Investigations On Newtonian And Non-newtonian Peristaltic Flows In A Two-dimensional Channel

Peristaltic flows of Newtonian and non-Newtonian fluids in a two-dimensional channel are studied in the present thesis, in which micropolar fluid model and Bingham fluid model are adopted to simulate the non-Newtonian fluids. Considering a horizontal two-dimensional channel with distensible walls, progressive waves, which are produced by periodic contraction and expansion of the walls, propagate symmetrically along the channel to transport the fluid ahead. Long wavelength and low Reynolds number approximations are used throughout the thesis. Furthermore, the channel flow in one wavelength is considered due to the periodicity of the flow with a constant pressure difference between two ends. Under such assumptions, analytical solutions are developed for the three peristaltic flows and investigations on flow characteristics and effects of parameters are presented.In the study of Newtonian peristaltic flow, from the basic equations, we choose the parameters of flow and dimensionless forms of variables and equations. In the wave frame, which moves with the travelling waves, the flow can be treated as steady. For Newtonian fluid, the peristaltic flow is determined only by wave amplitude and pressure difference. For given amplitude of the wave, the time mean flow rate in the fixed frame is linearly related to the pressure difference. When the pressure drop is small, the peristalsis effect on pumping the fluid appears evident, while it becomes obscure for large pressure drop where the pressure plays a leading role in transporting the fluid. For good match of wave amplitude and pressure drop, one can observe the phenomenon of trapping, the formation of an internally circulating bolus of fluid enclosed by a closed streamline. For the micropolar fluid, magnetic force is considered in the momentum equation and slip boundary condition is used for velocity and common boundary condition for micro-rotation vector. The influences on peristalsis and trapping of couple number, micropolar parameter and slip coefficient are analyzed. The asymmetrical stress tensor of micropolar fluid is also discussed. A paradox will be encountered in the problem of Bingham peristaltic flow if classical Bingham plastic fluid model is adopted; hence a bi-viscosity model for Bingham fluid is employed to solve the problem and the study in the thesis improves the investigations of peristaltic flow of yield-stress fluid. The investigation includes the discussion of existing conditions of two different yield interfaces, the analytical expressions for the interfaces and the relationships between the yielded section, unyielded section and re-yielded section. Critical flow rates, various flow types, correspondence of parameters and flow types are also studied. Non-linear relationship between pressure drop and flow rate is discovered due to the presence of yield stress. Limit flow rates for trapping are developed and how the yield stress affects the bolus in size is discussed as well.