Contact Radius Research Articles

Study on machining BK7 optical glass by ultrasonic vibration-assisted polishing considering the micro-contact state of the abrasive particles with the workpiece

Brittle materials such as glass and ceramics have fragile physical properties that result in poor stability in the machining process. Ultrasonic vibration-assisted polishing (UVAP) can improve the surface quality and machining efficiency of the workpiece, which is beneficial to solve the machining problems of brittle materials. In this paper, a theoretical model is established to predict the material removal rate (MRR), surface roughness, maximum contact radius, and maximum material removal depth of BK7 optical glass for different machining parameters. The new model mainly considers the following aspects: (1) Considering the randomness of the shape, the abrasive particle is modeled as a truncated polyhedron. (2) Due to the randomness of distribution, the abrasive particles are considered to be randomly distributed in the contact area between the polishing tool and the workpiece. (3) Based on the Preston equation, a material removal model is established which considers the micro-contact state of the abrasive particles with the workpiece. Compared with the experimental results of BK7 optical glass, the new model has high accuracy in predicting machining performance. It is meaningful to understand the mechanism of UVAP and improve the machining efficiency.

The surface tension effect revealed via the indentation scaling index

The axisymmetric frictionless indentation problem for an isotropic elastic half-space with the uniform surface tension is considered. The first-order regular and singular asymptotic models are constructed for the limit situations of relatively small (in the membrane limit) or large (in the Hertzian limit) values of the contact radius. By using the method of collocation, a two-parameter analytical approximate solution is developed with coefficients evaluated in triple quadratures. The accuracy of the obtained analytical models is investigated in the case of a paraboloidal indenter by comparison with numerical solutions available in the literature. Based on the asymptotic behavior of the solution in the limit situations, the so-called indentation scaling index is introduced for the analysis of the depth-sensing indentation data. By making use of the novel contact parameter it is possible to extract the surface tension effect independently of determining the reduced elastic modulus of a tested semi-infinite sample. It is shown that by employing an appropriate normalization, the contact problem can be reduced to that parameterized by only one parameter (relative contact radius), which implies that irrespectively of the combination of the material parameters, the force–displacement curve drawn in the normalized variables will be universal.

Lifetime Prediction of Sessile Droplet Evaporation with Coupled Fields

The evaporation of sessile droplets has wide applications in various industrial fields. Therefore, it is important to accurately predict the temporal evolution behavior of sessile droplets during evaporation. In this paper, both theoretical analysis and numerical simulation are carried out to explore the evolution of droplet evaporation, with internal thermocapillary convection, interfacial evaporative cooling, and external natural convection coupled together. It is found that internal thermocapillary convection and external natural convection can promote droplet evaporation, while interfacial evaporative cooling can impede it. When a droplet evaporates in a constant contact radius mode, there is a critical initial contact angle, below which the isothermal model can overestimate the evaporation lifetime, and the critical initial contact angle becomes large with increasing substrate superheat. Finally, when the droplet evaporates in the constant contact angle mode, the “2/3 power law” still holds for transient variation of droplet volume, as predicted by the isothermal model. These findings may help obtain insights into the mechanism of droplet evaporation and provide guidance for inkjet printing and surface cooling.

Topological heterogeneity and evaporation dynamics of irregular water droplets

Water droplets sitting between wires are ubiquitous in nature and industry, often showing irregular (non-spherical) droplet shapes. To understand their topological singularity and evaporation mechanism, measuring volume changes of irregular water droplets is essential but highly challenging for small-volume water droplets. Here we experimentally explore topological heterogeneity and evaporation dynamics for irregular water droplets between wires with four-dimensional X-ray microtomography that directly provides images in three spatial dimensions as a function of time, enabling us to get three-dimensional structural and geometric information changes with time. We find that the topological heterogeneity of an irregular droplet is due to the local contact lines and the evaporation dynamics of an irregular droplet is governed by the effective contact radius. This study may offer an opportunity to understand how the topological heterogeneity contributes to the evaporation dynamics of irregular water droplets.

