【作者】 徐鹏；

【导师】 郁伯铭； Arun S.Mujumdar；

【作者基本信息】 华中科技大学 ， 凝聚态物理， 2008， 博士

【摘要】 不管是在生命系统还是非生命系统中都大量存在着一种非常普遍而又很特殊的几何结构——树状分叉结构。其中最明显和典型的例子是植物躯干网络和叶片的脉络网络。生物组织中也大量存在这种结构,比如哺乳动物的血液循环系统、支气管、肺动脉以及神经网络等等,和植物的分叉网络不同的是,这些生理分叉网络一般隐藏于生理组织的内部而且具有更为复杂的结构。另外这种树状分叉网络的存在范围非常广泛,诸如河流盆地、三角洲、闪电、地下油藏、裂缝、材料科学等都存在典型的树状分叉结构。近年来随着多学科的交叉以及微电子冷却的需求,这种树状分叉网络又引发了全球范围内的多个领域的研究热潮,并且在很多新兴的工程领域得到广泛应用。其中比较典型的是树状分叉网络在电子器件微通道冷却技术、燃料电池流道设计、微流体流动控制以及城市水电气供给、通讯和信息网络等领域的应用。这类树状分叉网络,尤其是自然分叉结构,往往具有自相似的特征,并在一定尺度范围内具有分形结构,分形几何理论为研究这类复杂的结构提供了一个很好的理论工具。本文的研究目的是系统研究这类具有分形特征的树状分叉网络输运特性,本研究对于理解和揭示自然分叉结构的输运机理的科学理论以及工程应用都有非常重要的意义。本文共分六章,第一章介绍树状分叉网络的研究背景、最新研究进展以及分形和输运过程的基本理论,并且给出树状分形分叉网络的一般描述方法;第二章介绍了Murray定律及其推广形式,根据阻力最小化原理在不同输运过程中优化单分叉结构;第三章研究了树状分形分叉网络的传热特性,推导了分叉网络的有效热导率,计算了嵌入H型分叉网络的复合材料的导热特性,还通过计算流体力学的方法(CFD)数值计算了圆形分叉网络的对流换热特性;第四章研究了两种特殊分叉网络的层流流动和渗流特性,并且提出了由母体多孔介质和分形分叉网络模型组成双重多孔介质的理论模型、并计算了各向异性多孔介质的径向有效渗透率;第五章研究和总结树状分形分叉网络的输运特性,并较系统地给出了这类网络的传导性标度律;第六章总结了本文的主要内容并且对于树状分形分叉网络理论研究和应用提出了一些展望。更多还原

【Abstract】 The tree-like branching network structures abound in both living and non-living systems, such as tree, leaves, mammalian circulatory and respiratory systems, neural dendrites, river basins, deltas, lightning, oil/water reservior, streets, rapid solidification etc. The efficient transport characteristics of natural branching systems can provide useful hints for optimal solutions of many engineering problems, which have fascinated researchers in physics, chemistry, biology, physiology, engineering and geology for ages and been applied in microelectronic cooling, flow-field designs in fuel cell, microfluidic manifolds in lab-on-a-chip systems etc. The tree-like branching network has been shown to be a conventional self-similar fractal network and the ideas of fractal geometry can be implemented to study the network. The objective of the current research is to investigate the transport properties of tree-like branching network with fractal characteristics and the effect of microstructures on the transport properties of network, which will shed light on mechanism of natural network and application in engineering.This thesis is organized as six Chapters. In Chapter 1, the progress of tree-like branching network, fractal and transport theory, and general description of fractal tree-like branching network are introduced and reviewed. In Chapter 2, Murray’s law, which is the fundamental in this field, and its generalized forms are addressed, and the single branching structure is optimized by minimizing resistance under fixed volume for different transport processes. Chapter 3 focuses on the thermal properties of fractal tree-like branching network. In this chapter, the effective heat conductivity is derived, the heat conduction of composite material embedded with H shaped branching network is studied, and the disc-shaped branching network with/without loops is simulated with CFD for heat convection. In Chapter 4, the laminar flow and seepage flow in two kinds of fractal tree-like branching network are investigated, the radial effective permeability of heterogeneous porous media is calculated with the proposed dual-domain model of fractal tree-like branching network and homogeneous porous medium model. In Chapter 5, the scaling laws between various transport parameters and volume or surface area are derived. Finally, a summary of the present work is given in Chapter 6, and some potential research interests are commented for future study of tree-like branching network and its applications.更多还原