Heat transfer between elastic solids with randomly rough surfaces

We study the heat transfer between elastic solids with randomly rough surfaces. We include both the heat transfer from the area of real contact, and the heat transfer between the surfaces in the non-contact regions. We apply a recently developed contact mechanics theory, which accounts for the hierarchical nature of the contact between solids with roughness on many different length scales. For elastic contact, at the highest (atomic) resolution the area of real contact typically consists of atomic (nanometer) sized regions, and we discuss the implications of this for the heat transfer. For solids with very smooth surfaces, as is typical in many modern engineering applications, the interfacial separation in the non-contact regions will be very small, and for this case we show the importance of the radiative heat transfer associated with the evanescent electromagnetic waves which exist outside of all bodies.     

Elastic contact mechanics: Percolation of the contact area and fluid squeeze-out

The dynamics of fluid flow at the interface between elastic solids with rough surfaces depends sensitively on the area of real contact, in particular close to the percolation threshold, where an irregular network of narrow flow channels prevails. In this paper, numerical simulation and experimental results for the contact between elastic solids with isotropic and anisotropic surface roughness are compared with the predictions of a theory based on the Persson contact mechanics theory and the Bruggeman effective medium theory. The theory predictions are in good agreement with the experimental and numerical simulation results and the (small) deviation can be understood as a finite-size effect. The fluid squeeze-out at the interface between elastic solids with randomly rough surfaces is studied. We present results for such high contact pressures that the area of real contact percolates, giving rise to sealed-off domains with pressurized fluid at the interface. The theoretical predictions are compared to experimental data for a simple model system (a rubber block squeezed against a flat glass plate), and for prefilled syringes, where the rubber plunger stopper is lubricated by a high-viscosity silicon oil to ensure functionality of the delivery device. For the latter system we compare the breakloose (or static) friction, as a function of the time of stationary contact, to the theory prediction.     

The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: A review

A sessile drop is an isolated drop which has been deposited on a solid substrate where the wetted area is limited by the three-phase contact line and characterized by contact angle, contact radius and drop height. Although, wetting has been studied using contact angles of drops on solids for more than 200 years, the question remains unanswered: Is wetting of a rough and chemically heterogeneous surface controlled by the interactions within the solid/liquid contact area beneath the droplet or only at the three-phase contact line? After the publications of Pease in 1945, Extrand in 1997, 2003 and Gao and McCarthy in 2007 and 2009, it was proposed that advancing, receding contact angles, and contact angle hysteresis of rough and chemically heterogeneous surfaces are determined by interactions of the liquid and the solid at the three-phase contact line alone and the interfacial area within the contact perimeter is irrelevant. As a consequence of this statement, the well-known Wenzel (1934) and Cassie (1945) equations which were derived using the contact area approach are proposed to be invalid and should be abandoned. A hot debate started in the field of surface science after 2007, between the three-phase contact line and interfacial contact area approach defenders. This paper presents a review of the published articles on contact angles and summarizes the views of the both sides. After presenting a brief history of the contact angles and their measurement methods, we discussed the basic contact angle theory and applications of contact angles on the characterization of flat, rough and micropatterned superhydrophobic surfaces. The weak and strong sides of both three-phase contact line and contact area approaches were discussed in detail and some practical conclusions were drawn.     

Elastoplastic contact between randomly rough surfaces

I have developed a theory of contact mechanics between randomly rough surfaces. The solids are assumed to deform elastically when the stress sigma is below the yield stress sigma(Y), and plastically when sigma reaches sigma(Y). I study the dependence of the (apparent) area of contact on the magnification. I show that in most cases the area of real contact A is proportional to the load. If the rough surface is self-affine fractal (Hurst exponent H) the whole way up to the lateral size L of the nominal contact area, then (assuming no plastic deformation) A approximately L(H).     

Relation between interfacial separation and load: a general theory of contact mechanics

I study the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. I derive a relation between the (average) interfacial separation u and the applied normal squeezing pressure p. I show that, for nonadhesive interaction and small applied pressure, p approximately exp(-u/u(0)), in good agreement with recent experimental observations.     

