CHAPTER - I GENIERAL INTRODUCTION

CHAPTER - I GENIERAL INTRODUCTION

1. PERISTALSIS Peristalsis is an important mechanism for mixing and transporting fluids, which is generated by a progressive wave of contraction or expansion moving on the wall of the tube. Physiological fluids in animal and human bodies are, in general, pumped by the continuous periodic muscular oscillations of the ducts. These oscillations are presumed to be caused by the progressive transverse contraction waves that propagate along the walls of the ducts. Peristalsis is the mechanism of the fluid transport that occurs generally from a region of lower presswe to higher presswe when a progressive wave of area contraction and expansion travels along the flexible wall of the tube. Peristaltic flows occurs widely in the hctioning of the ureter, food mixing and chyme movement in the intestine, movement of eggs in the fallopian tube, the transport of the spermatozoa in cervical canal, transport of bile in the bile duct, transport of cilia, and circulation of blood in small blood vessels. 2. PHYSIOLOGICAL SYSTEMS ASSOCIATED WITH PERISTALSIS 2.1 GASTROINTESTINAL TRACT Two types of movements occur in the gastrointestinal tract: (1) Propulsive movements, which cause food to move forward along the tract at an appropriate rate to accommodate digestion and absorption and(2) mixing movements, which keep the intestinal contents thoroughly mixed at all times, Propulsive Movements - Peristalsis The basic propulsive movement of the gastrointestinal tract is peristalsis, which is illustrated in Fig. 1. A contractile ring appears around the gut and then moves forward; this is analogous to putting one's fingers around a thin distended tube, then constricting the fingers and sliding them forward along the tube. Any material in front of the contractile ring is moved forward.

Pehstaftic contraction I Leading wave of distention Zero time s 5 seconds later Mixing Movements Fig. 1 Peristalsis The mixing movements are quite different in different parts of the alimentary tract. In some areas, the peristaltic contractions themselves cause most of the mixing. This is especially true when f~nvard'~ro~ression of the intestinal contents is blocked by a sphincter, so that a peristaltic wave can then only churn the intestinal contents, rather than propelling them forward. 2.2 ESOPHAGUS The esophagus normally exhibits two types of peristaltic movements: primary peristalsis and secondary peristalsis. Primary peristalsis is simply a continuation of the peristaltic wave that begins in the pharynx and spreads into the esophagus during thc pharyngeal stage of swallowing. This wave passes all the way from the pharynx to the stomach in about 8 to LO seconds. Food swallowed by a person who is in the upright position is usually transmitted to the lower end of the esophagus even more rapidly than the peristaltic wave itself, in about 5 to 8 seconds, because of thiadditional effect of gravity pulling the food downward. If the primary peristaltic wave fails to move into the stomach all the food that has cntered the esophagus, secondary peristaltic waves result from the distention of the esophagus by the retained food, and these waves continue until all the food

has emptied into the stomach. These secondary waves are initiated partly by intrinsic neural circuits in the myenteric nervous system and partly by reflexes that begin in the pharynx, then are transmitted upward through vagal afferent fibers to the medulla and then back again to the esophagus through glossopharyngeal and vagal efferent nerve fibers. 2.3 SMALL INTESTINE Chyme is propelled through the small intestine by peristaltic waves. These can occur in any part of the small intestine, and they move analward at a velocity of 0.5 to 2.0 cdsec, much faster in the proximal intestine and much slower in the terminal intestine. They normally are very weak and usually die out atter travelling only 3 to 5 centimeters, very rarely farther than 10 centimeters, so that forward movement of the chyme is very slow, so that net movement along the small intestine normally averages only 1 cdmin. The function of the peristaltic waves in the small intestine is not only to cause progression of the chyme toward the ileocecal value but also to spread out the chyme along the intestinal mucosa. As the chyme enters the intestine from the stomach and causes initial distention of the proximal intestine, the elicited peristaltic waves begin immediately to spread the chyme along the intestine; this process intensifies as additional chyme enters the duodenum. Peristaltic Rush Although peristalsis in the small intestine is normally very weak, intense irritation of the intestinal mucosa, as occurs in some severe cases of infectious diarrhea, can cause both powerfi~l and rapid peristalsis, called the peristaltic rush. This is initiated partly by nervous reflexes that involve the autonomic nervous system and the brain system and partly by intrinsic enhancement of the myenteric plexus reflexes within the gut wall itself. The powerful peristaltic contractions travel long distances in the small intestine within minutes, sweeping the contents of the intestine into the colon and thereby relieving the small intestine of irritative chyme and excessive distention.

