An augmented method for free boundary problems with moving contact lines

An augmented immersed interface method (IIM) is proposed for simulating one-phase moving contact line problems in which a liquid drop spreads or recoils on a solid substrate. While the present two-dimensional mathematical model is a free boundary problem, in our new numerical method, the fluid domain enclosed by the free boundary is embedded into a rectangular one so that the problem can be solved by a regular Cartesian grid method. We introduce an augmented variable along the free boundary so that the stress balancing boundary condition is satisfied. A hybrid time discretization is used in the projection method for better stability. The resultant Helmholtz/Poisson equations with interfaces then are solved by the IIM in an efficient way. Several numerical tests including an accuracy check, and the spreading and recoiling processes of a liquid drop are presented in detail. (C) 2010 Elsevier Ltd. All rights reserved.

Simulations of oil spread on a water surface

Numerical simulation of an oil slick spreading on still and wavy surfaces is described in this paper. The so-called sigma transformation is used to transform the time-varying physical domain into a fixed calculation domain for the water wave motions and, at the same time, the continuity equation is changed into an advection equation of wave elevation. This evolution equation is discretized by the forward time and central space scheme, and the momentum equations by the projection method. A damping zone is set up in front of the outlet boundary coupled with a Sommerfeld-Orlanski condition at that boundary to minimize the wave reflection. The equations for the oil slick are depth-averaged and coupled with the water motions when solving numerically. As examples, sinusoidal and solitary water waves, the oil spread on a smooth plane and on still and wavy water surfaces are calculated to examine the accuracy of simulating water waves by Navier-Stokes equations, the effect of damping zone on wave reflection and the precise structures of oil spread on waves.

Coupling Of Evaporation And Thermocapillary Convection In A Liquid Layer With Mass And Heat Exchanging Interface

We propose and analyse a new model of thermocapillary convection with evaporation in a cavity subjected to horizontal temperature gradient, rather than the previously studied model without evaporation. The pure liquid layer with a top free surface in contact with its own vapour is considered in microgravity condition. The computing programme developed for simulating this model integrates the two-dimensional, time-dependent Navier-Stokes equations and energy equation by a second-order accurate projection method. We focus on the coupling of evaporation and thermocapillary convection by investigating the influence of evaporation Biot number and Marangoni number on the interfacial mass and heat transfer. Three different regimes of the coupling mechanisms are found and explained from our numerical results.

不同重力条件下不相溶流体层间界面波演化规律的数值模拟研究

报道了关于不相溶流体层间界面波演化规律的数值模拟研究及结果，重点考察了重力条件对界面波演化特性的影响。考虑在深度方向无限扩展的互不相容的两个流体层，上层流体比下层的轻，但比下层的运动速度快；两层流体间的界面上存在正弦波形的初始扰动，并随流体流动而不断变化。本文采用Level Set方法来实现对运动的相界面的追踪，用有限差分法来离散控制方程组。为了提高数值算法的稳定性，采用三阶的Runge-Kutta法来离散时间导数，而采用五阶的WENO（Weighted Essentially Non-oscillatory）格式来离散一阶对流输运项，并用压力修正投影法（Pressure Correction Projection Method）来实现离散控制方程组的求解。为了提高对复杂非稳态过程的解的准确度，采用了嵌套的三层迭代循环。本文对一系列工况条件下的界面波演化过程进行了计算；除了研究重力的作用之外，还考察了流体密度、粘性、表面张力、初始界面波频率、振幅及波数对界面波演化特性的影响。其中，上下流体层的最大密度比和粘性比可达3000/1，而重力加速度在0~5g0（g0=9.8m/s^2）之间变化，上下流体层间的最大速度差为8m/s。研究结果表明，随着重力、流体密度比、流体粘性比及表面张力的增加，界面波的演化受到不同程度的抑制，而界面波的传播速度也与重力及流体的密度、粘性和表面张力等因素相关。

A Hybrid Scheme Based on Finite Element/Volume Methods for Two Immiscible Fluid Flows

We have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix-free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid.

投影变换方法在光学测量投影仪系统圆度表示中的应用

针对光学测量投影仪测量圆形工件时圆度指标的图形表示,提出了一种几何投影变换方法,将原非单调区间的离散点投影在某单调区间内,在此单调区间内运用插值算法进行曲线拟合后,再对数据进行反向投影,使得原非单调区间内离散点光滑地连接起来,使圆度的图形表示更加合理。几何投影变换方法克服了一些用于连接离散数据点的插值算法不能在非单调区间使用的局限性,拓展了上述算法的应用范围。

一种基于多特征融合的汽车变速箱螺栓在线视觉检测系统

本文根据汽车变速箱装配线螺栓检测的要求,结合检测现场的实际图像特点,采用融合灰度投影与颜色直方图两种特征的方法,利用相似性测度的计算方法,设计了一种变速箱螺栓在线装配质量检测系统,该系统用于实现螺栓的的缺失及漏拧检测,试验结果表明,方法具有良好的实用性,取得了比较理想的效果。

Method for measuring the lateral aberrations of a lithographic projection system with mirror-symmetric FOCAL marks

A novel method for measuring the imaging quality of a projection system with mirror-symmetric FOCAL marks is proposed, and the principle of the method is described. Through experiments, it is demonstrated that not only the axial aberrations but also the lateral aberrations can be measured with high accuracy by the method. The advantages of the method include obtaining more aberrations than the FOCAL technique and making it much simpler to perform a full-scale measurement of the imaging quality of a lithographic projection system. (C) 2006 Society of Photo-Optical Instrumentation Engineers.

