Linearized analysis of the deformation of ultra-thin lubricant films under gas pressures by the long wave equation

Long wave theory was employed to examine the deformations of ultra-thin but continuum liquid films produced by applied pressures and shearing stresses. Long wave theory is based on the time-evolution equation for the shape and deformation of thin liquid films and includes surface tension and surface forces such as van der Waals forces. As the deformations caused by gas pressures are usually very small, the linearized long wave equation, which is applicable to infinitesimal deformations, was derived and employed to predict the steady-state liquid surface deformations of a non-polar lubricant produced by concentrated or distributed gas pressures. It was found that the results obtained using the linearized equation agree well with those obtained using the nonlinear long wave equation.     

Frequency domain analyses of a thin liquid film surface by repetitively applied stress (dynamic response analyses by the long wave equation)

Numerical results were calculated for the dynamic behavior of an ultrathin liquid (lubricant) surface resulting from repetitively applied pressure and shear stress using the frequency domain equation and compared with those obtained using the time domain equation. Frequency domain analyses of the dynamic behavior of the ultrathin liquid (lubricant) surface produced by sinusoidally applied pressure and shear stress clarified the dependence of the liquid surface deformation on the frequency of the stresses and the disk speed. The dynamic behavior resulting from sinusoidally applied pressure and shear stress calculated using the time domain equation were found to gradually coincide with those obtained using the frequency domain equation.     

Deformation characteristics of ultra-thin liquid film considering temperature and film thickness dependence of surface tension

Thermocapillary deformations of an ultra-thin liquid film caused by temperature distribution were three-dimensionally analyzed using the unsteady and linearized long wave equation considering the temperature and film thickness dependence of surface tension. The temperature and film thickness dependence equation for the surface tension of a liquid was firstly established. The temperature dependence of the surface tension was obtained experimentally using a surface tensiometer and the film thickness dependence was obtained theoretically from the corrected van der Waals pressure equation for a symmetric multilayer system. Time evolutions of depression and groove of the ultra-thin liquid film caused by local heating were obtained quantitatively.     

Long-wave interfacial instabilities in a thin electrolyte film undergoing coupled electrokinetic flows: a nonlinear analysis

Spatiotemporal deformations of the free charged surface of a thin electrolyte film undergoing a coupled electrokinetic flow composed of an electroosmotic flow (EOF) on a charged solid substrate and an electrophoretic flow (EPF) at its free surface are explored through linear stability analysis and the long-wave nonlinear simulations. The nonlinear evolution equation for the deforming surface is derived by considering both the Maxwell’s stresses and the hydrodynamic stresses. The electric potential across the film is obtained from the Poisson–Boltzmann equation under the Debye–Hückel approximation. The simulations show that at the charged electrolyte–air interface, the applied electric field generates an EPF similar to that of a large charged particle. The EOF near the solid–electrolyte interface and the EPF at the electrolyte–air interface are in the same (or opposite) directions when the zeta potentials at the two interfaces are of the opposite (or same) signs. The linear and nonlinear analyses of the evolution equation predict the presence of travelling waves, which is strongly modulated by the applied electric field and the magnitude/sign of the interface zeta potentials. The time and length scales of the unstable modes reduce as the sign of zeta potential at the two interfaces is varied from being opposite to same and also with the increasing applied electric field. The increased destabilization is caused by a reverse EPF near the free surface when the interfaces bear the same sign of zeta potentials. Flow reversal by EPF at the free surface occurs at smaller zeta potential of the free surface when the film is thicker because of less influence of the EOF arising at the solid–electrolyte boundary. The amplitude of the surface waves is found to be smaller when the unstable waves travel at a faster speed. The films can undergo pseudo-dewetting when the free surface is almost stationary under the combined influences of EPF and EOF. The free surface instability of the coupled EOF and EPF has some interesting implications in the development of micro/nano fluidic devices involving a free surface.     

