存在滑移时两圆球间的幂律流体挤压流动

基于Reynolds润滑理论分析了壁面滑移对任意圆球颗粒间幂律流体的挤压流动的影响。研究表明有壁面滑移时挤压流动的粘性力可通过引进本文定义的滑移修正系数分离出无滑移解。推导出的挤压力滑移修正系数是一积分表达式，依赖于滑移参数、幂律指数、球间隙和积分上限。一般地壁面滑移导致粘性力减小，粘性力的减小量随幂律指数的增大而增大，表明壁面滑移对剪切增稠流变材料有更大的影响；粘性力的减小量还随着滑移参数的增大而增加，而这恰与假设相符合；粘性力的减小量又随球间隙减小或积分上限的增大（从液桥情况到完全浸渍）而减小直到趋于常数，这一特性在离散元模拟时可以有效地减少计算量。     

界面滑移流体动压膜承载能力的形成

运用界面滑移可在两平行平板表面间形成具有承载能力的流体动压膜．在流体入口区,静止平板表面上流体-接触表面的界面剪切强度具有较低值,以在该界面处产生界面滑移,而在流体出口区,静止平板表面上流体-接触表面的界面剪切强度具有足够高的值,以避免在该界面处出现界面滑移．整个运动平板表面上流体-接触表面的界面剪切强度具有足够高的值,以避免在运动平板表面上出现界面滑移．分析表明,这种流体动压接触区具有显著承载能力．使整个接触区具有最大承载能力的流体出口区宽度与入口区宽度的比值为0.5．     

壁面效应对剪切稀化流体内气泡上浮特性的影响

数值研究了壁面效应对剪切稀化流体内气泡上浮运动特性的影响,气液两相的界面捕捉采用流体体积(VOF)法,剪切稀化流体流变特性和气液相间表面张力的计算分别采用Carreau模型和连续表面张力模型.详细研究了不同流变指数下,壁面效应对气泡形状、液相流场和气泡终端速度的影响.结果表明,强的壁面效应或弱的剪切稀化程度会限制气泡的变形和尾涡的形成,使气泡的终端速度减小;气泡终端速度最易受壁面效应的影响;强的壁面效应和强的剪切稀化程度会导致高剪切速率区域出现在壁面附近,引起壁面附近液相表观黏度大幅度的下降.     

作旋转流动时非线性流体的改进模型

在圆环结构中研究拟塑性流体作圆形的Couette流动.流体的粘度依赖于对守恒方程有直接影响的剪切率,守恒方程采用谱方法求解.可以证明所采用的拟塑性模型,可以被适当地表示为典型的非线性流动.在早期研究中,为了方便数值计算,粘度表达式中只考虑了剪切率的二次项,与此不同,这里考虑了二次幂项.圆形Couette流动中弯曲的流线,造成离心的不稳定性,引起环形的漩涡,称之为Taylor漩涡.进而发现,随着拟塑性影响的增加,临界Taylor数下降.与已有圆形Couette流动的实验相比较,两者有着良好的一致性.     

二阶流体通过径向延伸平面时滑移、黏性耗散、焦耳热对MHD流动的影响

研究了二阶导电的非Newton流体,在一个可径向放射状延伸,并伴有部分滑动表面上的流动及其热交换.部分滑移用一个无量纲的滑移因子控制,其取值范围从0(全黏着)到无穷大(全滑移).使用适当的相似变换,把待求的非线性偏微分方程转化为常微分方程.讨论了边界条件的不足,在无需增加任何边界条件下,使用有效的数值格式,求解所得到的微分方程.部分滑移、磁场交互参数以及二阶流体的参数对速度场和温度场的综合分析发现,滑移量的增加,流体的动力边界层和热边界层增厚.因为当滑移量的增加,允许更多的流体通过该平面,表面摩擦因数的数值下降,并在更高的滑移参数下,摩擦因数趋于0,即流体无黏性地通过.还研究了磁场对速度场和温度场的重要影响.     

