a considerable extent by the application of an external magnetic field as well as by increasing the slip parameter. Thus the study bears the promise to keep important applications in physiological systems.