2.4 LARGE INTESTINE Large intestines nonnally exhibit four types of motions: 1. Rhythmic variations oftone, 2. Peristalsis, 3. Mass peristalsis and 4. Anti-peristalsis. Rhythmic variations of tone This take places throughout the large intestine but not always and is not at all concerned with propulsion; it rather maintains adequate circulation through the wall and helps in the absorption of water. Peristalsis Peristalsis is not equivalent as rush peristalsis seen in the small intestine. It is a weak peristalsis alternately shortening and elongating in the transverse colon. Mass peristalsis A movement is a modified type of peristalsis characterized by the following sequence of events: First, a constrictive ring occurs in response to a distended or irritated point in the colon, usually in the transverse colon. Then, rapidly thereafter the 20 or more centimeters colon distal to the constriction lose their haustrations and instead contract as a unit, forcing the fecal material in this segment en masse further down the colon. The contractiondevelop progressively more force for about 30 seconds, and relaxation and then occurs during the next 2-3 minutes. Then, another mass movement occurs, this time perhaps farther along the colon. Anti-peristalsis In the early stages of excessive gastrointestinal irritation, anti-peristalsis begins to occur often many minutes before vomiting appears. The anti-peristalsis may begin as far down in the intestinal tract as the ileum, and the anti-peristaltic wave travels backward up the intestine at a rate of 2-3 cmlsec; this process can actually push a large share of the intestinal contents all the way back to the duodenum and stomach within 3-5 minutes. Then, as these upper portions of the gastrointestinal tract, especially the duodenum, become overly distended, this destination becomes the exiting factor that initiates the actual vomiting act. In man it is rarely seen but is well marked in animals such as cat.

2.5 RENAL SYSTEM Ureters The ureters propel the urine fiom the kidneys into the bladder by peristaltic contraction of smooth muscle layer. This is an intrinsic property of the smooth muscle and is not under autonomic nerve control. The waves of contraction originate in a pacemaker in the minor calyces. Peristaltic waves occur several times per minute, increasing in frequencies with the volume of urine produced, and send little spurts of urine into the bladder. 2.6 REPRODUCTIVE SYSTEM Fallopian tubes The uterine tubes are about locm long and extend from the sides of the uterus between the body and the fundus. They lie in the upper free border of the broad ligament and their trumpet-shaped lateral ends penetrate the posterior wall, opening into the peritoneal cavity close to the ovaries. The end of each tube has finger like projections called fimbriae. The longest of these is the ovarian fimbriae, which is in close association with ovary. The uterine tubes (fallopian tubes) convey the ovum from the ovary to the uterus by peristalsis and ciliary movements. 3. CLASSIFICATION OF nuids 1. Newtonian Fluid If shear stress is linearly proportional to the rate of strain, the fluid is called as a Newtonian fluid. Newtonian behaviour has been observed in all gases in liquids or solutions of materials of low molecular weight. In this thesis an attempt is made to study the flow of Newtonian fluids. The constitute equation for Newtonian fluid is r =py wherer, f is the shear rate, r is the stress andp is the viscosity of the fluid.

2. Non-Newtonian Fluid Non-Newtonian fluids generally exhibit a nonlinear relationship between the shear stress and rate of strain. Food stuffs (like banana juice, apple juice, chyme), blood, slurries, sperm, intra uterine fluid, etc. behave like non-newtonian fluids. In this thesis an attempt is made to study the following non-newtonian fluids: (a) Jeffrey Fluid The Jeffrey model is relatively simpler linear model using time derivatives instead of convected derivatives for example Oldroyd-B model does; it represents a rheology different from the Newtonian. The constitute equation for the Jeffrey fluid is where pis the dynamic viscosity of the fluid, j is the shear rate, A, is the ratio of relaxation to retardation times and & is the retardation time and dots over the quantities denote differentiation. (b) Third Order Fluid Third order fluid behaves like a non-newtonian fluid. Its viscosity and all other material parameters (non-newtonian coefficients) are taken as constants. These material parameters of third order fluid appropriate to shear thinning. The constitute equation for the third order fluid is -- --?=pxta,i: +F~(AIIAI ta~a~)+/?,(tr~)~i where p is the viscosity, a,,a,, 4, P2, P, are the material constants and the Rivlin- Ericksen tensors (An) are given through the following relations - A, = (pudf) + (grai)i