弹性动脉血管中血液流动特性的模拟和分析

研究了两个不同的非牛顿血液流动模型:低粘性剪切简单幂律模型和低粘性剪切及粘弹性振荡流的广义Maxwell模型．同时利用这两个非牛顿模型和牛顿模型,研究了磁场中刚性和弹性直血管中血液的正弦型脉动．在生理学条件下,大动脉中血液的弹性对其流动性态似乎并不产生影响,单纯低粘性剪切模型可以逼真地模拟这种血液流动．利用高剪切幂律模型模拟弹性血管中的正弦型脉动流,发现在同一压力梯度下,与牛顿流体相比较,幂律流体的平均流率和流率变化幅度都更小．控制方程用Crank-Niclson方法求解．弹性动脉中血液受磁场作用是产生此结果的直观原因．在主动脉生物流的模拟中,与牛顿流体模型比较,发现在匹配流率曲线上,幂律模型的平均壁面剪切应力增大,峰值壁面剪切应力减小．讨论了弹性血管横切磁场时的血液流动,评估了血管形状和表面不规则等因素的影响．     

具有Cauchy-Ventcel边界条件的有界域中亚临界半线性波方程的稳定与控制

分析RN 的有界域中半线性波方程解的指数衰减特性,有界域具有Cauchy-Ventcel型边界条件,并且球体外部作用着阻尼项.在对非线性作出适当又自然的假设后,倘若非线性在无穷大处为亚临界时,有限能量解的指数衰减性满足局部一致性.粗略地说,亚临界性意味着,在无穷大处非线性增长率次数不大于5.B.Dehman、G.Lebeau和E.Zuazua得到了R3 和RN 中的经典能量(用于估计局限于球体外部以能量形式表示的解的总能量)不等式和Strichartz估计的结果,使得研究RN 有界域(域内及其边界上是亚临界非线性,边界为Cauchy-Ventcel型连续)中半线性波方程的稳定性与可控性成为可能.     

列车荷载引起路基振动研究分析

为了研究地基特性和轨道结构对列车振动荷载作用下地基振动问题,通过无限元边界与有限元边界相结合的有限元分析方法进行模型建立,把路堤高度、列车速度、阻尼系数、振动频率及轨道抗弯刚度因素考虑在内.结果表明,无限元边界与有限元边界相结合的有限元计算方法可以有效反映出地基振动效果,由列车荷载引起的地基振动响应随着路堤高度增加而减小;速度增加地基振动响应相应增加,并且低速与高速情况相应情况变化很大;列车低速时,轨道刚度对地基振动影响较小,相反高速时轨道刚度对振动响应影响较大;当列车速度低于剪切波速时阻尼系数改变对振动影响较小,高于剪切波速时,阻尼系数增大路堤周围地基振动水平明显减小;随着列车荷载振动频率增加,地基振动响应变化较小,但是具有减小趋势.     

具有多重非线性的非牛顿多方渗流方程的整体存在性与非存在性

考虑了一个具有多重非线性的抛物模型中,非线性扩散项、非线性反应项和非线性边界流三种非线性机制之间的相互作用.通过构造自相似上解和自相似下解,获得了临界整体存在性曲线和临界Fujita曲线.     

非均匀温度场中组合热超弹性球体的动态孔穴生成

在有限变形动力学的框架下,研究了在非均匀温度场中组合热超弹性球体,在表面均布拉伸死载荷作用下的动态孔穴的生成和增长问题．首先建立了相应的非线性数学模型,利用换元积分方法求得了孔穴半径与外加载荷之间的一个精确的微分关系,并进行了数值计算,得到了不同温度下球体中孔穴生成时的临界载荷和分叉曲线．考察了参数对孔穴生成与增长的影响,并与相应的静态结果进行了比较．结果表明孔穴是以一个有限的半径突然出现的,且随时间的演变孔穴半径呈现周期性的非线性振动;当温度升高,临界值降低,同时在相同的条件下动态临界载荷低于静态临界载荷．     