Thermocapillary convection and interface deformation in a liquid film within a micro-slot with structured walls

Thermocapillary convection in a thin liquid film inside a micro-slot with structured walls kept at different temperatures is studied. The liquid film is wetting the substrate wall and is separated from the cover wall by a gas layer. If the slot walls are structured, the temperature at the liquid–gas interface is non-uniform. The temperature variation induces thermocapillary stresses which bring the liquid into motion and lead to the interface deformation. We investigate the film flow inside the micro-slot, the heat transfer, the liquid–gas interface deformations and the film stability in the framework of the long-wave theory. We show that the amplitude of the interface deformation increases with increasing of the wall structure period. We demonstrate that the structured walls lead to the heat transfer enhancement, which effect is for the studied range of parameters stronger if the cover wall is structured. We also show that the wall structure enhances the long-wave Marangoni instability. The destabilizing effect of the substrate structure is stronger than that of the cover wall structure. This work has been originally presented at the 3rd International Conference on Microchannels and Minichannels, 13–15 June 2005, Toronto, Canada.     

A new model for slab and beam structures––comparison with other models

In this paper an optimized model for the analysis of plates reinforced with beams is presented as compared with other models used by various researchers. The adopted model contrary to the models used previously takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beams, due to combined response of the system. According to this model the stiffening beams of the structure are isolated from the plate by sections parallel to the lower outer surface of the plate. The forces at the interface, which produce lateral deflection and inplane deformation to the plate and lateral deflection and axial deformation to the beam, are established using continuity conditions at the interface. The adopted model describes better the actual response of the plate-beams system and permits the evaluation of the shear forces at the interface, the knowledge of which is very important in the design of composite or prefabricated ribbed plates. Four additional models neglecting the shear forces at the interfaces are presented and used for comparison reasons, while a three-dimensional elasticity model is also employed for the verification of the accuracy of the results of the examined models. The findings from this investigation, using the adopted model, which approximates better the actual response of the plate-beams system, necessitate the consideration of the inplane forces and deformations.     

An image analysis method as applied to study the space-temporal evolution of waves in an annular gas-liquid flow

The secondary instability of the surface of a liquid film sheared by an intensive gas flow was first discovered using high-speed modification of the laser-induced fluorescence method. To study the space-temporal evolution of waves of different types, we used image analysis tools, in particular, the Canny method. As a result, we obtained the quantitative characteristics for both wave types and the phenomenon of the back slope instability of primary waves.     

Finite element modeling of blood flow-induced mechanical forces in the outflow tract of chick embryonic hearts

Forces exerted by the flow of blood on the walls of the embryonic heart, such as pressures and shear stresses, influence heart development; and deviations from normal flow conditions lead to structural defects. To better understand the effect of blood flow on the development of the heart, it is important to characterize the hemodynamic forces that act on the heart walls. Other studies have attempted to quantify such forces. However, shear stresses on the heart walls cannot be measured directly, and quantifications using in vivo velocity measurements are not yet accurate due to the challenges of obtaining velocity profiles near the moving walls of a beating heart. The objective of this work is to quantify hemodynamic forces on the heart wall of chick embryos that are about 3.5 days of incubation (stage HH21), using a combination of physiological data and finite element (FE) models. We focused on the heart outflow tract (OFT) since at this stage the development of the OFT is very sensitive to hemodynamic forces. In this paper, we present a three-dimensional dynamic FE model that is based on a series of ultrasound images of the OFT. Simulations of the FE model, performed for the ventricular ejection phase of the cardiac cycle, showed a complex blood flow pattern within the OFT and gave temporal and spatial distributions of shear stresses and pressures at the inner surface of the OFT wall.     

Finite element program for solution of geotechnical problems

A program, named RODSIM, based on the finite element displacement method has been developed, tested and applied to the solution of major geotechnical problems. It is specially suitable to analyze deformations due to sequential excavation of soil supported by diaphragm walls with anchors or struts in which case it produces the bending moments, shear forces, axial forces, horizontal and vertical pressures along the wall, after deformation. All element matrices are evaluated by exact integration considering the Young's modulus of the orthotropic, cross-anisotropic or isotropic material varying linearly within the six node triangular element. The node numbering system may be optimized automatically.     