d where -=is material derivative, V is the velocity and T is the superscript denotes dt the transpose. 4. A BRIEF SURVEY OF LITERATURE The problem of the mechanism of peristaltic transport has attracted the attention,of many investigators since the first investigation of Latham (1966). At the same time Burns and Parkes (1967) gave a perturbation solution to the mathematical formulation of peristaltic flow through a tube and a channel, in powers of the amplitude ratio. Barton and Raynor (1968) have studied the corresponding axisymmetric case. A contemporary investigation was reported by Shapiro (1967) for two-dimensional peristaltic pumping under conditions that the appropriate Reynolds number is so small that the flow may be considered inertia - free and long wavelength. Asymptotic solutions for the peristaltic transport in axisymmetric tubes in terms of the ratio of the small amplitude to the mean radius was given by Yin and Fung (1969) for a finite range of Reynolds number and wavelength, following the investigation of Fung and Yih (1968) in two - dimensional channel case. The small amplitude assumption has been relaxed under large wavelength approximation by Shapiro et al. (1969). Complete reviews on peristaltic pumping have been given by Jaffrin and Shapiro (1971) and in a book by Rath (1980). The experimental verification of these models by Weinberg et al. (1 97 1) confirmed that the Lagrangian approach should be used to obtain the criterion for the backward leakage of fluid particles with long wave approximation. Another experimental investigation by Yin and Fung (1969) confirmed the theoretical analysis of small amplitude peristaltic motion at finite Reynolds number and fmite wavelength. The unsteady peristaltic flow of a Newtonian fluid in a finite length tube was studied by Li and Brasseur (1993) with lubrication approach and they explore the pressure and shear rate (at the wall) distribution of a Newtonian viscous fluid flow. Also they compared the difference between integral number and non-

integral number of waves propagating along a tube of finite len%h. Antmovaskii and Ramkisson (1997) have studied the long-wave peristaltic transport of a compressible viscous fluid in a finite pipe subject to a the-dependent Pressure drop. Uterine contractions at the time of embryo transfer alter pregnancy rates after in-vivo fertilization has been discussed by Fanchin et al. (1998). An analysis of Intra-uterine fluid motion induced by uterine contractions has been investigated by Eytan and Elad (1999). They have obtained a time dependent flow solutions in a fixed frame by using lubrication approach. These results have been used to understand fluid flow in pattern in a non-pregnant uterus. Eytan et al. (2001) extended their previous model of uniform channel to a non-uniform (tapered) channel and discussed the application to embryo transport within the uterine cavity. On the other hand a numerical technique using boundary integral method has been developed by Powikidis (1987) to investigate peristaltic transport in an asymmetric channel under Stokes flow conditions to understand the fluid dynamics involved. He has studied the streamline patterns and mean flow rate due to different amplitudes and phases of the wall deformation. Peristaltic flow of a blood under effect of a magnetic field in non-uniform channel has been studied by Mekheimer (2004). Many researchers considered the fluid to behave like a Newtonian fluid for physiological peristalsis including the flow of blood in arterioles. But such a model cannot be suitable for blood flow unless the non-newtonian nature of the fluid is included in it. A theoretical investigation for blood flow by considering blood as a non-newtonian (power-law) fluid was reported by Raju and Devanathan (1972). They employed the perturbation technique used by Chow (1970) to solve the model of the flow in a cylindrical tube with a sinusoidal wave of small amplitude. Later Girija Devi and Devanathan (1975) extended the same problem to replace power-law nature of the fluid by micropolar nature. Consequently a similar solution for viscoelastic liquids was studied by Bohme and Friedrich (1983). Also they discussed mechanical efficiency of pumping for such

liquids. Peristaltic flow of non - Newtonian fluids containing small spherical particles has been discussed by Rath and Reese (1984). Shukla and Gupta (1982) was studied the peristaltic transport of a power-law fluid with variable consistency. Peristaltic transport of non - Newtonian fluids with the application to the vas deferens and small intestine was studied by Srivastava and Srivastava (1985). Consequently; peristaltic transport of power law fluid has been discussed by Srivastava and Srivastava (1988) with the application to the ductus efferentes of the reproductive tract. The non - Newtonian peristaltic flow using a constitutive equation for a second order fluid has been investigated by Siddiqui et al. (1991) for a planar channel and by Siddiqui and Schwarz (1994) for an axisymmetric tube. They have performed a perturbation analysis with a wave number, including curvature and inertia effects and have determined range of validity of their perturbation solutions. The effects of third order fluid on peristaltic transport in a planar channel were studied by Siddiqui et al. (1993) and the corresponding axisymmetric tube results are obtained by Hayat et al. (2002). The non- Newtonian effects of Maxwel fluid on peristaltic transport have been discussed by Tsiklauri and Beresnev (2001). El Naby and El Misiery (2002) investigate peristaltic transport of Carreau fluid in a tube, while Johnson - Segalman fluid has been used for study by Hayat et al. (2003). Hayat et al. (2004) have discussed the effects of an Oldroyd-B fluid on the peristaltic mechanism. Srivastava et al. (1983) studied the peristaltic transport of a fluid with variable viscosity through a non-uniform tube. Abd El Hakeem et al. (2003) have investigated the peristaltic flow of a fluid with variable viscosity under the effect of magnetic field. Abd El Hakeem et al. (2004) have discussed the effect of endoscope and fluid with variable viscosity on peristaltic motion. The non- Newtonian fluids are Bingham and Herschel- Bulkley fluids. Vajravelu et al. (2005 a, 2005 b) made a detailed study on the effect of yield stress on peristaltic pumping of a Herschel - Bukley fluid in an inclined tube and a channel. Hayat et al. (2006) have discussed the effect an endoscope on the peristaltic pumping of a