Numerical simulation of particle deposition patterns in evaporating droplets

Nanostructures are used for various chemical, biological, and even volatile organic compound (VOC) sensor applications, in which the inkjet printer provides an easy and convenient fabrication method. In particular, nanoparticles in injected droplets form various self-assembled nanostructures after evaporation such as flat films, rings, and domes, whose patterns are largely influenced by the flow fields within those droplets, temperature, humidity, and substrate wettability. In addition, the temperature at the liquid–gas interface of the droplets governs the local surface tension and evaporation flux, thereby determining the convection fluid flow and particle movement. In this study, we investigate four particle deposition patterns via numerical simulations. First, we reveal the formation of monolayered flat-films on a superhydrophilic substrate in the constant contact angle (CCA) mode during evaporation. Second, we confirm that particles in evaporated droplets usually form coffee-ring patterns on a hydrophilic substrate, which are mainly governed by capillary flows. Interestingly, we find that the coffee rings with low aspect ratios appear to be well-ordered in the constant contact radius mode, while those with high aspect ratios appear to be non-uniformly self-assembled in the CCA mode in an amorphous structure. Third, we prove that the Marangoni flow generated on a hydrophobic substrate accumulates particles at the center of the droplet, forming well-ordered dome-shaped patterns. Furthermore, we experimentally demonstrate four different particle deposition patterns to validate our simulation results and confirm that both sets of results are in reasonable agreement with each other. Hence, we believe that these theoretical model and simulation results can help to develop various nanostructure-based sensor applications by enhancing their performance.

An immersed boundary-lattice Boltzmann model for simulation of deposited particle patterns in an evaporating sessile droplet with dispersed particles

Use of numerical approach by tracking the particle dynamics and contact line motion to study the complex coffee-ring phenomenon can reveal the underlying transport mechanisms. Here we propose a lattice Boltzmann model coupled with the immersed boundary method to simulate the assembly and deposition of particles suspended inside a drying sessile droplet on a hot substrate. The model deals with sufficiently small size of particles with consideration of the surface contact angle hysteresis. Our simulations show that during the droplet evaporation process, the suspended particles are dragged to the contact line by the evaporation-induced flow, thereby forming the coffee-ring pattern. The formation of ring cluster, in turn, promotes the outward flow due to the capillary force. Furthermore, most of the deposited particles are present around the droplet initial contact line, and the particle ring cluster volume increases almost linearly with particle volumetric fraction. Also, when the contact line is more slippery on the surface, a more uniform deposited particle pattern is formed after the droplet gets dried out. If the substrate temperature is sufficiently high enough, the ring location changes from the droplet's edge to its center to form the “coffee eyes” because of the shorter pinning time of the initial contact line and the Marangoni convection flow inside the droplet. In addition, we discuss the evaporation mode transition from the constant contact radius (CCR) to the mixed mode during the droplet evaporation process.

Dewetting of non-polar thin lubricating films underneath polar liquid drops on slippery surfaces

HypothesisThe stability of thin lubricating fluid-coated slippery surfaces depends on the surface energy of the underlying solid surface. High energy solid surfaces coated with thin lubricating oil lead to the dewetting of the oil films upon depositing aqueous drops on them. Hence such surfaces are very suitable to investigate dewetting of thick films (thickness > 500 nm), which otherwise is not possible using a conventional dewetting system. ExperimentsLubricating films of different thicknesses are coated on hydrophilic solid surfaces, and glycerol drops are deposited on them. Fluorescence imaging of lubricating films and macroscopic wetting behavior of glycerol drops are analyzed to understand the dewetting phenomenon. FindingsUnderneath lubricating films undergo initial thinning and subsequently dewet. The dewetting dynamics during hole nucleation and growth and the final pattern of the dewetted oil droplets depend strongly on the thickness of the lubricating films. Ultrathin films dewet spontaneously via homogeneous nucleation, whereas thicker films dewet via heterogeneous nucleation. During dewetting, the apparent contact angle and radius of glycerol drops follow universal scaling behavior.

