Contact Radius Research Articles

Optomechanical measurement of single nanodroplet evaporation with millisecond time-resolution

Tracking the evolution of an individual nanodroplet of liquid in real-time remains an outstanding challenge. Here a miniature optomechanical resonator detects a single nanodroplet landing on a surface and measures its subsequent evaporation down to a volume of twenty attoliters. The ultra-high mechanical frequency and sensitivity of the device enable a time resolution below the millisecond, sufficient to resolve the fast evaporation dynamics under ambient conditions. Using the device dual optical and mechanical capability, we determine the evaporation in the first ten milliseconds to occur at constant contact radius with a dynamics ruled by the mere Kelvin effect, producing evaporation despite a saturated surrounding gas. Over the following hundred of milliseconds, the droplet further shrinks while being accompanied by the spreading of an underlying puddle. In the final steady-state after evaporation, an extended thin liquid film is stabilized on the surface. Our optomechanical technique opens the unique possibility of monitoring all these stages in real-time.

Axisymmetric contact of two different power-law graded elastic bodies and an integral equation with two Weber–Schafheitlin kernels

Summary This article analyzes the axisymmetric contact problem of two elastic inhomogeneous bodies whose Young moduli are power functions of depth and the exponents are not necessarily the same. It is shown that the model problem is equivalent to an integral equation with respect to the pressure distribution whose kernel is a linear combination of two Weber–Schafheitlin integrals. The pressure is expanded in terms of the Jacobi polynomials, and the expansion coefficients are recovered by solving an infinite system of linear algebraic equations of the second kind. The coefficients of the system are represented through Mellin convolution integrals and computed explicitly. The Hertzian and Johnson–Kendall–Robertson adhesive models are employed to determine the contact radius, the displacement of distant points of the contacting bodies, the pressure distribution and the elastic normal displacement of surface points outside the contact circular zone. The effects of the exponents of the Young moduli and the surface energy density on the pressure distribution and the displacements are numerically analyzed.

Determination of the rate-dependent adhesion of polydimethylsiloxane using an atomic force microscope

A JKR (Johnson-Kendall-Roberts) formalism is used to extract the Young modulus, the contact radius, and the energy release rate simply from the retraction curve of a borosilicate glass colloidal probe from a polydimethylsiloxane (PDMS) surface using an atomic force microscope. PDMS samples ranged from perfectly elastic to those with incipient viscoelasticity. The dependence of the release rate energy with the crack speed is verified using a fracture mechanics-based method.

Indentation of pre-deformed compressible soft electroactive layer on substrate

Layer-substrate system penetrated by a rigid indenter has been frequently used as the physical model for interpreting the indentation test of advanced materials. In this paper, the indentation of a pre-deformed compressible soft electroactive (SEA) layer on an elastic substrate is formulated as a Fredholm integral equation of the second kind, which is solved by a customized finite-difference scheme to fulfil the full-field analysis. Especially, the modified JKR model established in the half-space case is invoked to take account of surface adhesion for the peculiar layer-substrate system. As an example, the neo-Hookean ideal dielectric elastomer is considered, and the effects of adhesion (due to surface energy) and substrate (due to different mechanical and electrical properties from the layer) on the indentation responses are scrutinized. Numerical results indicate that, when a soft layer overlies a stiffer substrate, the contact radius should be smaller than the layer thickness for the validity of linear analysis. In this case, as the contact radius exceeds about 1/10 of the layer thickness, the indentation responses are found to vary significantly with the shear modulus ratio between the layer and the substrate while they are insensitive to the variation of Poisson's ratio of the substrate within the linear regime. Moreover, an interesting phenomenon is revealed that the indentation responses (e.g., the surface normal stress) induced by adhesion will be suppressed by stiffening of the substrate, and vice versa.