Method for measuring the lateral aberrations of a lithographic projection system with mirror-symmetric FOCAL marks

A novel method for measuring the imaging quality of a projection system with mirror-symmetric FOCAL marks is proposed, and the principle of the method is described. Through experiments, it is demonstrated that not only the axial aberrations but also the lateral aberrations can be measured with high accuracy by the method. The advantages of the method include obtaining more aberrations than the FOCAL technique and making it much simpler to perform a full-scale measurement of the imaging quality of a lithographic projection system. (C) 2006 Society of Photo-Optical Instrumentation Engineers.

A novel method to measure coma aberration of projection system

A novel method to measure coma aberration by pattern displacements at different defocus positions is proposed in this paper. The effect of defocus on coma-induced pattern displacement is analyzed. The measuring principle of the method is described in detail. Using the simulation program PROLITH, the proportionality factors between pattern displacement and coma aberration at different defocus positions are calculated. It is proved that the method is simple to perform and the measurement accuracy of coma can increase approximately by 25% by this novel method. (c) 2006 Elsevier GmbH. All rights reserved.

A novel method for measuring the coma of a lithographic projection system by use of mirror-symmetry marks

A novel method for measuring the coma of a lithographic projection system is proposed and the principle of the method is described. By utilizing mirror-symmetry marks, the adverse effects of axial aberrations on the coma measurement are avoided. Experimental results demonstrated that the method has high accuracy. Compared with TAMIS, the conventional technique used for coma measurement, the method is more reliable because the influences of the process factors on the lateral displacements have been considered. (c) 2006 Elsevier Ltd. All rights reserved.

Applications of the method of three-dimensional projection of a molecule in quantitative structure-activity relationship of phenol derivatives

Five variables for phenol derivatives were calculated by molecular projection in three-dimensional space which were combined with eight quantum-chemical parameters and three Am indices. These variables were selected by using leaps-and-bounds regression analysis. Multiple linear regression analysis and artificial neural networks' were performed, and the results obtained by using. artificial neural networks are superior than that obtained by using multiple linear regression.

Coma measurement of projection optics in lithographic tools based on relative image displacements at multiple illumination settings

In this paper, we propose a novel method for measuring the coma aberrations of lithographic projection optics based on relative image displacements at multiple illumination settings. The measurement accuracy of coma can be improved because the phase-shifting gratings are more sensitive to the aberrations than the binary gratings used in the TAMIS technique, and the impact of distortion on displacements of aerial image can be eliminated when the relative image displacements are measured. The PROLITH simulation results show that, the measurement accuracy of coma increases by more than 25% under conventional illumination, and the measurement accuracy of primary coma increases by more than 20% under annular illumination, compared with the TAMIS technique. (c) 2007 Optical Society of America.

Even aberration measurement of lithographic projection system based on optimized phase-shifting marks

In the present paper, we propose a novel method for measuring the even aberrations of lithographic projection optics by use of optimized phase-shifting marks on the test mask. The line/space ratio of the phase-shifting marks is optimized to obtain the maximum sensitivities of Zernike coefficients corresponding to even aberrations. Spherical aberration and astigmatism can be calculated from the focus shifts of phase-shifting gratings oriented at 0 degrees, 45 degrees, 90 degrees and 135 degrees at multiple illumination settings. The PROLITH simulation results show that, the measurement accuracy of spherical aberration and astigmatism obviously increase, after the optimization of the measurement mark. (C) 2008 Elsevier B.V. All rights reserved.

Design and fabrication of color filters for projection display system

Color filters are key components in an optical engine projection display system. In this paper, a new admittance-matching method for designing and fabricating the high performance filters is described, in which the optimized layers are limited to the interfaces between the stack (each combination of quarter-wave-optical-thickness film layers is called a stack) and stack, or between stack and substrate, or between stack and incident medium. This method works well in designing filters containing multiple stacks such as UV-IR cut and broadband filters. The tolerance and angle sensitivity for the designed film stacks are analyzed. The thermal stability of the sample color filters was measured. A good result in optical performance and thermal stability was obtained through the new design approach. (c) 2006 Society of Photo-Optical Instrumentation Engineers.