Concentration Distribution and Stresses in Porous Electrodes with Particle-Particle Contact

During the charge/discharge cycle or fabrication, stresses which arise from diffusion-induced stress (DIS) and particle-particle contact can cause mechanical degradation or failure of Li-ion battery porous electrodes. Here, we develop a new model of porous electrodes in which shape polydispersity and different contact types are considered. The influences of particle-particle contact, contact types, and shape polydispersity on the concentration profile and stresses were numerically investigated. For only spherical-spherical contact, the Li-ion concentration in the contact region of the particles significantly decreased compared with that in the noncontact region, and there is significant radial stress located near the contact area. For purely elliptical-elliptical contact, the best contact type was obtained with the minimum stress and maximum contact radius. For arbitrary contact with shape polydispersity particles, the Li-ion concentration of pole-spherical contact near the contact point is lower, and equator-spherical contacts have a lower contact stress but higher contact radius. Moreover, contact stresses were dominant over DIS for all studied cases. With the formulation and simulation of the particle direct contact process, this study refines our understanding of the electrochemical-mechanical coupling effect in Li-ion batteries porous electrode.

Droplet evaporation characteristics on heated superhydrophobic surface subjected to airflow

In a novel frost suppression method for air source heat pumps, the frost-free operation of the system is realized by vaporizing the condensed droplets on superhydrophobic heat exchanger fins before freezing. Due to the control requirements of this method, a multiphase flow model based on VOF method for droplet evaporation is proposed. The evaporation characteristics and survival time of a sessile water droplet on heated superhydrophobic surface subjected to airflow are investigated through the model. The convection and evaporative cooling effect are considered in the simulation, experiments showed that the prediction error for droplet survival time is within 8%. The effects of boundary layer thickness, substrate temperature, surface wettability, air temperature and humidity on the heat and mass transfer process of droplet evaporation are studied with this model. The survival time of water droplet with diameter below 100 μm evaporating in different evaporation modes is also calculated. The results showed that under the conditions of common parameters in winter, the survival time of a droplet evaporating in fully developed flow is in the range of 4∼20 s. The survival time of droplets evaporating in constant contact radius mode is 15.4% shorter than that evaporating in constant contact angle mode.

Contact mechanics of inflated circular membrane under large deformation: Analytical solutions

Pressurization of thin elastomeric membranes has been exploited as a key actuation mechanism in soft robotics, leading to soft pneumatic actuators that can deform reversibly upon inflation and deflation. The contact mechanics of an inflated membrane with another object underlies several important functionalities of soft pneumatic actuators such as gripping, haptic feedback and locomotion. Motivated by the technological relevance, we study the contact between an inflated circular membrane consisting of incompressible neo-Hookean solid and a substrate that is: i) flat and rigid, ii) spherically curved and rigid, iii) flat and elastic, or iv) spherically curved and elastic. By assuming that the contact interface is adhesionless and frictionless and that the membrane is subjected to very large stretch ratios, we obtained approximate analytical solutions for the membrane’s deformation profile as well as the relationship between the applied force, displacement and contact radius. These solutions agree well with results of numerical simulations. In particular, when the substrate is elastic, we obtained a dimensionless parameter γ that captures the transition between two limiting cases, i.e., either the substrate or the inflated membrane is effectively rigid relative to the other component and thus experiences negligible deformation upon contact. The analytical solutions provided in this work can offer insights towards designing soft pneumatic actuators with desired contact compliance.

Spherical Indentation of a Micropolar Solid: A Numerical Investigation Using the Local Point Interpolation–Boundary Element Method

The load-penetration curve in elastic nanoindentation of an elastic micropolar flat by a diamond spherical punch is analyzed. The presented results are obtained by a specifically developed numerical tool based on a judicious combination of the conventional boundary element method and strong form local point interpolation method. The results show that the usual linear relationship between the material depression and the square of the radius of the contact area is also valid in this case of micropolar elastic material. It is also shown that the relation between the indentation stress (applied load over the contact surface) and the indentation strain (ratio of contact radius by the punch radius) is linear. The proportionality coefficient which is none other than the indentation stiffness varies with the coupling factor of the micropolar elastic medium. A relation between the indentation stiffness of a micropolar solid and that of a conventional solid with the same Young modulus and Poisson ratio is derived.