Stokes flow past an assemblage of slip eccentric spherical particle‐in‐cell models

The quasisteady axisymmetrical flow of an incompressible viscous fluid past an assemblage of slip eccentric spherical particle‐in‐cell models with Happel and Kuwabara boundary conditions is investigated. A linear slip, Basset type, boundary condition on the surface of the spherical particle is used. Under the Stokesian approximation, a general solution is constructed from the superposition of the basic solutions in the two spherical coordinate systems based on the particle and fictitious spherical envelope. The boundary conditions on the particle's surface and fictitious spherical envelope are satisfied by a collocation technique. Numerical results for the normalized drag force acting on the particle are obtained with good convergence for various values of the volume fraction, the relative distance between the centers of the particle and fictitious envelope and the slip coefficient of the particle. In the limits of the motions of the spherical particle in the concentric position with cell surface and near the cell surface with a small curvature, the numerical values of the normalized drag force are in good agreement with the available values in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

Slip at the surface of a sphere translating perpendicular to a plane wall in micropolar fluid

The Stokes axisymmetrical flow caused by a sphere translating in a micropolar fluid perpendicular to a plane wall at an arbitrary position from the wall is presented using a combined analytical-numerical method. A linear slip, Basset type, boundary condition on the surface of the sphere has been used. To solve the Stokes equations for the fluid velocity field and the microrotation vector, a general solution is constructed from fundamental solutions in both cylindrical, and spherical coordinate systems. Boundary conditions are satisfied first at the plane wall by the Fourier transforms and then on the sphere surface by the collocation method. The drag acting on the sphere is evaluated with good convergence. Numerical results for the hydrodynamic drag force and wall effect with respect to the micropolarity, slip parameters and the separation distance parameter between the sphere and the wall are presented both in tabular and graphical forms. Comparisons are made between the classical fluid and micropolar fluid.      

Global Existence Results for Oldroyd Fluids with Wall Slip

We investigate the system of nonlinear partial differential equations governing the unsteady motion of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain under Navier’s slip boundary condition. We prove the existence of global weak solutions for the corresponding initial-boundary value problem without assuming that the model constants, body force or the initial values of the velocity and the stress tensor are small.     

Micro/nano sliding plate problem with Navier boundary condition

For Newtonian flow through micro or nano sized channels, the no-slip boundary condition does not apply and must be replaced by a condition which more properly reflects surface roughness. Here we adopt the so-called Navier boundary condition for the sliding plate problem, which is one of the fundamental problems of fluid mechanics. When the no-slip boundary condition is used in the study of the motion of a viscous Newtonian fluid near the intersection of fixed and moving rigid plane boundaries, singular pressure and stress profiles are obtained, leading to a non-integrable force on each boundary. Here we examine the effects of replacing the no-slip boundary condition by a boundary condition which attempts to account for boundary slip due to the tangential shear at the boundary. The Navier boundary condition, possesses a single parameter to account for the slip, the slip length ℓ, and two solutions are obtained; one integral transform solution and a similarity solution which is valid away from the corner. For the former the tangential stress on each boundary is obtained as a solution of a set of coupled integral equations. The particular case solved is right-angled corner flow and equal slip lengths on each boundary. It is found that when the slip length is non-zero the force on each boundary is finite. It is also found that for a suffciently large distance from the corner the tangential stress on each boundary is equal to that of the classical solution. The similarity solution involves two restrictions, either a right-angled corner flow or a dependence on the two slip lengths for each boundary. When the tangential stress on each boundary is calculated from the similarity solution, it is found that the similarity solution makes no additional contribution to the tangential stress of that of the classical solution, thus in agreement with the findings of the integral transform solution. Values of the radial component of velocity along the line θ = π /4 for increasing distance from the corner for the similarity and integral transform solutions are compared, confirming their agreement for sufficiently large distances from the corner. (Received: November 9, 2005)     

Three‐dimensional Stokes flow caused by a translating–rotating sphere bisected by a free surface bounding a semi‐infinite micropolar fluid