Jeffrey fluid. Subba Reddy et al. (2007) have studied the peristaltic motion of power-law fluid in an asymmetric channel. Hayat and Ali (2008) have investigated the effect of variable viscosity on the peristaltic flow of a Newtonian fluid in asymmetric channel. Flows through porous medium occur in filtration of fluids and seepage of water in river beds. Movement of underground, water and oils, limestone, rye bread, wood, the human lung, bile duct, gall blander with stones, and small blood vessels are some important examples of flow through porous medium. Another example is the seepage under a dam which is very important Rathy (1976). Several works have been published by using the generalized Darcy's law A.E. Scheidegger (1963), where the connection acceleration and viscous- stress are taken in to account Yamamoto (1976). The net flow of compressible viscous liquids induced by traveling waves in porous mdia has been studied by Aarts and Ooms (1998). The effects of porous boundaries on peristaltic transport through a porous medium in a two- dimensional channel have been studied by El Shehawey and Husseny (2003) in a futed frame analysis. The peristaltic transport in a cylindrical tube through a porous medium has been studied by El Shehwey and El Sebaei (2000). The non-linear and magneto-hydrodynamic flow effect in peristaltic transport through a porous medium was studied by Mekheimer and Ali Arabi (2003). Mekheimer (2003) have investigated the non linear peristaltic flow through a porous medium in an inclined planar channel. El - Shehawey et al. (2006) have studied peristaltic transport in an asymmetric channel through a porous medium. Hayat et al. (2007) have studied the effects on peristaltic flow of a Maxwell fluid in a porous medium. Peristaltic flow of MHD Jeffrey fluid through a porous medium with compliant walls ha been studied by Hayat et al. (2007). Most of the Physiological fluids prevail in living organisms are conducting fluids. For example blood in the arterial system is reported to be a conducting fluid (Sud et al. 1977). Hence a proper knowledge of the interaction of peristalsis with magnetic field may help in better understanding of the flow pattern of blood

in bio-medical instruments like hemodialyser, heart-lung machine. Agrawal and Anwaruddin (1984) have studied the effect of magnetic field on the peristaltic flow of blood using long wavelength approximation method and observed for the flow of blood in arteries with arterial stenosis or arteriosclerosis, that the influence of magnetic field may be utilized as blood pump in carrying out cardiac operations. The peristaltic transport of blood under the influence of a magnetic fieid in non uniform channels was studied by Mekheimer (2004). Elshahed and Haroun (2005) have studied the peristaltic transport of Johnson- Segalman fluid under the effect of a niagnetic field. Abd El Hakeem et al. (2006) have investigated the peristaltic flow of generalized Newtonian fluid through a uniform tube under the effect of a magnetic field. Recently Hayat and Ali (2007) have investigated the peristaltic motion of an incompressible non- Newtonian fluid in a deformable tube under the effect of a magnetic fluid. More Recently Hayat et al. (2007) have investigated the peristaltic motion of a third order fluid under the influence of a magnetic field in a uniform channel. Hayat et al. (2007) have studied the non-linear peristaltic flow of a fourth grade fluid in a planar channel.. Hayat et al. (2007) have investigated the peristaltic flow a Jeffrey fluid in an axisymmetric tube. Hayat et al. (2008) have studied the peristaltic flow of a Jeffrey fluid through a porous medium in a channel under the effect of magnetic field with compliant walls. The effect of an endoscope and magnet field on the peristaltic flow involving Jeffrey fluid have discussed by Hayat et al. (2008).