Experimental analysis of interface contact behavior using a novel image processing method

The spatial and temporal evolution of real contact area of contact interface with loads is a challenge. It is generally believed that there is a positive linear correlation between real contact area and normal load. However, with the development of measuring instruments and methods, some scholars have found that the growth rate of real contact area will slow down with the increase of normal load under certain conditions, such as large-scale interface contact with small roughness surface,which is called the nonlinear phenomenon of real contact area. At present, there is no unified conclusion on the explanation of this phenomenon. We set up an experimental apparatus based on the total reflection principle to verify this phenomenon and analyze its mechanism. An image processing method is proposed, which can be used to quantitative analysis micro contact behaviors on macro contact phenomenon. The weighted superposition method is used to identify micro contact spots, to calculate the real contact area, and the color superimposed image is used to identify micro contact behaviors.Based on this method, the spatiotemporal evolution mechanism of real contact area nonlinear phenomena is quantitatively analyzed. Furthermore, the influence of nonlinear phenomenon of real contact area on the whole loading and unloading process is analyzed experimentally. It is found that the effects of fluid between contact interface, normal load amplitude and initial contact state on contact behavior cannot be ignored in large-scale interface contact with small roughness surface.     

表面黏附导致的接触行为转变

应用大规模分子动力学方法, 模拟了具有不同原子级粗糙形貌的两种刚性球形探头与弹性平面基体的黏附接触行为. 研究了载荷与真实接触面积、接触界面排斥力与真实接触面积, 以及黏附力与真实接触面积之间的关系. 分子模拟得到的载荷与真实接触面积的关系, 与连续力学接触理论预测很好地定性一致. 无论是原子级光滑探头还是粗糙探头, 黏附接触下的排斥力与真实接触面积的关系, 都与无黏附接触时的规律相一致, 即黏附力对接触行为的影响作用, 可以等效为附加在真实外载荷基础上的虚拟载荷, 将对黏附接触行为的分析转变为无黏附接触分析. 两种探头的黏附力随真实接触面积都呈幂函数形式的增长, 但是, 原子级光滑探头的幂指数大于1, 而原子级粗糙探头的幂指数小于1. 关键词： 接触行为 表面黏附 分子动力学模拟     

A multiscale molecular dynamics approach to contact mechanics

The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces have roughness on many different length-scales, e.g., for self affine fractal surfaces. As an illustration we consider the contact between randomly rough surfaces, and show that the contact area varies linearly with the load for small load. We also analyze the contact morphology and the pressure distribution at different magnification, both with and without adhesion. The calculations are compared with analytical contact mechanics models based on continuum mechanics.     

Investigating interfacial contact configuration and behavior of single-walled carbon nanotube-based nanodevice with atomistic simulations

Carbon nanotubes (CNTs), including single-walled carbon nanotubes (SWNTs) and multi-walled carbon nanotubes (MWNTs), are considered to be the promising candidates for next-generation interconnects with excellent physical and chemical properties ranging from ultrahigh mechanical strength, to electrical properties, to thermal conductivity, to optical properties, etc. To further study the interfacial contact configurations of SWNT-based nanodevice with a 13.56-Å diameter, the corresponding simulations are carried out with the molecular dynamic method. The nanotube collapses dramatically into the surface with the complete collapse on the Au/Ag/graphite electrode surface and slight distortion on the Si/SiO₂ substrate surface, respectively. The related dominant mechanism is studied and explained. Meanwhile, the interfacial contact configuration and behavior, depended on other factors, are also analyzed in this article.     

An elastic-plastic contact model for line contact structures

Although numerical simulation tools are now very powerful,the development of analytical models is very important for the prediction of the mechanical behaviour of line contact structures for deeply understanding contact problems and engineering applications.For the line contact structures widely used in the engineering field,few analytical models are available for predicting the mechanical behaviour when the structures deform plastically,as the classic Hertz’s theory would be invalid.Thus,the present study proposed an elastic-plastic model for line contact structures based on the understanding of the yield mechanism.A mathematical expression describing the global relationship between load history and contact width evolution of line contact structures was obtained.The proposed model was verified through an actual line contact test and a corresponding numerical simulation.The results confirmed that this model can be used to accurately predict the elastic-plastic mechanical behaviour of a line contact structure.     

