Some applications of perturbation method in thin plate bending problems

In this paper, problems of bending of thin plates under the combined action of lateral loading and in-plane forces are studied by means of perturbation method.     

具有切应力梯度的平行平板流动腔的构造

在近年来关于流体切应力与细胞力学行为之间关系的研究中,流体切应力梯度被认为是诱发动脉粥样硬化和内膜增生的重要因素之一.本文探讨如何利用常用的离体细胞力学实验工具--平行平板流动腔模拟具有梯度的定常流切应力环境.结果表明,根据Hele-Shaw流的原理和常用复势W(Z)=AZn(n＞1)的特性,可构造出具有各种切应力梯度分布的流动腔.与其它模拟切应力梯度的方法比较,本文的方法更加简洁、可行.     

膨胀性非牛顿流体多孔介质流动的模拟分析

在表征体元尺度采用格子Boltzmann方法分析膨胀性非牛顿流体在多孔介质中的流动,基于二阶矩模型在演化方程中引入表征介质阻力的作用力项,求解描述渗流模型的广义Navier-Stokes方程．采用局部法计算形变速率张量,通过循环迭代得到非牛顿粘度和松弛时间．对多孔介质的Poiseuille流动进行分析,通过比较发现结果与孔隙尺度的解析解十分吻合,并且收敛较快,表明方法合理有效．分析了渗透率和幂律指数对速度和压力降的影响,研究结果表明,膨胀性流体的多孔介质流动不符合达西规律,压力降的增加幅度小于渗透率的减小幅度．当无量纲渗透率Da小于10-5时,流道中的速度呈现均匀分布,并且速度分布随着幂律指数的减小趋于平滑．压力降随着幂律指数的增加而增加,Da越大幂律指数对压力降的影响越明显．     

局部狭窄血管中血液振荡流的速度和切应力

本文建立一种分析局部缓慢狭窄血管中血液振荡流的数学模型，给出了血液的轴向流速，径向流速和切应力的包含压力梯度项的解析表达式，并讨论了血管内由局部狭窄引起的压力梯度沿轴向变化的规律。文章以局部余弦狭窄为例进行数值计算，详细讨论上游均匀管段压力梯度的定常部分和不同次谐波对狭窄管段内流速和切应力的影响。数值结果表明，与均匀管情况相比，在狭窄段内，血液振荡流轴向流速无论平均值还是脉动幅值均明显增大，且径向流速不再为零。但径向流速仍远小于轴向流速。同时，切应力也不再仅由轴向流速梯度提供，径向流速梯度也将产生切应力，但是在计算管壁切向上的切应力时，径向流速梯度的贡献仍相当大。与均匀管管壁切应力沿流运方向保持恒定不同。狭窄管管壁切应力（平均值和脉动值）将随着狭窄高度的增大而增大，在狭窄最大高度处达到最大，因而沿流动方向产生了较大的切应力梯度。     

狭窄血管内偶应力流体流动分析

本文考察了血管狭窄对血液流动的影响,血液以偶应力流体表示,并在求解过程中采用了在管壁上流体质点无相对涡量的边界条件,结果表明,和Young的经典工作相比流动阻抗和壁切应力大于同样程度狭窄下牛顿流体的相应值,偶应力流体对狭窄的敏感性大于牛顿流体;在狭窄发展过程中,偶应力流体的流量要小于牛顿流体的流量,和牛顿流体相比,这些结果更符合生理实际。     

Finite element Galerkin Approach for a Computational Study of Arterial Flow

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定常流下动脉狭窄局部流场的有限元分析

本文利用有限元数值模拟对定常流下动脉狭窄的局部流场进行了系统研究。在数值模拟中求解非线性轴对称Navier-Stokes方程,并对不同狭窄率、不同雷诺数、不同狭窄形状下的流场速度分布、压力降分布和壁面剪应力分布进行了全面细致的分析和讨论。     

A New Unsteady Three Dimensional Model for Macromolecular Transport and Water Filtration Across the Arterial Wall