Electrical and mechanical properties of Au–Si bonds for 3D interconnect applications

Driven by high-density and high-reliability demands on three-dimensional (3D) interconnections, electrical and mechanical properties of interconnection structures have been paid more attention. Aiming at the novel enable-3D interconnections realized by Au–Si wafer bonding, this study demonstrates the design, fabrication and test results of testing structures for dimension-define parameters of Au–Si bonds. In order to measure closely-realistic ohmic contact resistances of Au–Si bonds after wafer bonding processes implemented under certain bonding pressures and temperatures, the convex Si structures formed by the local oxidation of silicon process have been designed. Therefrom the specific contact resistance values of Au–Si bonds have been measured as 3.9–8.1 × 10−10Ω m2 for different contact radii (3–20 μm), which indicates the low-resistance potentiality for Au–Si bonds applied on 3D interconnections. On the other hand, two findings on bonding strengths are summarized from finite element simulations and tensile experiments: (a) Au–Si bonding strengths of circular bonding patterns (35–75 MPa) are superior to the ones of square bonding patterns (18–30 MPa) due to the stress concentration phenomenon on four corners of square bonding patterns; (b) there is an inverse relationship between bonding strengths and bonding areas owing to uneven stress distributions in bonding structures. Overall, this study provides a basic optimization design strategy at electrical and mechanical levels for 3D interconnections actualized by Au–Si bonding. Incidentally, these introduced analysis methods are also feasible for homologous Si-based eutectic bonding techniques to extend the forms of 3D interconnections.

On the mechanics of inflated hyperelastic membrane–membrane contact problem

The membrane–membrane contact mechanics plays an important role in several biological processes, such as drug delivery, cell infection, cell destruction, etc. at microscales. The problem at macroscales is relevant to air inflated and air supported structures. In this work, we have chosen a simple system in which contact mechanics of two inflated membranes (initially flat circular membranes parallelly placed, fixed circumferentially and pressurized in opposite direction to make contact) has been studied. Friction and effects of adhesion are neglected for simplicity. We have considered the Mooney–Rivlin hyperelastic membrane material. The governing equations are derived using the principle of minimum potential energy. The problem has been solved separately for contacting and non-contacting region and joined by appropriate junction and boundary conditions. Indentation on the low-pressure membrane by the high-pressure membrane for different loading and rigidity constants has been studied. We observe a critical radius of contact of the low-pressure membrane, which depends upon the characteristics of high-pressure membrane, beyond which the stretch and stress values start to rise with indentation. At this critical radius, maximum meridional curvature discontinuity jump exists. Variation of contact force, along with principal stretches and stresses, are also discussed.

Dynamic mechanical contact behaviors and sintering mechanism of Al nanoparticles subjected to high-speed impact

In this work, dynamic mechanical contact behaviors and sintering mechanism of Al nanoparticles subjected to high-speed impact have been investigated using molecular dynamic simulations by analyzing radial distribution function (RDF), atomic average displacement, mean square displacement (MSD), the sintering neck radius, shrinkage, nanoparticle temperature and the proportion of amorphous atoms. The results shows that the long-ranged ordered structure of Al nanoparticles gradually transforms into short-range ordered structure and finally amorphous structure during the head-on impact. The atomic average displacement, MSD, radius ratio (x/R) and shrinkage at different initial impact speeds first experience a rapid increase to a maximum, followed by a slow decrease and subsequent a recovery to an almost constant. The displacement of surface atoms is always larger than the internal atoms during the head-on impact. There exists one critical impact velocity (e.g., 2800 m/s for given 4 nm in diameter) beyond which the ordered aluminum atoms completely transform into amorphous structure. The contact force, contact radius and contact stress obtained under a given low impact velocity and small strain are quite consistent with the predictions of the continuous Hertz model, but as the impact velocity and normal displacement further increase, the predictions of Hertz model underestimate these contact parameters. The influence of nanoparticle size on the relationship of contact radius and number of contacting atoms is inappreciable. The nanoparticles undergo elastic deformation, and then plastic deformation, followed by mechanical failure and shock-induced melting process into a whole. This work could strengthen our understanding of the industrial processes with applications in energetic nanomaterials, rocket propellant, metal sintering, etc.

