Effects of oxidation and surface roughness on contact angle

Contact angle is known to be a parameter that effects boiling. This study was undertaken to measure contact angle of high and low surface tension fluids on copper and aluminum surfaces.Data were taken for polished, oxidized, and rough surfaces. A simple, yet fairly accurate method of measuring the static equilibrium contact angle of a solid/liquid interface is presented. The principles of a line light source and tilting plate were modified and then combined in the design of this apparatus. The angles obtained and their variation with the solid surface properties were in good agreement with previously published data. The contact angle of distilled water o of the organic fluids and refrigerants tested were in the range of 2–5°. Roughness and oxidation reduce the contact angle. If the depth of the roughness is less than 0.5 μm contact angle. The apparatus is fairly simple in construction, is inexpensive, and has good reproductibity. The measured angles were then compared to those measured with the sessile drop method.     

The wetting problem of fluids on solid surfaces. Part 2: the contact angle hysteresis

In part 1 (Gouin, [13]), we proposed a model of dynamics of wetting for slow movements near a contact line formed at the interface of two immiscible fluids and a solid when viscous dissipation remains bounded. The contact line is not a material line and a Young-Dupré equation for the apparent dynamic contact angle taking into account the line celerity was proposed. In this paper we consider a form of the interfacial energy of a solid surface in which many small oscillations are superposed on a slowly varying function. For a capillary tube, a scaling analysis of the microscopic law associated with the Young-Dupré dynamic equation yields a macroscopic equation for the motion of the contact line. The value of the deduced apparent dynamic contact angle yields for the average response of the line motion a phenomenon akin to the stick-slip motion of the contact line on the solid wall. The contact angle hysteresis phenomenon and the modelling of experimentally well-known results expressing the dependence of the apparent dynamic contact angle on the celerity of the line are obtained. Furthermore, a qualitative explanation of the maximum speed of wetting (and dewetting) can be given.Received: 5 June 2001, Accepted: 24 May 2003, Published online: 29 July 2003PACS: 02.90, 47.50, 66.20, 68.03, 68.08     

Improved method for implementing contact angle condition in simulation of liquid sloshing under microgravity

The finite element simulation of liquid sloshing under microgravity is focused on in this paper. For this class of flows, an important issue is to implement the contact angle boundary condition appropriately. A novel method of adding infinitely small free-surface mesh just adjacent to the contact line is proposed here, which coincides with the physical definition of the contact angle. This free-surface mesh has its orientation determined according to the contact angle, and the mean curvature at the contact line can be computed using this orientation. Hence, surface tension force can be computed and incorporated as an essential boundary condition into the pressure solve. This method is convenient to be applied in three-dimensional simulations, and the use of relatively coarse meshes near the contact line is allowed. In order to validate the proposed method, several numerical simulations of flows in two-dimensional circular and three-dimensional cylindrical and spherical containers are presented, including calculation of equilibrium positions of the free surfaces, unsteady flows of liquid reorientation, and large-amplitude nonlinear liquid sloshing under lateral excitation in microgravity. Parts of the numerical results are compared with the theoretical and published experimental results.     

Numerical simulation of dynamic contact angle using a force based formulation

A method for the numerical simulation of the dynamic response of the contact angle is presented and its development discussed. The proposed method was developed within a level-set framework by modelling forced capillary flows and it is based on the introduction of a force function to capture the balance of forces in the contact region between solid boundaries and a diffuse free-surface fluid interface. The proposed approach allows the system to define its own dynamic contact angle and its own contact line dynamics, without introducing numerical discontinuities such as locally prescribed angles or slip-length. The method was developed through numerical testing and comparisons with experimental and empirical models reported in the literature. These showed the validity of the proposed approach, which was able to reproduce the experimental correlation between the capillary number and the dynamic contact angle reported by [R.L. Hoffman, Study of advancing interface. 1. Interface shape in liquid-gas systems, J. Colloid Interf. Sci. 50 (1975) 228-241]. By using a single constitutive model for the force function, the simulation results of the dynamic contact angle showed an excellent agreement with the values predicted by Jiang’s empirical equation [T.S. Jiang, O.H. Soo-Gun, J.C. Slattery, Correlation for dynamic contact angle, J. Colloid Interf. Sci. 69 (1979) 74-77] through different material properties and flow speeds. The proposed approach also demonstrated the ability to work with meshes of low resolution.     

