异质材料有限长微通道电渗流热效应

采用数值方法,分析有限长PDMS/玻璃微通道电渗流热效应．数值求解双电层的Poisson-Boltzmann方程,液体流动的Navier-Stokes方程和流-固耦合的热输运方程,分析二维微通道电渗流的温度特性．考虑温度变化对流体特性（介电系数、粘度、热和电传导率）的反馈效应．数值结果表明,在通道进口附近有一段热发展长度,这里的流动速度、温度、压强和电场快速变化,然后趋向到一个稳定状态．在高电场和厚芯片的情况下,热发展长度可以占据相当一部分的微通道．电渗流稳定态温度随外加电场和芯片厚度的增加而升高．由于壁面材料的热特性差异,在稳定态时的PDMS壁面温度比玻璃壁面温度高．研究还发现在微通道的纵向和横向截面有温度变化．壁面温升降低双电层电荷密度．微通道纵向温度变化诱发流体压强梯度和改变微通道电场特性．微通道进流温度不改变热稳定态的温度和热发展长度．     

电场诱导的微乳液旋光及其可调节行为

通过实验发现在外电场作用下微乳液不仅具有旋光效应, 而且随电场强度改变可调控旋光角大小. 用微乳液法制备了不同含水量的油包水微乳液样品, 并利用自动旋光仪对样品随外加电场强度E和入射线偏振光振动方向与电场方向间夹角θ变化的旋光行为进行了测量. 实验表明, 电场强度E, 浓度C及θ 3个量全不为零时, 微乳液出现旋光效应; 对于一定浓度的微乳液, 旋光角Ψ 随E增大而增大; 同一电场强度作用下, 旋光角Ψ 随浓度C先增大后减小且存在一个浓度最佳值C₀, 此时Ψ 取极大值; 在浓度C与场强E一定的情况下, 旋光角Ψ 还随入射光的电矢量振动方向与电场方向间夹角θ而变化. 由电场作用下液滴空间对称破缺导致各向异性定性解释了实验现象.     

微通道内电渗压力混合驱动幂律流体流动模拟

为了研究微通道内电渗压力混合驱动幂律流体的流动特性,建立了微通道内电渗压力混合驱动幂律流体的计算模型,其双电层电势、流体的流场分布分别由Poisson-Boltzmann(P-B)方程和Navier-Stokes(N-S)方程描述.讨论了无量纲Debye(德拜)参数K、壁面ζ*电势和幂律指数n对流体流动特性和Poiseuille数的影响.结果表明,当压力梯度与外加电场方向一致(Γ0)时,剪切变稀流体的速度大于剪切变稠流体;压力梯度与外加电场方向相反(Γ0)时,结果相反.Poiseuille数是无量纲Debye常数K、壁面ζ*电势和幂律指数n的增函数.     

微通道周期流动电位势及电粘性效应

求解了双电层的Poisson-Boltzmann方程和流体运动的Navier-Stokes方程,得到在周期压差作用下,二维微通道的周期流动电位势,流动诱导电场和液体流动速度的解析解．量纲分析表明,流体电粘性力与以下3个参数有关:1) 电粘性数,它表示定常流动时,通道最大电粘性力与压力梯度的比;2) 形状函数,它表示电粘性力在通道横截面的分布形态; 3) 耦合系数,它表示电粘性力的振幅衰减特征和相位差．分析结果表明,微通道周期流动诱导电场、流动速度与频率Reynolds数有关．在频率Reynolds数小于1时,流动诱导电场随频率Reynolds数变化很慢．在频率Reynolds数大于1时,流动诱导电场随频率Reynolds数的增加快速衰减．在通道宽度与双电层厚度比值较小情况下,电粘性效应对周期流动速度和流动诱导电场有重要影响．     

微通道中电渗流及微混合的离子浓度效应

电渗流广泛应用于微流控芯片中的流体输运与混合.该文提出了一种离子浓度梯度对电渗流及微混合产生影响的变量模型,采用有限元分析方法对微通道中电渗流及微混合的离子浓度效应进行了数值模拟,分别讨论了zeta电势、介电常数等对微通道内流场和浓度场的影响规律,定量分析了微混合效率.结果表明,当zeta电势和介电常数随浓度变化时,微通道中流场分布不均匀,离子分布不对称.当溶液浓度趋近1 mol/L时,溶液基本无法进入微通道.微混合效率随溶液间浓度差的增大而减小,而且浓度差越大越能在较短距离内到达充分混合.     