大直径瓦斯抽采钻孔非凝固膏体材料封孔技术及设备研究

针对大直径瓦斯抽采钻孔密封方法采用固体材料封孔初期密封效果好,但随着时间推移,存在封孔变形破坏后的钻孔抽采瓦斯浓度急速衰减的问题,提出了一种大直径瓦斯抽采钻孔非凝固膏体材料封孔技术。该技术利用膨胀水泥与非凝固膏体材料配合形成多段"固、液、固"结构,利用膨胀水泥材料形成三段固体封孔段,然后在不同抽采时间段在固体封孔段中注入非凝固膏体材料,实现了钻孔抽采全过程的有效密封及抽采不同时间段的二次、多次封孔。基于大直径钻孔孔周裂隙半径的理论分析结果,对最佳注浆压力和黏度的关系进行了数值模拟,研究了非凝固膏体材料封孔的相关技术参数,得到最佳注浆压力为1.2 MPa,最佳黏度为0.001~0.03 Pa·s。根据研究得到的注浆压力和黏度研制了一种封孔设备,设备利用"固、液、固"技术原理形成多段封孔结构,实现了固封液、液封气的抽采封孔模式。现场工业试验结果表明,大直径瓦斯抽采钻孔非凝固膏体材料封孔技术利用膏体材料具有随钻孔时空变化的特征,能有效解决固体材料封孔因钻孔变形而形成新裂隙,造成封孔失败、抽放浓度衰减过快的难题,且二次补浆后抽采体积分数能提升10%左右,有效提高了瓦斯抽采率。     

Semi-analytical solution of time-dependent electro-thermo-mechanical creep for radially polarized piezoelectric cylinder

History of strains, stresses, deformations and electric potentials of hollow cylinders made from PZT_5 have been investigated using successive elastic solution method. A differential equation containing creep strains for displacement is obtained. Since creep strains are time, temperature and stress dependent, the closed form solution cannot be found for this constitutive differential equation. Hence, a semi-analytical method is proposed. Electric potentials increase with time (similar to the radial stress histories), since it is induced by the radial stress histories during creep deformation of the cylinder, justifying industrial application of such a material as efficient actuators and sensors.     

Subdivision elements for large deformation of liquid capsules enclosed by thin shells

This paper presents a numerical method for studying the large deformation of a liquid capsule enclosed by a thin shell in a simple shear flow. An implicit immersed boundary method is employed for calculating the hydrodynamics and fluid–structure interaction effects. A thin-shell model for computing the forces acting on the shell middle surface during the deformation is described within the framework of the Kirchhoff–Love theory of thin shells. This thin-shell model takes full account of finite-deformation kinematics which allows thickness stretching as well as large deflections and bending strains. The interpolation of the reference and deformed surfaces of the shell is accomplished through the use of Loop's subdivision surfaces. The resulting limit surface is C¹-continuous which significantly improves the ability of the method in simulating capsules enclosed by hyperelastic thin shells with different physical properties. The present numerical technique has been validated by several examples including an inflation of a spherical shell and deformations of spherical, oblate spheroidal and biconcave capsules in the shear flow. In addition, different types of motion such as tank-treading, tumbling and transition from tumbling to tank-treading have been studied over a range of shear rates and viscosity ratios.     

基于倾斜AlN薄膜的体声波质量传感器的制备及性能分析

提出通过改变溅射气压获得倾斜于C轴的AlN薄膜的制备方法,探讨了倾斜AlN薄膜的生长机理。以3对交替沉积的Ti—Mo金属层为布拉格声学反射层,采用MEMS工艺制备了基于倾斜AlN薄膜的、以剪切模式振动的体声波液体传感器,并对器件的S11参数进行测试分析,得到传感器的中心频率为0.8GHz,表明该器件在生物液相检测领域具有一定的应用前景。     

Adaptive modelling of plates in bending and shear

As an alternative to a direct finite element approximation of the Reissner–Mindlin plate equations we propose an adaptive modeling starting with a finite element solution according to the Germain–Kirchhofff equation and in an adaptive manner adding shear deformations calculated from the Germain–Kirchhoff shear forces. The system matrix need not be changed, so the extra cost, compared to the first solution, can be kept small.     