A height function based momentum balance model to simulate contact angle dynamics with hysteresis

We report a combined method to deal with the contact angle dynamics with hysteresis. The momentum balance model is applied to obtain the transient contact angle by balancing the inertia and the capillary force where the curvatures are estimated by the height function at the contact line. This integrated approach provides a great convenience that no need for a prior knowledge of the contact angle, and possesses the good property of the sharp interface approximation. In order to facilitate the wider use of the present method, we incorporate a dynamic contact line model to estimate the contact angle when the contact line starts to move. This combination plus the hysteresis region will take the ability to solve most of problems related to wetting with more physical sense. This proposed model is finally validated by the droplet equilibrium, spreading, and sliding tests.     

Effects of hysteresis of static contact angle (HSCA) and boundary slip on the hydrodynamics of water striders

It is known that contact lines keep relatively still on solids until static contact angles exceed an interval of hysteresis of static contact angle(HSCA), and contact angles keep changing as contact lines relatively slide on the solid.Here, the effects of HSCA and boundary slip were first distinguished on the micro-curvature force(MCF) on the seta.Hence, the total MCF is partitioned into static and dynamic MCFs correspondingly. The static MCF was found proportional to the HSCA and related with the asymmetry of the micro-meniscus near the seta. The dynamic MCF, exerting on the relatively sliding contact line, is aroused by the boundary slip. Based on the Blake–Haynes mechanism, the dynamic MCF was proved important for water walking insects with legs slower than the minimum wave speed 23 cm · s-1. As insects brush the water by laterally swinging legs backwards,setae on the front side of the leg are pulled and the ones on the back side are pushed to cooperatively propel bodies forward.If they pierce the water surface by vertically swinging legs downwards, setae on the upside of the legs are pulled, and the ones on the downside are pushed to cooperatively obtain a jumping force. Based on the dependency between the slip length and shear rate, the dynamic MCF was found correlated with the leg speed U, as F~C_1 U + C_2U~(2+ε), where C_1 and C_2 are determined by the dimple depth. Discrete points on this curve could give fitted relations as F~U~b(Suter et al., J. Exp. Biol. 200, 2523–2538, 1997). Finally,the axial torque on the inclined and partially submerged seta was found determined by the surface tension, contact angle,HSCA, seta width, and tilt angle. The torque direction coincides with the orientation of the spiral grooves of the seta,which encourages us to surmise it is a mechanical incentive for the formation of the spiral morphology of the setae of water striders.     

回转支承构件牵引滚动接触应力解析

回转支承构件是重型机械的重要基础元件,其失效往往导致灾难性的设备事故和人身事故以及巨大的经济损失.及时、充分地了解回转支承构件牵引滚动接触应力分布特点,对于保证整机安全生产和提高企业经济效益具有非常重要的意义.本文将回转支承构件接触模型简化为轴线平行的圆柱体二维平面应变模型,从接触力学理论中McEwen关于轴线平行的圆柱体二维法向接触理论出发,重点讨论牵引滚动与常规法向接触状态的切向分布力的相同点和不同点,从而推导出牵引滚动接触状态下接触区应力场各应力分量解析式,将McEw-en法向理论公式推广到法、切向复合分布力综合作用下.在此基础上,探讨了表面拉应力与摩擦系数的关系,摩擦系数越大则表面拉应力水平越高.最后,运用材料力学二向应力状态受力分析方法,计算了接触应力场最大剪应力位置、大小和方向角与深度的关系,发现与无表面摩擦情况相比,最大主剪应力发生位置变浅,幅值反而变小.     