Partial slip contact problem between a transversely isotropic half-space of multi-ferroic composite medium and a spherical indenter

This article concerns partial slip contact problem of a composite medium half-space punched by a spherical indenter. The indenter is subjected to the normal indentation force, electric and magnetic loads, and then exerted by a progressively increasing tangential load. The tangential load, which is not sufficient to cause complete sliding, results in the contact region split into the slip region and the stick region. Coulomb friction law is adopted in the slip region and four possible physical cases are considered in view of the magneto-electric properties of indenter. Three-dimensional (3D) magneto-electro-elastic coupling fields associated with four cases are obtained in terms of the elementary functions by use of the potential theory and ignoring effect of the tangential load on the generalized normal stresses in the contact region. The contact radius and the stick radius are determined by the equilibrium equations. The stress intensity factors are introduced to characterize the stress singularity. The obtained solutions are verified by comparing with results related to the frictionless contact problem and the fundamental solutions. Influence of the frictional coefficient and the magneto-electric properties of indenter on the physical quantities are analyzed. It is worth noting that the frictional coefficients have obvious effect on the von Mises stress and the maximum shear stress. The suitable electric and magnetic loads may eliminate the stress concentration. These results not only are the theoretical fundamental to the forthcoming indentation experiments and the fretting contact, but also serve as guiding design of the smart devices.

Effects of micro-pin-fins on the bubble growth and movement of nucleate pool boiling on vertical surfaces

Observing bubble behaviors on the heating surface during the boiling process is a convenient and effective method to study the boiling mechanism. In recent decades, many researchers have studied the bubble growth and departure processes on the boiling surface and proposed numerous theoretical models and empirical correlations. With the increasing demand on heat dissipation of the high-power equipment, various modified surfaces with great heat transfer performance have emerged. However, it is difficult to explain bubble behaviors on the surfaces with different structures by traditional bubble dynamics on smooth surfaces. In this paper, the pool boiling experiments on vertical surfaces under subcooled and near-saturated conditions were carried out. With the help of a high-speed camera with high temporal and spatial resolution, bubble behaviors on micro-pin-finned surfaces were observed. Different bubble growth modes on different surfaces were obtained and the influence of the micro-pin-fins on the bubble growth and departure processes was learned. The effects of heat transfer from the thermal boundary layer and the micro-pin-fins on the bubble growth rate were considered. The influence of the surface tension, inertia and reaction forces on the bubble movement was analyzed. Based on these two aspects, a bubble growth-movement model was established. The pin effect on the contact radius, the inertia induced by the variation of bubble growth rate and reaction force induced by the local differential pressure are the main mechanisms of the micro-pin-fins to promote the bubble departure.

Molecular dynamics of rolling and twisting motion of amorphous nanoparticles

Granular mechanics codes use macroscopic laws to describe the damping of rolling and twisting motion in granular ensembles. We employ molecular dynamics simulation of amorphous Lennard–Jones grains to explore the applicability of these laws for nm-sized particles. We find the adhesive force to be linear in the intergrain attraction, as in the macroscopic theory. However, the damping torque of rolling motion is strongly superlinear in the intergrain attraction. This is caused by the strong increase of the ‘lever arm’ responsible for the damping torque—characterizing the asymmetry of the adhesive neck during rolling motion—with the surface energy of the grains. Also the damping torque of twisting motion follows the macroscopic theory based on sliding friction, which predicts the torque to increase whit the cube of the contact radius; here the dynamic increase of the contact radius with angular velocity is taken into account.