A numerical method for two phase flows with insoluble surfactants

In many practical multiphase flow problems, i.e. treatment of gas emboli and various microfluidic applications, the effect of interfacial surfactants, or surface reacting agents, on the surface tension between the fluids is important. The surfactant concentration on an interface separating the fluids can be modeled with a time dependent differential equation defined on the moving and deforming interface. The equations for the location of the interface and the surfactant concentration on the interface are coupled with the Navier–Stokes equations. These equations include the singular surface tension forces from the interface on the fluid, which depend on the interfacial surfactant concentration.A new accurate and inexpensive numerical method for simulating the evolution of insoluble surfactants is presented in this paper. It is based on an explicit yet Eulerian discretization of the interface, which for two dimensional flows allows for the use of uniform one dimensional grids to discretize the equation for the interfacial surfactant concentration. A finite difference method is used to solve the Navier–Stokes equations on a regular grid with the forces from the interface spread to this grid using a regularized delta function. The timestepping is based on a Strang splitting approach.Drop deformation in shear flows in two dimensions is considered. Specifically, the effect of surfactant concentration on the deformation of the drops is studied for different sets of flow parameters.     

A Computational Design Methodology for Assembly and Actuation of Thin-Film Structures via Patterning of Eigenstrains

We develop a computational approach to design 3-D structures that can be fabricated and then assembled and/or actuated by spatially tailoring the layout of multilayer films with eigenstrains. Eigenstrains are stress-free strains when they occur in an unconstrained solid. They are almost an inevitable companion, albeit often unwanted, of thin-film processes. When they vary through the thickness, the constraint of the layers leads to internal stresses and bending and buckling deformations can occur; when they additionally vary in the plane of the film, more complex deformations can result. To advantageously use this phenomenon, we build on relatively simple mechanics ideas in a continuum formulation and combine geometrically nonlinear finite-element analysis of arbitrary-shaped multilayer films with a topology optimization methodology to determine the material layout in each layer so the film deforms into a prescribed shape. We expand our previous experimentally validated approach to include initially curved films and anisotropic eigenstrains. Using an extended system formulation for directly computing instability points allows us to tailor postbuckling response while explicitly controlling the design at limit and bifurcation points. We demonstrate the potential and versatility of our approach by applying it to a series of problems of contemporary and emerging interest.     

Ripple phenomenon of displays with nematic liquid crystal

Liquid crystal displays will show ripple if the display surface or display bracket is subjected to tactile forces. In this paper, the ripple of liquid crystal displays is investigated by dealing with elastic wave propagation in a liquid crystal layer. The model proposed for a visco‐elastic medium like liquid crystals (LCs) is generalized by combining the properties of a crystalline solid and an anisotropic fluid. The governing equation is derived by using visco‐elastic and wave equations. In the experiments, a linear motor is used to touch the display panel for producing ripple. Displays of three different amounts of LCs are compared. Experimental results also show that each display panel has its own wave propagation velocity that is not changed by different motor touch speeds. In addition, both theoretical analysis and experimental results depict that displays with a larger amount of LCs lead to slower ripple speed.     

Numerical bifurcation analysis of the travelling waves on a falling liquid film

Experiments for films flowing down a vertical substrate demonstrate a wide spectrum of wave regimes which are strongly dependent on flow conditions and liquid properties. This paper presents a comprehensive numerical bifurcation analysis of the steady travelling waves on a falling film described by an equation containing two parameters. It is shown that the sensitivity of observed wave regimes to physical parameters is related to a set of bifurcations associated with the variation of these parameters.     

Numerical simulation of molecularly thin lubricant film flow due to the air bearing slider in hard disk drives

In this paper we numerically study the evolution of depletion tracks on molecularly thin lubricant films due to a flying head slider in a hard disk drive. Here the lubricant thickness evolution model is based on continuum thin film lubrication theory with inter-molecular forces. Our numerical simulation involves air bearing pressure, air bearing shear stress, Laplace pressure, the dispersive component of surface free energy and disjoining pressure, a polynomial modeled polar component of surface free energy and disjoining pressure and shear stress caused by the surface free energy gradient. Using these models we perform the lubricant thickness evolution on the disk under a two-rail taper flat slider. The results illustrate the forming process of two depletion tracks of the thin lubricant film on the disk. We also quantify the relative contributions of the various components of the physical models. We find that the polar components of surface free energy and disjoining pressure and the shear stress due to the surface free energy gradient, as well as other physical models, play important rolls in thin lubricant film thickness change.