SOME FLOW PROBLEMS IN PERISTALSIS ON DISPERSION: EFFECTS OF WALL PROPERTIES

Abstract

Bio-fluid mechanics is part of biomechanics which describes the kinematics and dynamics of body fluids in humans, animals and plants. It uses the general principles of fluid mechanics which involve some new applications to biological systems. Modern bio-fluid mechanics measures and analyzes the fluid flow in the blood vessels, the respiratory system, the lymphatic system, the gastrointestinal system, the urinary system and many other physiological situations. Studies in this area are important for clinical applications such as artificial organs, vascular vessel development, and design of medical tools and fabrication of materials membranes for orthopedics. The interaction of peristalsis with dispersion studies in this thesis since they are very important phenomena in biological, chemical, environmental and bio-medical processes. We briefly describe below the concepts of peristalsis and dispersion so that the problems studied in this thesis can be properly understood. Peristalsis is a form of material transport induced by a progressive wave of area contraction or expansion travelling along the length of a distensible tube or channel containing the fluid. Physiologically, peristaltic action is an inherent property of smooth muscle contraction. Peristalsis is an automatic and vital process that drives the urine from the kidney to the bladder through the ureter, food through the digestive tract, bile from the gall bladder into the duodenum, the movement of spermatozoa in the ducts efferents of the male reproductive tract, movement of the ovum in the Fallopian tube, vasomotion in small blood vessels and many others. Peristaltic flows play an indispensable role in some biomedical instruments such as heart-lung machine. A major industrial application of this mechanism is in the design of the finger and roller pumps, which are used in pumping fluids without being contaminated due to the contact with the pumping machinery. This mechanism is also used for transport of vii sensitive or corrosive fluids, sanitary fluids, slurries and noxious fluids in the nuclear industry. Although the peristaltic action is quite prevalent in biological systems, the first theoretical and experimental aspects of its fluid dynamics were discussed about four decades ago. Several theoretical and experimental studies have been made to understand the phenomenon of peristalsis using various geometries, fluids, wave shapes, etc. In view of its importance, a number of researchers have investigated peristaltic transport of Newtonian and non- Newtonian fluids under different circumstances. Flow through porous medium has captivated significant attention in recent years due to its prospective applications in nearly all fields of engineering, biomechanics and Geo-fluid dynamics. Also, as most of the tissues in the body are deformable porous media. Peristaltic transportation of a bio-fluid through a conduit with permeable walls is of considerable importance in biology and medicine. Analysis of flow past a permeable medium is used immensely in biomedical problems to understand the transportation process in the lungs, gall bladder and kidneys, to investigate inter vertebral disc tissues, cartilage and bones etc. Some of the physiological systems such as blood vessel consists of porous layers. Peristalsis is also important in blood vessels; it will be interesting to know the effects of permeability on the peristaltic pumping. Flow through porous media has been of significant interest to understand the complexity of disease like bladder stones, intestinal cystitis, and bacterial infections of the kidneys. Porous medium models are applied to identify the various medical conditions and treatments. As the fluid displays a loss of adhesion at the wetted wall, the fluid is made to slide along the wall, resulting in slip flow, as seen in several applications like flow through pipes in wherein chemical reactions occur in the walls. Slippage is claimed to occur in Newtonian and non-Newtonian fluids, molten polymer and concentrated polymer solution. Dispersion is the process by which matter is transported from one part of a system to another as a result of random molecular motions. Dispersion plays a chief role in applications like chromatographic separations in chemical engineering, pollutant transport in the environment, mixing and transport of drugs viii or toxins in physiological systems, and so on. Further, it is known to balance material in the bio artificial kidney and transporting of oxygen in the human body. The fluid mechanical aspects of hydrodynamic dispersion of a solute in a viscous fluid have received the attention of several investigators. It is envisaged that peristalsis may enhance the dispersion of a solute in the fluid flow. This, in turn, may help in better absorption of nutrients and drugs in physiological systems. Further, the dynamical interaction between the fluid flow and movement of flexible boundaries may also be significant in peristaltic transport. Hence, the study of the interaction of peristalsis with dispersion under different conditions may lead to better understanding of the flow situation in physiological systems. This is the core reason why this thesis is aimed at these physiologically relevant phenomena. In view of the above discussion, an attempt has been made in this thesis, to study dispersion of a solute in peristaltic motion of Newtonian and non- Newtonian fluids with wall properties by considering different characteristics such as porous media and magnetic field in a channel with elastic wall. The incompressible viscous fluid and couple stress fluid models are used since these are known to be better models for physiological fluids such as blood, bile, and chyme. The expression for the mean effective coefficient of dispersion is developed by using long wavelenght hypothesis and Taylor’s limiting condition. Mathematica software is used to analyze the results graphically. ix