Rate-dependent adhesion in dynamic contact of spherical-tip fibrillar structures

Fibrillar adhesives that rely on the Van der Waals interactions exhibit fascinating prospects in dynamic attachment applications like perching of aerial robots and capture of orbital debris. Understanding the dynamic attachment/detachment behaviors of fibrillar adhesive structures plays a crucial role in realizing reliable attachment to target surfaces. In this paper, we investigate the dynamic contact of a single spherical-tip fibrillar structure model and emphasize the significance of rate-dependent adhesion. A theoretical model considering both crack-tip and bulk viscoelasticity is presented. The proposed model is verified by comparing with elaborate collision tests under different dynamic contact conditions. The dynamic evolution of contact radius, displacement and force are investigated in detail. The energy dissipation mechanism is discussed by analyzing the variation of coefficient of restitution vs. initial contact velocity. Under the combined effect of rate-dependent adhesion and inertia force, the radius-displacement curve in sticking mode appears peculiar superposition loops, and a new critical sticking mode is found which can broaden the initial velocity range that ensures successful attachment. It is demonstrated that rate-dependent adhesion and bulk dissipation are coupled closely while the former is dominant near the critical sticking velocity. Moreover, the decrease of the reference speed, pillar size, and modulus of materials are favorable for increasing the critical sticking velocity, thereby enhancing the capacity to resist dynamic detachment. This work provides an underlying theoretical support on the dynamic contact of fibrillar adhesives and offers a clear insight on the role of the rate-dependent adhesion during the process.

Wetting of aqueous sodium dodecyl sulfate droplets on polydimethylsiloxane surfaces during evaporation

Wetting of aqueous sodium dodecyl sulfate (SDS) droplets on polydimethylsiloxane (PDMS) surfaces during evaporation were experimentally studied. After a short-time spontaneous spreading, sessile droplets experienced a period of the constant contact radius (CCR) stage. And it was found that substrate elasticity was found to have an influence on the duration of the CCR stage during the evaporation of aqueous SDS droplets on PDMS surfaces. Moreover, a local contact angle minimum was found during the evaporation of aqueous SDS droplets with an initial SDS concentration below 0.5 CMC. A physical mechanism taking into account the structure of SDS molecules adsorbed at PDMS surfaces was developed for the occurrence of the CCR stage and the local contact angle minimum. Furthermore, two-third power of the instantaneous droplet volume nearly varies linearly with time for all cases.

Modeling Contact Behavior of Multiparticles and Particle–Current Collector Contact in Porous Electrode

There are various component contacts in porous electrodes, such as the direct contact between the active particles and the particle–current collector, during electrode manufacturing and lithium‐ion battery electrochemical cycles. Herein, an electrochemical–mechanical representative volume element model is developed to study the contact behavior of porous electrodes. For the direct contact behavior of multiple particles, stronger battery constraints and larger size differences enhance the reduction in Li‐ion concentration in the contact area of the active particles in the porous electrode and the contact stress in the porous electrode particles. For the contact between the active particles and current collector, the decrease in the elastic modulus of the current collector slightly increases the contact radius and significantly reduces the contact stress. By comparing the contact area and contact stress of the smooth and rough current collectors, the latter has a smaller contact area and larger contact stress when in contact with active particles. These findings provide insights into designing Li‐ion batteries from the perspective of contact stress to minimize the mechanical failure of porous electrodes.

Mathematical Modeling and Experimental Validation of Surface Roughness in Ball Burnishing Process

Burnishing is a cold working technique used as a surface enrichment to meet the desired surface properties of the workpiece. It improves the visual properties, dimensional tolerances, fatigue strength, surface roughness, and hardness of the work material by applying appropriate pressure through a complex ball burnishing tool to cause plastic deformation. In the current work, the mathematical modeling of the burnishing process was carried out to predict surface roughness by considering the process parameters such as contact radius, penetration depth, and elastic rebound. Further, a customized tungsten carbide (W.C.) insert having a hardness of 80 HRC was developed for the burnishing operation. The micro-hardness of the resulting burnished surface improved from 44 to 48 HRC. The surface quality of the tungsten carbide insert improved by up to 17.1 nm through polishing. Several experiments were performed by selecting appropriate process parameters using developed model feedback. The surface quality of the workpiece improved by up to 45 nm, which resulted in automatic improvements in fatigue strength up to seven times that of the virgin material. The results predicted from the mathematical model were in good agreement (less than 5% deviation) with the experimental results. This study helps to understand the surface formation mechanism in the burnishing process in more detail. Additionally, the achieved results show a significant improvement in the surface finish (~95%), indicating the potential of the burnishing process and how fast and cost-effective it is. The novelty of this paper lies in the improvement in surface roughness and the validation of our mathematical model results with the experimental results.

