A Fractal Analysis Of Flow Properties In Roughened Microchannles

Tremendous attention has been given to fluid flow properties in the field of science and technology due to the rapid development of Micro-Electro-Mechanical Systems (MEMS), microelectronic devices, micro mechanical and micro processing technology, etc. such as materials science and engineering, petroleum engineering, biomedical application, biological transport phenomena, fuel cell, environment and engineering, etc. In nature, smooth surface is almost non-existent, or very rare. Most of surfaces (such as engineering surfaces) are rough by microscope observation. Surfaces of capillaries in porous media, surfaces of pores, surfaces of micro channels are also rough. Therefore, appropriate methods should be selected to characterize and study the rough surface of capillaries in porous media and in roughened microchannels, which renders scientific significance and application value of research. It has been shown that natural porous media have fractal characters, such as disordered, random, and self-similar properties. Therefore, the fractal geometry theory has been applied to describe the microstructural characteristics of porous media. Moreover, applications of the fractal geometry theory in description and study of porous media and the effects of microstructures of solid surfaces on fluid flow characters become one of the hot topics in the disciplines of condensed matter physics, complex sciences and engineering thermal physics.At present numerical simulations or experimental methods have been used to study the fluid flow characteristics in the rough microchannels. However, these methods cannot get the analytical experessions for the fluid flow characteristics, such as velocity distribution, pressure drop, etc. In this dissertation, the theory and method of fractal geometry are applied to describe the properties of the surface structure of rough microchannels, and the analytical expressions, which do not contain any empirical constants, are derived.In this dissertation, Chapter1briefly introduces porous media and the fractal geometry theory for the rough surface, the fractal-like tree branching network model and the models composed of a bundle of capillaries, respectively. Then, the permeability of fluid flow through porous media is reviewed briefly. At last, this chapter outlines the continuous medium model and Hagen Poiseuille law of fluid flow.Then, in Chapter2, considering the fluid flow through roughened microchannels, and based on the contact spots (roughness elements) on engineering surfaces following the fractal scaling law, we assume that the spots on surfaces are cone-shaped, and the base diameters of cone-shaped follow the fractal scaling law. Based on the results of the numerical simulations and exprimantal data, the fractal geometry method is used to study the fluid flow characteristics in rough micro channels. The pressure gradients, friction factors and Poiseuille numbers for laminar flow through microchannels with roughened surfaces are derived and found to be the functions of the microstructural parameters of roughness surfaces (such as the fractal dimension, maximum peak, minimum peak, and the ratio of the minimum diameter to the maximum diameter of conic peaks on roughened surfaces). Moreover, every parameter in the proposed models has clear physical meaning.Pores in porous media may connect into tortuous capillaries or form fractal-like branching structures, therefore, based on the fractal-like tree branching network model and the model composed of a bundle of capillaries, in Chapter3, we derive the permeability for laminar flow through fractal-like tree networks with roughened channels and a bundle of rough capillaries. Then the relationships between the relative roughness and the permeability are found and discussed.The heat transfer coefficient based on numerical simulation or experiments was extensively studied for flow through roughened channels, but no analytical solution was reported so far. Therefore, in Chapter4, the roughness model is used to study the single-phase forced convective heat transfer inside rough micro channels. The expressions of the heat transfer coefficient, the heat transferred by convection and the equivalent dimensionless thermal conductivity are also derived and expressed as functions of structure parameters of rough surfaces and the relative roughness.Finally, In Chapter5, the conclusions and innovations of the present thesis are sumarrized, and some comments are also made on the potential research subjects and directions about fluid flow in rough porous media.