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水平旋转空腔环流的壁面应力

通过对典型的水平旋转内消能泄洪洞空腔环流的试验观测，研究了其壁面应力的变化规律。空腔环流的壁面压强在水平洞的起始段壁面压强急剧减小然后回升，具有过渡段的性质，沿程波状减小，符合对数变化规律，但不同的流态，对数律的参数的变化是不同的：内界面相对压强Po/Pwz。在淹沿流流态时，随(H-h)/h的变化率显著不同，在吸允流流态时却基本相同；壁面切应力沿z的变化规律为先急剧减小，随后缓慢减小至零，主要与环流特性有密切的关系。     

非牛顿流体在渐变管中压力和剪切应力的二次摄动解

本文利用双摄动方法求解缓慢变化管道中Johnson-Segalman(J-S)流体流动的渐近解．将管道的扩张（或收缩）角度和粘弹性参数分别作为双摄动的参数,由流函数和涡量函数的形式,推导出压力和壁面剪切应力的渐近解．在此基础上,分析了管道角度,粘弹性参数和雷诺数等参数对压力以及剪切力影响．主要结论如下：(1) 管道扩张角度增加时,流向同一位置处径向压力以及壁面剪切应力随扩张角度减小;(2) 在同一扩张管道中,径向压力随着流向位移减小,收缩管与之相反;(3) 扩张角度与雷诺数对流场起主导作用,粘弹性系数起次要作用．     

脉动流条件下动脉狭窄血管内脂质浓度极化现象的计算机数值模拟

在脉动流条件下,用计算机数值模拟的方法对低密度脂蛋白(LDL)在动脉狭窄血管段内的质量传输进行了研究。计算结果表明．无论是在定常流还是在脉动流条件下．LDL都将聚积于血管狭窄处峰口附近的流动分离点,LDL壁面浓度在此处最高。在脉动流条件下,LDL在血流受扰动区的聚积高于定常流的值;而且．流动分离点处LDL壁面浓度峰值覆盖的区域也宽于定常流。本文所揭示出的LDL在血管狭窄处的质量传输现象可能在动脉粥样硬化的局部性和动脉狭窄的形成中起着很重要的作用。     

动脉粥样硬化成因和大分子跨血管的传质

动脉硬化形成机理是当前心血管系统中主要关心的问题。30多年来对这个问题的研究已取得了很大进展。本文介绍了当前最重要的两个课题,即动脉壁细胞对血液流动的反应和大分子跨血管壁传质的研究成果。指出一些现已认为不对的旧认识和目前关于动脉硬化的新观点,以及当前的热门课题。      

关于二相流、多相流、多流体模型和非牛顿流等概念的探讨

本文分析了单相流、二相流和多相流等概念上的差异,也分析了单流体模型、双流体模型和多流体模型等概念上的差异,指出前面三种概念是按流动介质的客观物理构成划分的,而后者是按主观采用的研究方法划分的．目前这些概念在使用中存在一些混乱,如二相流与多相流,多相流与多流体模型等．本文还研究了扩散模型、非牛顿流模型和颗粒流模型等,指出前两种模型在分类上属于单流体模型,分析了非牛顿流模型、扩散模型和双（多）流体模型的特点和应用范围,最后,以泥石流为例讨论了以上概念的应用．      

动脉瘤内流场以及瘤体尺寸的影响的数值研究

采用计算流体动力学(CFD)数值模拟的方法,在周期性脉动速度入流条件下,建立刚性动脉瘤模型并研究了动脉瘤模型中流场的特征(速度、压力、壁面剪切应力)。得到了脉动入流一个周期内流场特征的变化规律,发现动脉瘤的后端有相当高的压力和壁面剪切应力,而且高压力和壁面剪切应力分布的位置几乎是固定的。探讨了不同动脉瘤尺寸对内部流场的影响,动脉瘤的直径与瘤体长度之比越大,瘤壁承受的剪切应力就越大,动脉瘤破裂的危险性就越高。     

颈动脉分支的血流动力学数值模拟

采用有限元法数值模拟颈动脉分支的血流动力学。根据在体测量的实际尺寸来构造颈动脉分支的几何模型,以保持模型的解剖精确度;利用在体测量的颈内动脉和颈外动脉流量波形以及主颈动脉的压力波形来确定数值计算的边界条件,以保持数值计算的生理真实性。关注的重点是颈动脉窦内的局部血流形态、二次流和壁面剪应力。在心脏收缩的减速期和舒张期的某些时刻,颈动脉窦中部外侧壁面附近产生了流动分离,形成了一个低速回流区。该流动分离是瞬态的,导致了壁面剪应力的振荡,其振荡范围在-2～6dyn／cm^2之间。同时,颈动脉窦中部横截面内的二次流存在于整个心动周期,最大的二次流速度为同时刻轴向速度平均值的1／3左右。     

