Peristaltic flow analysis in different geometrical aspects under the effect of electro-osmotic forces

Abstract

Biofluid mechanics is the branch of biomechanics that mainly focuses on the dynamics and kinematics of various physiological fluids. One of the prominent mechanisms which are responsible for bio-liquid transport is called peristalsis. This mechanism involves embryo transport in the uterus, swallowing of food through the esophagus, and vasomotion of blood vessels. This mechanism is extensively utilized in the industrial domain for designing various pumps such as finger and roller pumps in which transported medium and machinery are not connected directly. Electroosmosis is the transport of fluids in response to the application of an external electric field across the fluid conduit such as microchannels, capillary tubes, membranes, etc. This phenomenon is extensively used in diverse microfluidic devices which are commonly used in biophysics, microchips, membrane technology, and many more. The core objective of this thesis is to investigate the peristaltically driven electroosmotic transport of various nanofluids (Newtonian and non-Newtonian) in different flow geometries. Poisson Boltzmann and Nernst-Planck equations are employed in different coordinate systems, such as Cartesian coordinates, cylindrical coordinates, and curvilinear coordinates, depending on the considered geometry to model electroosmotic phenomena mathematically. The Tiwari-Das model and modified Buongiorno model are used to characterize the heat transfer properties of nanofluids. The problems under consideration are solved either for an exact solution or approximate solutions through different perturbation and numerical techniques depending on the complexity and nonlinearity of the resulting equations. The present dissertation is divided into ten chapters. Chapter 1 provides an insight into basic concepts of fluid dynamics and includes a detailed literature review of peristalsis and electroosmosis under different physical conditions. It also contains some basic mathematical equations characterizing the electroosmotic phenomenon and mathematical forms of non-Newtonian models being used in this thesis. The next two chapters include the analysis of the combined electroosmotic and peristaltic phenomenon of nanofluids in symmetrical and asymmetrical channels using the Tiwari-Das approach. In the next seven chapters, the properties of both Newtonian and non-Newtonian nanofluids are characterized by a modified Buongiorno model. In these chapters, fluid flows of nanofluids are considered in inclined asymmetrical channels, tubes, and curved channels due to their widespread applications in various biological and industrial domains such as cooling devices. A chapter-wise detailed review is given as: Chapter 2 gives the comparison of the fluid flow properties of viscous fluid by dispersing two different nanoparticles in an aqueous ionic solution. Here, the Tiwari Das model is employed for nanofluid properties, and the effect of mixed convection is also considered. The fluid flow problem is simplified subject to lubrication and the Debye- Hückel linearization principle. Exact analytical solutions are computed for the considered problem, and graphical results are prepared for velocity, temperature, and pressure gradient for both types of nanofluid. Moreover, the trapping phenomenon is also visualized by preparing the contour plots for the streamline function. This chapter has been published in Alexandria Engineering Journal, 59, 943–956 (2020). Chapter 3 presents the electroosmotically modulated peristaltic transport of an aqueous ionic solution with the suspension of single-walled carbon nanotubes. The aspects of velocity and thermal slip are included in the mathematical formulation of the problem. The approximate analytical solutions for the nonlinear problem are obtained with the regular perturbation technique. The results of this finding are compared with previously published literature, and a very good agreement is found. The graphical results for various parameters of interest are prepared and physically interpreted. The observations of this research have been published in the Journal of Thermal Analysis and Calorimetry (2021) https://doi.org/10.1007/s10973-021- 10562-3. Chapter 4 contains the fluid flow analysis of nanofluids driven by the combined forces of peristalsis and electroosmosis in an asymmetric channel. Here the modified Buongiorno nanofluid model is utilized in mathematical modeling, and the Corcione model for thermal conductivity is employed instead of the Maxwell model. The impacts of mixed convection and viscous dissipation are also considered. The mathematical model is subjected to a long-wavelength assumption for simplification. The highly coupled and nonlinear problems are treated numerically through the “dsolve, numeric” command of Maple 17. The findings of this chapter have been published in the Chinese Journal of Physics, 68, 745-763 (2020). Chapter 5 exploresthe electroosmotic flow of methanol-based aluminum oxide nanofluid through a tapered asymmetric channel. The shear-thinning aspect of methanol is characterized by the Sisko fluid model. The modified Darcy’s law is used to model the porosity of the channel. The particular features of electroosmotic flows, i.e., joule heating and viscous dissipation, are not ignored in this investigation. Numerical simulations are performed for the resulting mathematical model simplified under the lubrication approach, and the behavior of fluid flow properties under the influence of various physical parameters is analyzed through graphical results. This research work has been published in Applied Nanoscience, 10 4161-4176, (2020). Chapter 6 investigates the impact of electroosmotic forces on the peristaltically driven flow of blood-based nanofluid through a capillary. The Sutterby fluid model is employed to study blood rheology. The impact of uniform magnetic field and thermal radiation are also accounted and the effective electrical conductivity of nanofluid is estimated through the Maxwell-Garnett model. The graphical results are plotted after solving the resulting mathematical system numerically and a brief physical interpretation is also provided. The outcomes of the conducted research have been published in Microvascular Research, 132 104062, (2020). Chapter 7 contains the study of the heat transfer properties of hybrid nanofluids in comparison with mono nanofluids. Here fluid conduit is chosen to be an inclined asymmetrical channel and fluid is set into motion by combined electroosmosis and peristalsis mechanism. The influence of buoyancy forces is included through the mixed convection phenomenon. The physical significance of physical parameters is assessed through graphs. The key findings of this work have been published in Arabian Journal for Science and Engineering 46, 2911–2927 (2021). Chapter 8 presents the peristaltically induced electroosmotic flow of Ethylene glycol-based boron nitride nanotube in a curved conduit. The analysis is performed in the presence of a radial magnetic field and the impact of Hall and ion slip is also considered. The non-Newtonian Carreau fluid model is utilized to study the rheology of considered nanofluids. Further, the channel walls are assumed to be convectively heated. The mathematical problem linearized under lubrication and Debye- Hückel is executed numerically. The contents of this research work have been published in Arabian Journal for Science and Engineering (2021), https://doi.org/10.1007/s13369-021-06173-7. Chapter 9 includes a comparative analysis of fluid flow properties of two different nanofluids i.e., kerosene oil-based nanofluid and 0.3wt% CMC-water solution-based nanofluid. Here the Newtonian and shear thinning attributes of kerosene oil and CMC-water solution respectively are characterized by the Rabinowitsch fluid model by different choices of the power-law index. The entropy generation analysis is also carried out for both nanofluids. The exact analytical solution expressions are obtained for velocity and streamline function. However, the homotopy perturbation technique is used for obtaining approximate solution expressions for temperature and nanoparticle volume fraction. The key features of this chapter are published in Fluid Dynamic Research. Chapter 10 includes the description of fluid flow and heat transfer properties of nanoparticles-enhanced water-based muds (NWBM) by considering a special kind of mud namely aphron-drilling fluid. Such fluids are very effective in reducing fluid loss during drilling in depleted regions and their rheology is predicted here with the Herschel-Bulkley fluid model. Here the exact solution expressions are obtained for velocity and stream function by limiting the electroosmotic effects only in boundary conditions. Further, the nonlinear energy and concentration equations are executed numerically with the built-in bvp4c command of MATLAB. The observations of this analysis are published in the Mathematical Modelling of Natural Phenomenon.