THE NONLINEAR STABILITY OF PLANE PARALLEL SHEAR FLOWS WITH RESPECT TO TILTED

The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.

ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅱ)——THE LINEAR STABILITY ANALYSIS OF DISTORTED PARALLEL SHEAR FLOW

Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the linear stability behaviour of parallel shear flow, presents unstable results of plane Couette flow and pipe Poiseuille flow to two-dimensional or axisymmetric disturbances for the first time, and obtains neutral curves of these two motions under certain definition.

ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅲ)—THE NONLINEAR STABILITY ANALYSIS OF DISTORTED PARALLEL SHEAR FLOW

Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the nonlinear stability behaviour of parallel shear flow, carries on stability calculation taking account of the perturbations of background turbulence noise under certain assumption, and obtains some results in accordance qualitatively with those of experiment for plane Poiseuille flow and pipe Poiseuille flow.

A NEW APPROACH TO THE NONLINEAR STABILITY OF PARALLEL SHEAR FLOWS

Lyapunov’s second method was used to study the nonlinear stability of parallel shear flows for stress free boundaries. By introducing an energy functional, it was shown that the plane Couette and plane Poiseuille flows are conditionally and asymptotically stable for all Reynolds numbers. In particular, to two dimensional perturbations, by defining new energy functionals the unconditional stability of the basic flows was proved.

Converging Parallel Plate Flow Chambers for Studies on the Effect of the Spatial Gradient of Wall Shear Stress on Endothelial Cells

Many in vitro studies focus on effects of wall shear stress (WSS) and wall shear stress gradient (WSSG) on endothelial cells, which are linked to the initiation and progression of atherosclerosis in the arterial system. Limitation in available flow chambers with a constant WSSG in the testing region makes it difficult to quantify cellular responses to WSSG. The current study proposes and characterizes a type of converging parallel plate flow chamber (PPFC) featuring a constant gradient of WSS. A simple formula was derived for the curvature of side walls, which relates WSSG to flow rate (Q), height of the PPFC (h), length of the convergent section (L), its widths at the entrance (w0) and exit (w1). CFD simulation of flow in the chamber is carried out. Constant WSSG is observed in most regions of the top and bottom plates except those in close proximity of side walls. A change in Q or h induces equally proportional changes in WSS and WSSG whereas an alteration in the ratio between w0 and w1 results in a more significant change in WSSG than that in WSS. The current design makes possible an easy quantification of WSSG on endothelial cells in the flow chamber.

ON ANALYSIS OF THE STEADY FLOW IN AN IRRECTANGULARPARALLEL-PLATE FLOW CHAMBER

The parallel-plate flow chamber (PPFC), of which the height is far smaller than its own length and width, is one of the main apparatus for the in vitro study of the mechanical behaviors of cultured cells at the bottom of PPFC undergoing shear stress. The PPFC of which the upper and lower plates are rectangular is usually used by research workers, and the flow field in this kind of PPFC (except for the regions near the entrance and exit) is uniform([1]), so only the effect the shear stress with one value has on cultured cells can be observed during each experiment. A kind of PPFC of which the upper and lower plates are not rectangular is proposed in this paper. The distributions of the velocities inside and the shear stresses at the bottom of the chamber are given by analyzing the flow field of the steady flow in the PPFC. The results show that the mechanical behaviors of cultured cells undergoing the shear stresses with various values may be simultaneously observed by the use of this kind of irrectangular PPFC. The theoretical and experimental results obtained by Ultrasonic Doppler Technique show good agreement.