The Influence of Mechanical Deformations on Surface Force Measurements

Surface Force Balance (SFB) experiments have been performed in a dry atmosphere and across an ionic liquid, combining the analysis of surface interactions and deformations, and illustrate that the mechanical deformations of the surfaces have important consequences for the force measurements. First, we find that the variation of the contact radius with the force across the ionic liquid is well described only by the Derjaguin–Muller–Toporov (DMT) model, in contrast with the usual consideration that SFB experiments are always in the Johnson–Kendall–Roberts (JKR) regime. Secondly, we observe that mica does not only bend but can also experience a compression, of order 1nm with 7μm mica. We present a modified procedure to calibrate the mica thickness in a dry atmosphere, and we show that the structural forces measured across the ionic liquid cannot be described by the usual exponentially decaying harmonic oscillation, but should be considered as a convolution of the surface forces across the liquid and the mechanical response of the confining solids. The measured structural force profile is fitted with a heuristic formulation supposing that mica compression is dominant over liquid compression, and a scaling criterion is proposed to distinguish situations where the solid deformation is negligible or dominant.

Lattice Boltzmann Modeling of Drying of Porous Media Considering Contact Angle Hysteresis

Drying of porous media is governed by a combination of evaporation and movement of the liquid phase within the porous structure. Contact angle hysteresis induced by surface roughness is shown to influence multi-phase flows, such as contact line motion of droplet, phase distribution during drainage and coffee ring formed after droplet drying in constant contact radius mode. However, the influence of contact angle hysteresis on liquid drying in porous media is still an unanswered question. Lattice Boltzmann model (LBM) is an advanced numerical approach increasingly used to study phase change problems including drying. In this paper, based on a geometric formulation scheme to prescribe contact angle, we implement a contact angle hysteresis model within the framework of a two-phase pseudopotential LBM. The capability and accuracy of prescribing and automatically measuring contact angles over a large range are tested and validated by simulating droplets sitting on flat and curved surfaces. Afterward, the proposed contact angle hysteresis model is validated by modeling droplet drying on flat and curved surfaces. Then, drying of two connected capillary tubes is studied, considering the influence of different contact angle hysteresis ranges on drying dynamics. Finally, the model is applied to study drying of a dual-porosity porous medium, where phase distribution and drying rate are compared with and without contact angle hysteresis. The proposed model is shown to be capable of dealing with different contact angle hysteresis ranges accurately and of capturing the physical mechanisms during drying in different porous media including flat and curved geometries.

Evaporation of a sessile droplet on flat surfaces: An axisymmetric lattice Boltzmann model with consideration of contact angle hysteresis

Droplet evaporation is a widely encountered heat and mass transfer phenomenon. Due to its 3D in nature, it is challenging to simulate the complex 3D droplet evaporation process. Here, we propose an axisymmetric lattice Boltzmann (LB) model to simulate the dynamics of contact line motion during sessile droplet evaporation on a flat heated surface, taking contact angle hysteresis into consideration. We demonstrate that this LB model can numerically simulate the evaporation processes of sessile droplet evaporation processes undergoing constant contact angle (CCA), constant contact radius (CCR), and mixed modes sequentially. The classical D2-law for droplet surface mass transfer is confirmed numerically by using the case of a floating droplet evaporation, thereby proving that the axisymmetric LB model is capable of 3D simulation. Our simulated results on temporal variations of contact radius, contact angle are found in good agreement with two different sets of literature experimental data. Specifically, we compute the local mass transfer rate on the droplet surface from the simulated velocity field to show that the evaporation rate near the triple-phase contact region is much higher than that at the droplet apex region, with the peak heat flux occurring near the location of the dynamic contact line. The contact angle fluctuates with stick-slip motion are found during the CCA stage of the evaporation process at higher substrate temperatures. Additionally, we analyse the non-quasi-equilibrium evaporation mode and contact line slip velocity on substrates surface at higher temperatures.