Stiffness of contacts between rough surfaces

The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal stiffness rise linearly with the applied load, and the load rises exponentially with decreasing separation between surfaces. Results for a wide range of roughness, system size, and Poisson ratio can be collapsed using Persson's contact theory for continuous elastic media. The compliance due to atomic-scale motion at the interface between solids has little effect on the area and normal stiffness, but can reduce the total transverse stiffness by orders of magnitude. The scaling of this effect with system size is discussed.     

Assessing the equation of state and comparing it with other relationships used for determining the surface tension of solids

Some facts regarding the equation of state (EQS) in calculating the surface tension of solids by means of contact angle measurements were manifested. In the present investigation, it was mathematically proved that the surface tension of a solid as estimated by the EQS is in fact equivalent to the Zisman critical surface tension for that same solid. Additionally, the applicability of the EQS's approach in attaining the surface tension of powdered solids by the aid of the capillary rise procedure is also discussed and its limitations are clarified. Furthermore, a methodology was devised so that the surface tension of solids as determined by the EQS could be compared with those calculated by approaches using components of surface tension. This methodology revealed that the applications of approaches based on the geometric mean (i.e. Owens/Wendt and van Oss et al. relationships) are restricted to achieving only high surface tensions of solids.     

纳米接触过程中黏着规律的变化

本文应用大规模分子动力学方法, 模拟了两种具有不同粗糙形貌的、刚性球形探头与弹性平面基体之间的纳米尺度接触, 计算了探头与基体之间的拉离力和黏着功, 研究了接触过程中界面黏着力随载荷的变化规律, 分析了接触界面原子的法向应力分布. 研究发现, 原子级光滑接触的黏着力随着载荷的增大而线性增大, 而原子级粗糙接触的黏着力-载荷曲线分为以不同斜率增长的两个阶段. 相比于原子级光滑探头, 原子级粗糙探头与基体之间具有较小的拉离力和黏着功, 却在接触过程中形成了较大的黏着力. 因此, 拉离力和黏着功不能表征出纳米接触过程中原子吸引作用对界面法向力的贡献大小.     

Calibrating a nanoindenter for very shallow depth indentation using equivalent contact radius

Nanoindenter tips are usually modelled as axisymmetric cones, with calibration involving finding a fitting function that relates contact area to contact depth. For accurate calibration of shallow depth indentation, this is not ideal because it means that deeper indents tend to dominate the fitting function. For an axisymmetric object, it is always possible to define an equivalent contact radius (which, in the case, of nanoindentation is linearly related to the reduced modulus) and to obtain a fitting function that relates this equivalent contact radius to indentation depth. The equivalent contact radius approach is used here to provide shallow depth calibration of a nanoindenter tip at three separate times. The advantage of the equivalent contact radius methodology is that it provides a clearer physical interpretation of the changes in tip shape than a conventional area-based fit. We also show that the minimum depth for a reliable hardness measurement is obtainable and increases as the tip blunts with age but that consistent measurements of very near surface elastic moduli can be made if the blunting of the tip over time is fully accounted for in the tip area function calibration.     

基于织构表面的摩擦静电发电机制备及其输出性能研究

摩擦电纳米发电机(TENG)是基于摩擦生电和静电感应复合原理将机械能转换为电能的一种新型能源获取方式. 本文采用模板法制备了几种不同参数的聚二甲基硅氧烷(PDMS)微圆柱结构, 并组装成TENG, 实验研究了接触区表面积、外加载荷对TENGs输出性能的影响. 结果表明, 圆形微柱阵列的存在有效提高了TENG的作用面积及电输出性能, 相同载荷下, 电输出随微柱间距离减小而增加, 在间距为15 μm、载荷为5 N时, 输出的平均开路电压和短路电流分别为88 V 和15 μA, 是同等条件下、微柱间距为50 μm电输出的1.5倍以上; 电输出随载荷增加呈准线性增加, ANSYS软件模拟载荷作用下PDMS微圆柱织构的变形行为, 结果表明, 压力作用下, 微圆柱主要发生压缩变形, 基底的变形导致微柱与上电极之间产生侧向摩擦, 从而产生更多电荷, 提升了电输出性能.     