Mechanics of shape-locking-governed R2G adhesion with shape memory polymers

Shape memory polymers (SMPs), with unique properties such as tunable elastic modulus, temporary shape locking and shape recovery upon external stimulation, are emerging as a new class of smart materials with switchable adhesion capabilities. A prominent feature of the adhesion between SMP and a spherical indenter is the so-called R2G adhesion, defined as making contact in the rubbery state to a certain indentation depth followed by detachment in the glassy state. While it has been demonstrated that the R2G adhesion with SMPs can achieve orders of magnitude higher adhesive strength compared to conventional elastic adhesive systems with similar geometrical and adhesion parameters, the fundamental mechanics of R2G adhesion and why it leads to such tremendous adhesion enhancement remain largely mysterious at this point. Here, combined experimental testing, theoretical analysis, and finite element analysis (FEA) based on a thermomechanical constitutive model of SMP are performed to investigate the mechanics of R2G adhesion with a rigid spherical indenter. It is shown that the orders of magnitude enhancement of R2G adhesion over conventional elastic adhesion systems is mostly governed by the shape locking effect during the transition from the rubbery to glassy states. The shape locking effect freezes the deformed configuration of the SMP substrate, resulting in nearly conformal contact between the spherical indenter and the glassy-state SMP substrate, thus greatly increases the effective radius of curvature of the contact surface. Our experimental measurements and FEA simulations demonstrate that the net effect of shape locking leads to a pull-off force of a sphere nearly the same as that of a flat punch on an elastic half-space with the same contact radius. An explicit expression of the pull-off force for R2G adhesion is proposed based on flat-punch adhesion. Our results from combined experimentation, modeling and simulations reveal the fundamental mechanics of R2G adhesion. Such understanding provides guidance for the design of SMP smart adhesives.

Interactive Evaporation of Neighboring Pendant and Sessile Droplet Pair

Abstract In this article, we experimentally probe the vapor-mediated interaction behavior of evaporating sessile and pendant droplets in an interacting droplet (ID) system. For this purpose, a pendant droplet was introduced in the vapor diffusion domain of a sessile droplet and both were allowed to evaporate simultaneously. The evaporation dynamics were monitored using optical imaging techniques for varied separation (both horizontal and vertical) distances between them. Our observations reveal curtailed mass transfer rate from both the droplets although the evolution of droplet morphology (such as pendant droplet radius, contact radius, and contact angle of sessile droplet) at different stages of evaporation remain similar. The evaporative fluxes from these two droplets interact with one another and thereby reduce the diffusive mobility of vapor molecules in the liquid–vapor interface of both. This condition suppresses the diffusion mechanism and thereby impedes the evaporation rate. We show that the evaporation behavior for two droplets in an interacting droplet system is solely dictated by an effective external vapor concentration depending on the problem geometry. Therefore, to characterize the vapor diffusion domain we hypothesize a vapor front enfolding both the droplets and put forward a theoretical model by applying conservation of mass across it. We also propose a relationship to show the variation of the effective external vapor concentration with the relative separation distance between the droplets. The predictions from theoretical models are found to be in good agreement with our detailed experimental observations.

Effect of osmolarity and displacement rate on cartilage microfracture clusters failure into two regimes

Articular cartilage is a poroviscoelastic (PVE) material with remarkable resistance to fracture and fatigue failure. Cartilage failure mechanisms and material properties that govern failure are incompletely understood. Because cartilage is partially comprised of negatively charged glycosaminoglycans, altering solvent osmolarity can influence PVE relaxations. Therefore, this study aims to use osmolarity as a tool to provide additional data to interpret the role of PVE relaxations and identify cartilage failure regimes. Cartilage fracture was induced using a 100 μm radius spheroconical indenter at controlled displacement rates under three different osmolarity solvents. Secondarily, contact pressure (CP) and strain energy density (SED) were estimated to cluster data into two failure regimes with an expectation maximization algorithm. Critical displacement, critical load, critical time, and critical work to fracture increased with increasing osmolarity at a slow displacement rate whereas no significant effect was observed at a fast displacement rate. Clustering provided two distinct failure regimes, with regime (I) at lower normalized thickness (contact radius divided by sample thickness), and regime (II) at higher normalized thickness. Varied CP and SED in regime (I) suggest that failure in the regime is strain-governed. Constant CP and SED in regime (II) suggests that failure in the regime is dominantly governed by stress. These regimes can be interpreted as ductile versus brittle, or using a pressurized fragmentation interpretation. These findings demonstrated fundamental failure properties and postulate failure regimes for articular cartilage.

