Theoretical Investigations of Peristaltic and Ciliary Transport

Abstract

Fluid transport induced by a progressive wave of area contraction or expansion along the flexible walls of the tube or channel is termed as peristalsis. In human body, this mechanism starts from the lower pharynx and continues in esophagus, stomach and intestines. It is also responsible for the transportation in reproductive and glandular ducts. In the industry, this mechanism is assumed for controlled transport of fluids inside the tracts. To avoid the blockage and to keep apart the fluid contents from the tract boundaries, it is also used to provide additional pumping to the flows in heart- lung machines, artificial heart pumps, etc. On the other hand a sub branch of peristalsis is known as cilia that are small hair like structures, which protrude from cell surfaces and play important roles in motility, sensory perception and development in a wide range of eukaryotes including human. In the adult human body, epithelial cells with motile cilia are highly rich in airways, reproductive tracts and specific brain regions. In these tissues, motile cilia are important for clearance of mucosa (airways), transport of oocytes (fallopian tubes) and circulation of cerebrospinal fluid (brain). While many human tissues have non-motile or (primary cilia), cilia generally occur one per cell examples of primary cilia can be found in human sensory organs such as the eye and the nose.Ciliary motion has become the attention of many researchers due to its possible use of ciliabased actuators as micromixers, for flow control in tiny bio sensors, or as micropumps for drug-delivery systems. The purpose of the present research is to explore the cilia and peristaltic transport phenomenon in the presence of the nanoparticles in different flow geometries such asannulus, non-uniform tube and a curved channel. Keeping all above appreciated applications in mind, the challenge now is to understand in detail mechanisms of ciliary beating and peristaltic motion for viscous and different non-Newtonian fluids in different geometries. Nanofluid is also taken into account for both the phenomenon. The mathematical analysis are carried out in the wave frame of reference under the assumption of long wave length and low Reynolds number approximation. For the purpose of simplification non-dimensionalization of the variables are used. We have managed exact solution for the viscous fluid equations and semi analytical solution are obtained for equations appearing for the non-Newtonian fluid. Analysis for the fluid velocity, nanoparticles temperature, nanoparticle concentration, pressure gradient and stream function is presented. Graphical results are presented to observe the physical behavior of various rising parameters on these flow characteristics. The streamlines pattern along with trapping phenomena is discussed in detail. Numerical integration are carried out for the graphical representation of pressure rise in order to discuss pumping characteristics. The thesis consists of nine chapters which are designated as follow: Chapter one is devoted to the brief introduction of peristaltic as well as ciliary flows. Chapter two examinesexploration of single wall carbon nanotubes for the peristaltic motion in a curved channel with variable viscosity. In this chapter nanoparticles impact as wellas variable viscosity effect on fluid flow are mathematically examined. Exact solution is managed for temperature and for velocity profiles. Contents of this chapter are published in the J ournal of "Brazilian Society of Mechanical Sciences and Engineering" (2016) DOl. 10.1007/s40430-016-0612-9. Chapter three deals with the hypothetical analysis for peristaltic transport of metallic nanoparticles in an inclined annulus with variable viscosity. Exact solution is calculated for temperature and velocity profiles. Results for horizontal, inclined and vertical annulus are also compared. This chapter's contents are published in the Journal "Bulletin of the Polish Academy of Sciences: Technical Sciences" 64(2)(2016) 447--454. Analysis of nanoparticles on peristaltic flow of Prandtl fluid model in an endoscope is studied in chapter four. The flow is modelled in both fixed and wave frame of reference. Homotopy perturbation method for the solutions of velocity profile, nanoparticle concentration and temperature profile is used. However, the expression for pressure rise is intended by numerical integration. Contents of this chapter are published in the Journal of "Current Nanoscience"10(2014)709-721. In chapter five,metachronal wave of cilia transport in a curved channel are discussed. The features of ciliary structures are determined by the dominance of viscous effects over inertial effects using the longwavelength approximation. Flow properties for the viscous fluid are determined as a function of the cilia and metachronal wave velocity. The resulting relations for pressure gradient and pressure rise are designed for numerous pertinent parameters. The streamlines are drained for various quantities to deliberate the trapping phenomenon. Contents of this chapter are published in the Journal of'ZeitschriftfiirNaturforschung A"70(2015)33-38. In chapter six, the study is dragging by introducing the nanoparticles effect. The flow is modeled in both fixed and wave frame of reference. Exact solution is obtained for the velocity as well as for temperature profile.The flow properties for the Cu-blood nanofluid is determined as a function of the cilia and metachronal wave velocity. Results for straight channel are also recovered. Contents of this chapter are published in the Journal of "IEEE Transactions on NanoBioscience"14(2015)447-454. Influences of slip and Cu-blood nanofluid in a physiological study of cilia is deliberated in chapter seven. In this study the right wall and the left wall possess metachronal wave that is travelling along the outer boundary of the channel. Exact solutions of obtained dimensionless boundary value problem are presented. Contents of this chapter are published in the journal of "Computer Methods and Programs in Biomedicine" 131(2016)169-180. In chapter eight, ciliary motion phenomenon of viscous nanofluid in a curved channel with wall properties are discussed. Closed form solutions for the nanoparticles temperature, velocity and streamlines are calculated and deliberated. Contents of this chapter arepublished in the Journal of "TheEuropean Physical Journal Plus" 65(2016)131. In chapter nine, trapping study of nanofluids In an annulus with cilia is investigated. The current theoretical model may be supposed as mathematical illustration to the movement of ciliary motion in the occurrence of an endoscopic tube (or catheter tube). The inner tube is rigid, while the outer tube takes a metachronal wave. Results are discussed through graphs and the trapping phenomenon is presented at the end of this chapter. Contents of this chapter are published in the Journal of "AlP advances"5(2016)127204.