Effects of symmetric and asymmetric contact angles and division of menisci during separation

Meniscus and viscous forces are sources of adhesive force when two surfaces are separated with a micro-meniscus present at the interface. The adhesive force can be one of the main reliability issues when the contacting surfaces are ultra-smooth and the normal load is small, as is common for micro/nano devices. In this paper, both meniscus and viscous forces of menisci with symmetric and asymmetric contact angles are modelled. Equations for both meniscus and viscous forces in division of menisci are analytically formulated. The role of these two forces is evaluated during the separation process. The effects of the contact angles, division of menisci, as well as liquid thicknesses, surface tension and viscosity of the liquid, and separation distance and time during separation are presented. It is found that contact angles significantly affect the break point and meniscus force, and the magnitude of meniscus force can be largely reduced by choosing proper asymmetric contact angles. ‘Force scaling’ effects are found to be true for both meniscus and viscous forces when one larger meniscus is divided into large numbers of identical micro-menisci. Meniscus force increases with the number of divisions whereas viscous force decreases by an order of inverse the number of division (1/N). Optimal configurations for low adhesion are identified. This study presents a comprehensive analysis of meniscus and viscous forces during separation of menisci under different physical configurations. It provides a fundamental understanding of the physics of the process and knowledge for control of adhesion due to liquid menisci.     

Formation of surface nanobubbles and the universality of their contact angles: a molecular dynamics approach

We study surface nanobubbles using molecular dynamics simulation of ternary (gas, liquid, solid) systems of Lennard-Jones fluids. They form for a sufficiently low gas solubility in the liquid, i.e., for a large relative gas concentration. For a strong enough gas-solid attraction, the surface nanobubble is sitting on a gas layer, which forms in between the liquid and the solid. This gas layer is the reason for the universality of the contact angle, which we calculate from the microscopic parameters. Under the present equilibrium conditions the nanobubbles dissolve within less of a microsecond, consistent with the view that the experimentally found nanobubbles are stabilized by a nonequilibrium mechanism.     

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

The authors have employed a numerical procedure to analyse the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution to the problem, which belongs to the class of the free boundary problems, is obtained by calculating Green’s function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel. The boundaries of the contact area are calculated by requiring the energy of the system to be stationary. This methodology has been employed to study the adhesive contact between an elastic semi-infinite solid and a randomly rough rigid profile with a self-affine fractal geometry. We show that, even in the presence of adhesion, the true contact area still linearly depends on the applied load. The numerical results are then critically compared with the predictions of an extended version of Persson’s contact mechanics theory, which is able to handle anisotropic surfaces, as 1D interfaces. It is shown that, for any given load, Persson’s theory underestimates the contact area by about 50% in comparison with our numerical calculations. We find that this discrepancy is larger than for 2D rough surfaces in the case of adhesionless contact. We argue that this increased difference might be explained, at least partially, by considering that Persson’s theory is a mean-field theory in spirit, so it should work better for 2D rough surfaces rather than for 1D rough surfaces. We also observe that the predicted value of separation is in agreement with our numerical results as well as the exponents of the power spectral density of the contact pressure distribution and of the elastic displacement of the solid. Therefore, we conclude that Persson’s theory captures almost exactly the main qualitative behaviour of the rough contact phenomena.     

Electrification following the contact of solids

The charge found on solids after they have been rubbed together can only be a direct consequence of friction when the rubbing is vigorous; more usually, the charging is the result of contact, rubbing complicating the phenomenon. Opinions differ regarding the origin of contact charging, but certain experiments suggest a working hypothesis, according to which the charging is due to electron transfer when both materials are either semiconductors or metals, but to ions when insulators take part. Electron transfer is associated with the setting up of a contact potential. Ion transfer can be caused either by a potential difference, in which case the current flows with the e.m.f., or it can be caused by forces that are not electrical in nature, in which case the current flows against the potential difference generated by the ‘mechanical transfer’ of charge.     

Adhesion between elastic bodies with randomly rough surfaces

I have developed a theory of adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account the fact that partial contact may occur between the solids on all length scales. I present numerical results for the case where the substrate surface is self-affine fractal. When the fractal dimension is close to 2, complete contact typically occurs in the macroasperity contact areas. For a fractal dimension larger than 2.5, the area of (apparent) contact decreases continuously when the magnification is increased.