基于金属型碳纳米管在电场中变形的柱壳理论

提出了关于金属型碳纳米管在电场中变形的柱壳理论．借助于半球模型,得到了金属型碳纳米管在电场中的电荷与电场分布的解析解．将带电碳原子所受的电场力看作是碳纳米管的内力,根据柱壳理论碳纳米管在电场中的变形被解析地给出．结果表明:碳纳米管的长径比对碳纳米管在电场中的变形有重大影响,长径比越大,碳纳米管的变形越明显;碳纳米管的径向变形沿轴向是不均匀的,最大的径向变形出现于碳纳米管的端部;更为有意义的是,即使外加电场不够大,对于长径比很大的碳纳米管仍然可以表现出明显的变形．     

T型微混合器内混合强化的数值模拟

为了研究不同混合强化方式对微混合的影响,采用有限元法对T型微混合器内增加壁面非均匀Zeta电势的主动式混合以及嵌入肋板的被动式混合进行了数值模拟.对比分析了3种T型微混合器内流场、速度场和浓度场的分布,并研究了不同T型微混合器内溶液混合效率与Re和Sc之间的关系.研究结果表明,两种溶液的混合效率随着Re和Sc的增加非线性减小,且减小趋势变缓;嵌入肋板的被动式T型微混合器内的混合效率沿水平微通道方向上存在较大的波动;增加壁面非均匀Zeta电势的主动式T型微混合器内的混合效率沿水平微通道方向上的波动较小,且这种波动在高Re或低Sc时会被抑制.Re对混合方式的强化效果也有很大的影响.当Re较小时,增加壁面非均匀Zeta电势的主动式混合能更好地提高溶液的混合效率,但当Re较大时,嵌入肋板的被动式混合的混合效果更好.     

外加电场作用下BaTiO3:Ce晶体对Gauss光束的空间调制

从数值计算和实验两方面的研究表明,当一束Gauss光束通过处于外加电场中的BaTiO₃:Ce晶体时,在异常光偏振面内(或外加电场方向上)表现出很强的空间调制和自聚焦效应. 数值结果和实验观察完全一致.     

矩形微通道热沉内单相稳态层流流体的流动与传热分析

采用解析方法分析了矩形微通道热沉内单相稳态层流流体的流动与传热．基于y方向流速和导热不变的假设,建立流体在矩形微通道内流动的流速方程和传热的温度方程,进而推导出Nusselt数和Poiseuille数的理论表达式．通过计算结果可以看出,推导的Nusselt数和Poiseuille数的解析解与其他文献的结果吻合较好,而且当宽高比趋于无穷大时,Nusselt数和Poiseuille数分别趋近于8.235和96,这与其他文献结果完全相同．在Reynolds数相同时,摩擦因数随着宽高比的增加而增加,而在相同宽高比时,摩擦因数随Reynolds数的增加而减小．     

微通道液体流动双电层阻力效应

采用数值方法求解双电层的Poisson-Boltzmann方程和液体运动的Navier-Stokes方程,研究微通道双电层对压强梯度液体流动的阻力效应． 量纲分析表明,双电层阻力大小可以用一个无量纲的电阻力数表示．它与液体的介电系数、固体表面的zeta电位平方成正比,与液体的动力粘性系数、电导率以及微通道的宽度平方成反比．在计算流动诱导的流动电位势和电阻力时,提出电流密度平衡条件,可以消除传统电流平衡条件导致的固壁附近产生局部回流的不合理物理现象．还给出不同电阻力数的微通道流量、流量损失率、速度剖面的数值结果,合理解释了双电层对微通道液体流动的阻力效应．     

Variable electrical and thermal conductivity in the theory of generalized thermoelastic diffusion

This paper deals with the problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time and with variable electrical and thermal conductivity. The bounding surface of the half-space is taken to be traction free and subjected to a time dependent thermal shock. The solution is obtained in the Laplace transform domain by a direct approach. A numerical technique is employed to obtain the solution in the physical domain. It is found that there exist two coupled waves, one of which is elastic and the other is thermal, and a third wave affects diffusion mainly. A comparison is made with the results obtained in a thermoelastic medium with and without diffusion in the following cases : (a) the electrical and thermal conductivities have constant values, (b) the presence of magnetic field and (c) the generalized theory in thermoelasticity. Received: June 1, 2005     

Variable electrical and thermal conductivity in the theory of generalized thermoelastic diffusion

This paper deals with the problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time and with variable electrical and thermal conductivity. The bounding surface of the half-space is taken to be traction free and subjected to a time dependent thermal shock. The solution is obtained in the Laplace transform domain by a direct approach. A numerical technique is employed to obtain the solution in the physical domain. It is found that there exist two coupled waves, one of which is elastic and the other is thermal, and a third wave affects diffusion mainly. A comparison is made with the results obtained in a thermoelastic medium with and without diffusion in the following cases : (a) the electrical and thermal conductivities have constant values, (b) the presence of magnetic field and (c) the generalized theory in thermoelasticity.     

Mathematical programming formulations for approximate simulation of multistage production systems

Mathematical programming representation has been recently used to describe the behavior of discrete event systems as well as their formal properties. This new way of representing discrete event systems paves the way to the creation of simpler mathematical programming models that reduce the complexity of the system analysis. The paper proposes an approximate representation for a class of production systems characterized by several stages, limited buffer capacities and stochastic production times. The approximation exploits the concept of a time buffer, modeled as a constraint that put into a temporal relationship the completion times of two customers in a sample path. The main advantage of the proposed formulation is that it preserves its linearity even when used for optimization and, for such a reason, it can be adopted in simulation–optimization problems to reduce the initial solution space. The approximate formulation is applied to relevant problems such as buffer capacity allocation in manufacturing systems and control parameters setting in pull systems.     