Explicit velocity and microrotation components and systematic calculation of hydrodynamic quasistatic drag and couple in terms of nondimensional coefficients are presented for the flow problem of an incompressible asymmetrical steady semi‐infinite micropolar fluid arising from the motion of a sphere bisected by a free surface bounding a semi‐infinite micropolar fluid. Two asymmetrical cases are considered for the motion of the sphere: parallel translation to the free surface and rotation about a diameter which is lying in the free surface. The speed of the translational motion and the angular speed for the rotational motion of the sphere are assumed to be small so that the nonlinear terms in the equations of motion can be neglected under the usual Stokesian approximation. A linear slip, Basset‐type, boundary condition has been used. The variation of the resistance coefficients is studied numerically and plotted versus the micropolarity parameter and slip parameter. The two limiting cases of no‐slip and perfect slip are then recovered. Copyright © 2008 John Wiley & Sons, Ltd.     

Plastic flow in very low temperature regime within annular micropores

The rate of deformation for glassy (amorphous) matter confined in microscopic domain at very low temperature regime was investigated using a rate-state-dependent model considering the shear thinning behavior which means, once material being subjected to high shear rates, the viscosity diminishes with increasing shear rate. The preliminary results show that there might be the enhanced rate of deformation and (shear) yield stress due to the almost vanishing viscosity in micropores subjected to some surface conditions: The relatively larger roughness (compared to the macroscopic domain) inside micropores and the slip. As the pore size decreases, the surface-to-volume ratio increases and therefore, surface roughness will greatly affect the (plastic) flow in micropores. By using the boundary perturbation method, we obtained a class of microscopic fields for the rate of deformation and yield stress at low temperature regime with the presumed small wavy roughness distributed along the walls of an annular micropore.     

Plastic flow in very low temperature regime within annular micropores

The rate of deformation for glassy (amorphous) matter confined in microscopic domain at very low temperature regime was investigated using a rate-state-dependent model considering the shear thinning behavior which means, once material being subjected to high shear rates, the viscosity diminishes with increasing shear rate. The preliminary results show that there might be the enhanced rate of deformation and (shear) yield stress due to the almost vanishing viscosity in micropores subjected to some surface conditions: The relatively larger roughness (compared to the macroscopic domain) inside micropores and the slip. As the pore size decreases, the surface-to-volume ratio increases and therefore, surface roughness will greatly affect the (plastic) flow in micropores. By using the boundary perturbation method, we obtained a class of microscopic fields for the rate of deformation and yield stress at low temperature regime with the presumed small wavy roughness distributed along the walls of an annular micropore.     

Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition

In this paper the boundary layer flow over a flat plat with slip flow and constant heat flux surface condition is studied. Because the plate surface temperature varies along the x direction, the momentum and energy equations are coupled due to the presence of the temperature gradient along the plate surface. This coupling, which is due to the presence of the thermal jump term in Maxwell slip condition, renders the momentum and energy equations non-similar. As a preliminary study, this paper ignores this coupling due to thermal jump condition so that the self-similar nature of the equations is preserved. Even this fundamental problem for the case of a constant heat flux boundary condition has remained unexplored in the literature. It was therefore chosen for study in this paper. For the hydrodynamic boundary layer, velocity and shear stress distributions are presented for a range of values of the parameter characterizing the slip flow. This slip parameter is a function of the local Reynolds number, the local Knudsen number, and the tangential momentum accommodation coefficient representing the fraction of the molecules reflected diffusively at the surface. As the slip parameter increases, the slip velocity increases and the wall shear stress decreases. These results confirm the conclusions reached in other recent studies. The energy equation is solved to determine the temperature distribution in the thermal boundary layer for a range of values for both the slip parameter as well as the fluid Prandtl number. The increase in Prandtl number and/or the slip parameter reduces the dimensionless surface temperature. The actual surface temperature at any location of x is a function of the local Knudsen number, the local Reynolds number, the momentum accommodation coefficient, Prandtl number, other flow properties, and the applied heat flux.