考虑股线接触与摩擦行为的710 mm2碳纤维复合芯导线(ACCC)股线损伤分析

利用扫描电镜观察710 mm~2碳纤维复合芯导线(ACCC)过滑车试验后股线的磨损形貌,分析滑车底径对股线损伤的影响及股线损伤机制.同时,考虑股线间的接触与摩擦行为,建立导线全尺寸模型进行导线过滑车非线性动力学有限元分析.试验结果表明:导线过滑车后股线出现塑性变形与磨损,在股线表面初始磨损处以黏着磨损的形式扩展,且股线损伤随滑车底径的增大有所改善;数值分析表明:股线等效塑性应变与摩擦能量损耗开始于导线过滑车时的弯曲过程,且随滑车底径增大而减小,股线损伤的模拟结果与试验情况吻合.在此基础上,研究股线间摩擦系数对股线损伤影响,得到股线损伤随摩擦系数的减小而减小.研究初步认为滑车底径为30倍导线直径时股线损伤在可接受范围内.     

Experimental study of evaporation of sessile water droplet on PDMS surfaces

Evaporation of sessile water droplet on polydimethylsiloxane （PDMS） surfaces with three different curing ratios （5：1, 10：1, and 20：1） was experimentally investigated in this paper. We show that the constant contact radius （CCR） evaporation on surface with high curing ratio lasts longer than that with low curing ratio. We also measured Young＇s moduli of PDMS films by using atomic force microscopy （AFM） and simulated surface deformation of PDMS films induced by sessile water droplet. With increasing curing ratio of PDMS film, Young＇s modulus of PDMS film is getting lower, and then there will be larger surface deformation and more elastic stored energy. Since such energy acts as a barrier to keep the three-phase contact line pinned, thus it will result in longer CCR evaporation on PDMS surface with higher curing ratio.     

The effect of the VOF–CSF static contact angle boundary condition on the dynamics of sliding and bouncing ellipsoidal bubbles

The static contact angle is the only empiricism introduced in a Volume of Fluid–Continuum Surface Force (VOF–CSF) model of bubbly flow. Although it has previously been shown to have a relatively limited effect on the accuracy of velocity and shape predictions in the case of large gas bubbles sliding under inclined walls (e.g. Cook and Behnia, 2001), it may have a more determining influence on the numerical prediction of the dynamics of smaller ellipsoidal bubbles which were shown by Tsao and Koch (1997) to bounce repeatedly when sliding under inclined walls at certain wall inclinations. The present paper reports on the influence of surface tension and the static contact angle on the dynamics of an ellipsoidal air bubble of equivalent diameter D_e = 3.4 mm. The bubble Eötvös and Morton numbers are Eo = 1.56 and Mo = 2 × 10⁻¹¹ respectively. The computational results are achieved with a Piecewise Linear Construction (PLIC) of the interface and are reviewed with reference to experimental measurements of bubble velocity and interface shape oscillations recorded using a high speed digital camera. Tests are performed at plate inclination angles θ ∈ {10°, 20°, 30°, 45°} to the horizontal and computational models consider three static contact angles θ_c ∈ {10°, 20°, 30°}. The static contact angle has been found to have a significant effect on the bubble dynamics but to varying degree depending on the plate inclination. It is shown to promote lift off and bouncing when the plate inclination angle reaches 30° in a way that does not necessarily reflect experimental observations.     

RV减速器主支撑角接触球轴承混合润滑分析

针对RV减速器角接触球轴承承受预紧力、轴向力和径向力等联合外载荷作用的工况,分析得出了内、外圈滚道接触界面的接触区几何参数和接触载荷.在此基础上,综合考虑了角接触球轴承的接触区宏观几何、接触载荷、真实表面粗糙度、瞬态效应等因素,建立了角接触球轴承混合润滑数学模型,分析了在不同工况下角接触轴承的润滑状况及表面以下应力分布.结果表明:随着载荷的不断增加,钢球与内圈沟道之间的油膜厚度会不断减少,导致干接触面积迅速扩大,接触点表面以下最大应力增大;转速的增加会使油膜变厚,干接触面积缩小.该结果对角接触球轴承的实际工程应用具有重要借鉴意义.     