ANALYSIS OF PULSATILE FLOW IN THE PARALLEL-PLATE FLOW CHAMBER WITH SPATIAL SHEAR STRESS GRADIENT

The Parallel-Plate Flow Chamber （PPFC）, of which the height is far smaller than its own length and width, is one of the main apparatus for the in-vitro study of the mechanical behavior of cultured vascular Endothelical Cells （ECs） exposed to fluid shear stress. The steady flow in different kinds of PPFC has been extensively investigated, whereas, the pulsatile flow in the PPFC has received little attention. In consideration of the characteristics of geometrical size and pulsatile flow in the PPFC, the 3-D pulsatile flow was decomposed into a 2-D pulsatile flow in the vertical plane, and an incompressible plane potential flow in the horizontal plane. A simple method was then proposed to analyze the pulsatile flow in the PPFC with spatial shear stress gradient. On the basis of the method, the pulsatile fluid shear stresses in several reported PPFCs with spatial shear stress gradients were calculated. The results were theoretically meaningful for applying the PPFCs in-vitro, to simulate the pulsatile fluid shear stress environment, to which cultured ECs were exposed.

用马赫探针阵列测量HL-1M装置边缘涨落和流速

利用一组马赫探针研究了ＨＬ－１Ｍ装置刮离层（ＳＯＬ）和边缘等离子体流在欧姆放电、壁硼化、偏压抽气孔栏、偏压电极、低杂波电流驱动（ＬＨＣＤ）和电子回旋共振加热（ＥＣＲＨ）等情况下的平行流马赫数、离子饱和电流扰动、平行流速度剪切和极向流速度的分布。

平行板流动腔法评价生物素化脂质微泡制备效果

目的制备生物素化脂质微泡,并应用平行板流动腔检测流体切应力对生物素化脂质微泡与链亲和素结合稳定性的影响,为进一步开展超声分子成像研究奠定基础。方法采用声振法制备出表面携有生物素分子的脂质微泡,与普通脂质微泡对照,应用平行板流动腔模型,设置不同流体剪切应力,观察与链亲和素靶向结合的生物素化微泡的黏附效果。结果在不同浓度链亲和素包被的平行板流动腔中均见生物素化微泡结合;随着链亲和素包被浓度的提高,靶向结合的生物素化脂质微泡抗流体剪切应力能力明显提高。结论应用平行板流动腔模型能成功检测生物素化微泡的靶向黏附效果,该模型可推广应用于其他靶向微泡制备成功后靶向黏附能力的体外检测。

矩形喷嘴平行射流组流体动力学特性

依据动量和质量守恒原理，建立了描述平行射流组流动行为的数学模型，并获得了该模型的解析解。研究了矩形喷嘴平行射流组的流动行为特性。最后，计算结果与实验结果进行了比较。

一种平板流动腔重力灌流系统的力学分析

本文分析了一种采用重力灌流的平板流动腔灌流系统，并根据实验结果确定出相应的阻力系数，获得平板流动腔剪应力、雷诺数以及入口长度与流体重力灌流高度的关系。

圆形喷嘴平行射流组流体动力学特性

本文在簿剪切层理论基础上,建立了平行射流组的理论模型,并依据Prandtl混合长度理论,求出了该模型的分析解。通过该模型的计算分析,得出:(1)沿流动方向轴向速度逐渐衰减,其轴心最大速度衰减与单射流相同;(2)沿y方向,轴向速度按余弦规律分布,并且随着向射流组下游发展,其速度振幅逐渐减少,直到趋于平坦。在离喷嘴足够远的流动相似区,计算结果与实验结果是一致的。

平行平板流动腔在研究人骨髓间充质干细胞流体力学方面的应用

目的探讨改良制作的平行平板流动腔在对人骨髓间充质干细胞流体力学方面的应用。方法利用改良制作的平行平板流动腔对人骨髓间充质干细胞进行流体剪切力刺激,观察细胞形态学变化及超微结构。结果经强度为3dyne/cm2的流体剪切力作用30min作用后,细胞形态发生变化,透射电镜观察提示细胞成熟。结论平行平板流动腔可以作为研究人骨髓间充质干细胞流体力学方面的模型,人骨髓间充质干细胞经流体剪切力作用后,细胞形态发生变化,显示细胞成熟。