Wick-stochastic finite element solution of reaction–diffusion problems

Real life reaction–diffusion problems are characterized by their inherent or externally induced uncertainties in the design parameters. This paper presents a finite element solution of reaction–diffusion equations of Wick type. Using the Wick-product properties and the Wiener–Itô chaos expansion, the stochastic variational problem is reformulated to a set of deterministic variational problems. To obtain the chaos coefficients in the corresponding deterministic reaction–diffusion, we implement the usual Galerkin finite element method using standard techniques. Once this representation is computed, the statistics of the numerical solution can be easily evaluated. Computational results are shown for one- and two-dimensional test examples.     

Stability of solutions to extremum problems for the nonlinear convection–diffusion–reaction equation with the Dirichlet condition

The solvability of the boundary value and extremum problems for the convection–diffusion–reaction equation in which the reaction coefficient depends nonlinearly on the concentration of substances is proven. The role of the control in the extremum problem is played by the boundary function in the Dirichlet condition. For a particular reaction coefficient in the extremum problem, the optimality system and estimates of the local stability of its solution to small perturbations of the quality functional and one of specified functions is established.     

Optimum Externally Pressurized Magnetohydrodynamic Bearing

An externally pressurized bearing with variable film thicknessusing conducting, incompressible lubricant, in the presenceof a non-uniform axial magnetic field is investigated. By usingthe techniques of calculus of variation, it has been shown that,for the maximum load capacity of the bearing both the film thicknessand magnetic field profiles should be step functions at a giveninlet pressure. It has also been indicated that this maximumload increases as the strength of the magnetic field, appliedin the region of minimum film thickness, increases.     

热-压电效应对轴压混合层合圆柱曲板后屈曲的影响

基于Karman-Donnell型非线性壳体方程，给出带压电作动器混合层合圆柱曲板在机械荷载、电荷载和热荷载作用下的后屈曲分析．假定温度场为均匀分布，电场仅有沿板厚方向的分量Ez，且假定材料性能常数与温度和电场的变化无关。将壳体屈曲的边界层理论推广到混合层合圆柱曲板受复合荷载作用的情况.相应的奇异摄动法用于确定圆柱曲板的屈曲荷载和后屈曲平衡路径.分析中同时考虑非线性前屈曲变形和初始几何缺陷的影响．数值算例给出完善和非完善，含整体覆盖或内埋压电作动器正交铺设层合圆柱曲板的后屈曲平衡路径。讨论了温度变化、控制电压、铺层方式、面内边界条件和初始几何缺陷等各种参数变化的影响。     

Numerical and experimental investigations of phase segragation effects in binary brazing solders

Solder materials occupy many of fields for technical application (e.g. solder joints in automotive control units or in microelectronic packages). They are required to provide electrical and mechanical connections between different components. Due to their wide range of applications solder alloys are subject to a great variety of microstructural changes such as phase separation and coarsening processes. The micromorphological variations influence strength and life expectation of solder materials, in particular, in very small components such as solder joints in microelectronic packages. In order to analyze the microstructural evolution with a diffusion theory of heterogeneous solid mixtures we employ an extended Cahn-Hilliard phase field model. The diffusion equation under consideration constitutes a partial differential equation involving spatial derivatives of fourth order. Thus, the variational formulation of the problem requires approximation functions which are piecewise smooth and globally C1-continuous. In our contribution we fulfil the continuity requirement by means of rational B-spline finite element basis functions. To illustrate the versatility of this approach numerical simulations of phase decomposition and coarsening controlled by diffusion and by mechanical loading are discussed and compared with experimental results. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations

In this paper, the coupled equations in velocity and magnetic field for unsteady magnetohydrodynamic (MHD) flow through a pipe of rectangular section are solved using combined finite volume method and spectral element technique, improved by means of Hermit interpolation. The transverse applied magnetic field may have an arbitrary orientation relative to the section of the pipe. The velocity and induced magnetic field are studied for various values of Hartmann number, wall conductivity and orientation of the applied magnetic field. Comparisons with the exact solution and also some other numerical methods are made in the special cases where the exact solution exists. The numerical results for these sample problems compare very well to analytical results.     

Fractional variational principles and their applications

Variational calculus and fractional calculus have played a significant role in various areas of applied sciences such as, among others, Physics, Engineering and Economics. This topic is deeply connected to the very recent developments in theoretical aspects and especially in the numerical schemes of fractional differential equations. Based on 1+1 field formalism, a new fractional Lagrangian and Hamiltonian formalisms are presented within the Riemann-Liouville fractional derivatives and the an-harmonic oscillator is analyzed. This formalism can be applied to analyze the control problems as well as for the fractional quantization procedure. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)