一种基于极小化极大接触压力的交界面修形新方法

针对轴承和齿轮等零部件接触压力分布不均问题,提出了一种极小化极大接触压力的弹性交界面修形新方法,仅需要一次结构分析就可以实现理想的修形结果。基于弹性接触理论与有限元法,推导建立了接触节点修形量与接触压力之间的数学方程;以极小化各接触节点的最大接触压力为目标,建立了计算修形量的极小极大模型;并利用最优化方法将其转化为线性规划问题,有效提高了求解的全局收敛性和计算效率。通过两个弹性接触修形实例,验证了新方法对一般弹性接触修形问题的适用性和高效性。     

The wetting problem of fluids on solid surfaces. Part 1: the dynamics of contact lines

The understanding of the spreading of liquids on solid surfaces is an important challenge for contemporary physics. Today, the motion of the contact line formed at the intersection of two immiscible fluids and a solid is still subject to dispute. In this paper, a new picture of the dynamics of wetting is offered through an example of non-Newtonian slow liquid movements. The kinematics of liquids at the contact line and equations of motion are revisited. Adherence conditions are required except at the contact line. Consequently, for each fluid, the velocity field is multivalued at the contact line and generates an equivalent concept of line friction but stresses and viscous dissipation remain bounded. A Young-Dupré equation for the apparent dynamic contact angle between the interface and solid surface depending on the movements of the fluid near the contact line is proposed.Received: 5 June 2001, Accepted: 24 May 2003, Published online: 29 July 2003PACS: 47.17., 47.50, 66.20, 68.08, 83.50     

Measurements of the contact angle between R134a and both aluminum and copper surfaces

Measurements of quasi-static advancing contact angles of refrigerant R134a on copper and aluminum surfaces are reported over a temperature range from 0 °C to 80 °C. The metal surfaces tested were aluminum (alloy 3003) and copper (alloy 101) plates. Measurements were done using a direct optical observation technique where the liquid meniscus at the surface of a vertical plate was captured using a high magnification camera system. The contact angle of solid–liquid interface was deduced by enhancing and manipulating the digital image using solid modeling software by drawing a tangent line to the meniscus at the intersection location of the solid, liquid and vapor. Values of the contact angle were found to vary between 8.3° and 5.6° for aluminum and between 5.1° and 6.5° for copper when the temperature rose from 0 °C to 80 °C. Maximum standard deviation amongst the measured values of contact angles was 1.3°.     

On the Computer Formulations of the Wheel/Rail Contact Problem

In this investigation, four nonlinear dynamic formulations that can be used in the analysis of the wheel/rail contact are presented, compared and their performance is evaluated. Two of these formulations employ nonlinear algebraic kinematic constraint equations to describe the contact between the wheel and the rail (constraint approach), while in the other two formulations the contact force is modeled using a compliant force element (elastic approach). The goal of the four formulations is to provide accurate nonlinear modeling of the contact between the wheel and the rail, which is crucial to the success of any computational algorithm used in the dynamic analysis of railroad vehicle systems. In the formulations based on the elastic approach, the wheel has six degrees of freedom with respect to the rail, and the normal contact forces are defined as function of the penetration using Hertzs contact theory or using assumed stiffness and damping coefficients. The first elastic method is based on a search for the contact locations using discrete nodal points. As previously presented in the literature, this method can lead to impulsive forces due to the abrupt change in the location of the contact point from one time step to the next. This difficulty is avoided in the second elastic approach in which the contact points are determined by solving a set of algebraic equations. In the formulations based on the constraint approach, on the other hand, the case of a non-conformal contact is assumed, and nonlinear kinematic contact constraint equations are used to impose the contact conditions at the position, velocity and acceleration levels. This approach leads to a model, in which the wheel has five degrees of freedom with respect to the rail. In the constraint approach, the wheel penetration and lift are not permitted, and the normal contact forces are calculated using the technique of Lagrange multipliers and the augmented form of the system dynamic equations. Two equivalent constraint formulations that employ two different solution procedures are discussed in this investigation. The first method leads to a larger system of equations by augmenting all the contact constraint equations to the dynamic equations of motion, while in the second method an embedding procedure is used to obtain a reduced system of equations from which the surface parameter accelerations are systematically eliminated. Numerical results are presented in order to examine the performance of various methods discussed in this study.     