A Model of Arterial Adaptation to Alterations in Blood Flow

Mechanisms of arterial adaptation to changes in blood flow rates were tested by comparing the predictions of a proposed theoretical model with available experimental data. The artery was modeled as an elastic membrane made of a nonlinear, incompressible, elastic material. Stimulation of the vascular smooth muscle was modeled through the generation of an active component of circumferential stress. The muscular tone was modulated by flow-induced shear stress sensed by the arterial endothelium, and is responsible for the vasomotor adjustment of the deformed arterial diameter in response to changes in blood flow. This study addresses the hypothesis that the synthetic and proliferative activity of smooth muscle cells, leading to a change in arterial dimensions, is shear stress dependent and is associated with changes in the contractile state of the smooth muscle cells and changes in the circumferential wall stress. Remodeling to a step change in flow was formulated as an initial-value problem for a system of first order autonomous differential equations for the evolution of muscular tone and evolution of arterial geometry. The governing equations were solved numerically for model parameters identified from experimental data available in the literature. The model predictions for the time variation of the geometrical dimensions and their asymptotic values were found to be in qualitative agreement with available experimental data. Experiments for validating the introduced hypotheses and further generalizations of the model were discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Transport of Viruses Through Saturated and Unsaturated Columns Packed with Sand

Laboratory-scale virus transport experiments were conducted in columns packed with sand under saturated and unsaturated conditions. The viruses employed were the male-specific RNA coliphage, MS2, and the Salmonella typhimurium phage, PRD1. The mathematical model developed by Sim and Chrysikopoulos (Water Resour Res 36:173–179, 2000) that accounts for processes responsible for removal of viruses during vertical transport in one-dimensional, unsaturated porous media was used to fit the data collected from the laboratory experiments. The liquid to liquid–solid and liquid to air–liquid interface mass transfer rate coefficients were shown to increase for both bacteriophage as saturation levels were reduced. The experimental results indicate that even for unfavorable attachment conditions within a sand column (e.g., phosphate-buffered saline solution; pH = 7.5; ionic strength = 2 mM), saturation levels can affect virus transport through porous media.     

Steady Film Flow of a Highly Viscous Heavy Fluid with Mass Supply

Asymptotic models of a thin layer of highly viscous heavy incompressible Newtonian fluid are constructed for steady axisymmetric (plane) flow on a curved rigid surface with distributed or point mass supply on a surface section near the axis (plane) of symmetry. Examples of analytical and numerical investigations of the free-surface shape and hydrodynamic-parameter fields are given. The models constructed are generalized for the case of a viscoplastic fluid and solutions which can be used for describing extrusive volcanic eruptions are obtained.     

动脉中非平稳流动壁面剪切力及其Hilbert-Huang变换

本文通过数值方法求解均匀动脉中的非平稳脉动流,给出了通过测量非平稳脉动血流量确定壁面切应力的方法.作为算例,采用实测的大鼠颈总动脉流量信号,求出了均匀动脉壁面切应力波形.进一步对求得的切应力波形进行经验模态分解(EMD),得到了切应力波形的各内在模态(IMF),以及Hilbert幅值谱.从切应力波形经Hilbert-Huang变换得到的IMF和Hilbert谱图可以明显地看出切应力各频率成分的物理意义.所得结果为进一步深入研究非平稳脉动切应力与血管重建的关系提供了一种方法学基础.     

On Analytical Solutions of Advective Transport by Infiltration–Redistribution Gravitational Flow

Contaminant transport in the upper layers of soil during the multiple cycles of short infiltration and prolonged redistribution is investigated. Analytical solutions for the two typical problems encountered in agricultural engineering are derived. The first problem considers the penetration of fertilizer initially applied at the soil surface. The second one is the propagation of contaminant injected with the applied water. Explicit analytical expressions for the solute concentration are obtained under assumptions of one-dimensional gravitational flow and advective solute transport under equilibrium conditions. The properties of the solute penetration are analyzed for the case of contaminant initially applied at the soil surface and picked up by the water flow during ten infiltration–redistribution cycles. P. Indelman - (deceased)