HL-1M装置边缘扰动和流速的实验研究

利用一组马赫探针研究HL-1M装置刮离层和边缘等离子体流在欧姆放电、壁硼化、偏压抽气孔栏、偏压电极、低混杂波电流驱动、电子回旋共振加热、弹丸注入、分子束注入、激光吹气和补充送气等情况下的平行流马赫数、离子饱和电流扰动、平行流速度剪切和极向流速度的分布。实验中发现局部等离子体电位快速变化，改变了电场分布，改变了边缘等离子体的流速和方向。从而改善了等离子体约束性能。

端点条件对平行平板流动腔底部切应力的影响

高度远小于横向和纵向几何尺寸的平行平板流动腔是当前用以体外研究细胞在切应力场作用下的力学行为 ,特别是粘附特性的主要工具之一。本文对实际使用的具有不同入口和出口边界条件的流动腔内流体定常流动的流场进行详细分析 ,计算出几种常用的不同入口和出口流量分布所对应平行平板流动腔底部的切应力场分布 ,详细讨论端点条件对腔室底部切应力的影响情况 ,指出端点条件的影响只局限在离开腔室差不多为腔室宽度的区域之内 ,本文结果对于分析流动腔内细胞的力学行为和讨论切应力对细胞的影响有重要实际意义。

平行平板流动腔脉动流切应力的计算

高度远小于横向和纵向几何尺寸的矩形平行平板流动腔是人们用以体外研究细胞在切应力作用下力学行为的主要工具之一。大多数研究者主要对定常层流情形进行研究。本文通过对矩形平行平板流动腔内的层流脉动流进行详细分析,给出腔内流速和腔室底部切应力的准确计算公式。当Womersley数较小时,准确公式简化为准定常公式。数值计算结果表明,在脉动流条件下,对于人们常用的流动腔几何尺寸,准定常公式具有相当高的精度。这为在脉动流情况下平行平板流动腔切应力的简便计算方法提供了理论依据。

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)=AZ^n(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。

平行平板流动腔中Casson流体脉动流的摄动解

高度远小于横向和纵向几何尺寸的矩形平行平板流动腔是人们用以体外研究细胞在切应力作用下力学行为的主要工具之一。考虑到通常采用的矩形平行平板流动腔内的流动属于小雷诺数流动 ,本文用雷诺数作为摄动参数求出了矩形平行平板流动腔内 Casson流体脉动流的摄动解 ,给出了腔内切应力随压力梯度和流量的变化规律。数值结果表明 ,相同压力梯度下 Casson流体和牛顿流体对应的腔内切应力分布无明显不同 ;而在相同流量条件下 ,Casson流体和牛顿流体对应的腔内切应力分布有明显差异。本文为

二平行流之间幂率流体层流剪切流动的数学模型

非牛顿流体的平行剪切流动是一种在自然界和工程实践中常见的流动。本文应用流体力学和非牛顿流体力学理论，利用 Ｐｒａｎｄｔｌ边界层方程，在未作任何其它假设的情况下，得出了幂率流体平行剪切层流流动时的相似变量，给出了两种流体指数 ｎ 相同时的常微分方程和定解条件。

平行平板流动腔中脉动流的摄动解

高度远小于横向和纵向几何尺寸的矩形平行平板流动腔是人们用以体外研究细胞在切应力作用下力学行为的主要工具之一。大多数研究者主要对定常层流情形进行研究。考虑到通常采用的矩形平行平板流动腔内的流动属小雷诺数流动,本文用雷诺数作为摄动参数求出矩形平行平板流动腔内的层流脉动流的摄动解,给出腔内流速和腔室底部切应力的0级、I级、II级近似计算公式。数值计算结果及其与Fourier解的比较表明,在脉动流条件下,对于人们常用的流动腔几何尺寸,近似公式具有相当高的精度,特别是0级近似公式(即准定常公式)适用的雷诺数范围更大。这为在脉动流情况下平行平板流动腔切应力的简便计算方法提供了理论依据。