表面织构对界面接触参数影响的实验研究

机械接触表面的接触刚度和接触阻尼是直接影响界面振动水平的两个重要动力学参数。本文介绍了一种测试机械连接界面接触刚度和接触阻尼的实验装置和方法,并针对用两种不同加工方法(激光加工及线切割)加工出的具有不同尺寸织构的试样与光滑平面相接触的界面进行了测量,初步探索了平面接触刚度和接触阻尼的表面织构效应,并得出结论：织构及润滑对接触刚度会产生一定影响,而实验中均未观察到这两者对接触阻尼有明显影响。     

Applicability of the Hertz contact theory to rail-wheel contact problems

Summary Rail-wheel contact problems have been analyzed by applying three-dimensional finite element models. Based on these models, the applicability of the Hertz contact theory (HCT) to rail-wheel contact problems is verified in the present paper. Beside a standard rail, also a crane rail and a switching component are considered in the verification. In the case of a contact between the standard rail UIC60 and the standard wheel UICORE, different transverse contact positions are analyzed. Numerically calculated distributions of the contact pressure for different types of rails with respect to different initial contact positions agree with the results from the HCT only if either the contact zone does not spread into a region of changed surface curvature or if plastification does not occur. Finally, the convective part of the dissipation power due to friction is calculated, which cannot be provided directly by the HCT. Received 5 August 1998; accepted for publication 6 May 1999     

On unilateral contact of two plates aligned at an angle to each other

The contact problem for two elastic plates aligned at a prescribed angle to each other is considered. The set of contact points is assumed to be unknown in advance and to be determined only after the problem is solved. Various formulations of the problem are given, and their equivalence is proved. A complete set of boundary conditions fulfilled on the contact domain is found, and the character of satisfaction of these conditions is described. The asymptotic properties of solutions are studied for rigidity parameters of the contacting plates tending to infinity. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 42–58, July–August, 2008.     

Approximate Solution of an Axisymmetric Contact Problem with Allowance for Tangential Displacements on the Contact Surface

A structurally nonlinear contact problem of a punch shaped like a paraboloid of revolution is studied. An equation for the contactpressure density is derived with allowance for the radial tangential displacements of the boundary points of an elastic halfspace. A method for constructing a closedform approximate solution is proposed. The effect of the tangential displacements on the main contact parameters is discussed.     

Dynamic behaviors of droplet impact and spreading: A universal relationship study of dimensionless wetting diameter and droplet height

A notable universal relationship has been proposed in the literature for the evolution of dimensionless droplet height and wetting diameter during the initial spreading stage of droplet impingement. In this study, this universal relationship was investigated by employing three sets of measurements. Sequential images were recorded, and the whole droplet profile ensembles were plotted to facilitate this study. These sets of experiments were designed by changing impact velocity, surface hydrophobicity, or solution property. The experimental results illustrate that the importance of parameters causing the data variation is in the order of surface hydrophobicity > initial impact velocity > surfactant on wetting diameter, and surface hydrophobicity ≈ initial impact velocity > surfactant on droplet height. No universal relationship was observed for dimensionless droplet height and wetting diameter.