Multi-physics electrical contact analysis considering the electrical resistance and Joule heating

A multi-physics electrical contact model is developed to predict the contact pressure, temperature, and electric current density (ECD) distributions on the contact surface. The theoretical model takes the interfacial electrical resistance and its resultant Joule heating into account. The contact pressure and contact radius are calculated by solving the first kind of Cauchy singular integral equation. The temperature and ECD are obtained based on the obtained contact pressure. Then, a three-dimensional finite element model is established to simulate the mechanical, thermal, and electrical behaviors of electrical contact. The finite element model can consider both the interfacial electrical resistance and the constriction electrical resistance. The theoretical results of the electrical contact behaviors are compared with the numerical results. The influences of the electrical resistance, normal force, electric potential, and distribution form of the heat flux on the contact pressure, temperature, and ECD distributions are investigated. The results indicate that the proposed multi-physics contact model can provide an accurate prediction of electrical contact behaviors.

Impact contact behaviors of elastic coated medium with imperfect interfaces

Imperfect interface of coating-substrate system, where displacement and stress are transmitted discontinuously, affects mechanical response of coated medium subjected to impact loading a lot. This paper proposes an impact contact model between an elastic moving ball and imperfectly bonded semi-infinite coating-substrate system with combined dislocation-like and force-like interfaces. Impact contact process obeys the second-order Newmark theory and contact theory for coated medium. Impact velocity, acceleration and reaction force of the ball are cost-effectively determined by a step by step iterative strategy, binary search method and conjugate gradient method (CGM). Analytical explicit expressions of displacement and stress fields of imperfectly bonded coating-substrate system are derived with the assistance of the Papkovich–Neuber potentials, which are further transformed to frequency domain aiming at improving calculating efficiency through employing a fast Fourier transform (FFT) algorithm. Six jumping coefficients for interfacial displacement and stress are introduced to describe different interface conditions, and their effects on impact reaction force, contact radius, contact pressure and subsurface stress of imperfectly bonded coating-substrate system under different impact velocities are studied.

A Refined Closed-Form Solution for Laterally Loaded Circular Membranes in Frictionless Contact with Rigid Flat Plates: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation

Essential to the design and development of circular contact mode capacitive pressure sensors is the ability to accurately predict the contact radius, maximum stress, and shape of a laterally loaded circular membrane in frictionless contact with a concentric circular rigid flat plate. In this paper, this plate/membrane contact problem is solved analytically again by simultaneously improving both out-of-plane equilibrium equation and geometric equation, and a new and more refined closed-form solution is given to meet the need of accurate prediction. The new closed-form solution is numerically discussed in convergence and effectiveness and compared with the previous one, showing that it can greatly improve the prediction accuracy of the contact radius, maximum stress, and shape of the circular membrane in frictionless contact with the rigid flat plate.

The Dynamic Evaporation Characteristics of Thiophanate-Methyl Droplets and Their Enhancement under Different Wind Conditions

The dynamic evaporation of single droplets was investigated under controlled conditions. In the evaporation process, a droplet was placed on a peach leaf surface. In this research, the relative humidity and temperature were kept constant, and the wind speeds and thiophanate-methyl concentrations varied. Based on these conditions, this study aimed to determine the droplets’ dynamic transforming characteristics, including the contact angle, the height of the droplets, and the evaporation rate. Five concentrations and five wind speeds were chosen, and pure water droplets at different wind speeds were used as a control group. All single droplets were generated by a syringe. The results showed that the pure water and thiophanate-methyl droplets’ evaporation mode was CCR (constant contact radius) mode. An increase in the wind speed accelerated the evaporation process, when the wind speed was 0 m/s, the evaporation was the longest, and the shortest evaporation was achieved with 2.0 m/s wind speed. An increase in wind speed enhanced the pure water droplets’ dynamic evaporation process with a maximum enhancement ratio of 3.44 times in the present work. Under the same conditions, the thiophanate-methyl droplets’ evaporation time was shorter than that of the pure water droplets. For thiophanate-methyl droplets, the higher the concentration, the shorter the dynamic evaporation process. A 1250 ppm thiophanate-methyl solution with 2.0 m/s wind speed, had an evaporation ratio that was 2.83 times greater than that measured with 0 m/s wind speed. These results could benefit farmers by suggesting that they should adjust the concentration of thiophanate-methyl depending on the wind speed in order to reduce pollution.

Nano-sized single-asperity friction behavior: Insight from molecular dynamics simulations

Friction phenomenon plays an essential role in contact pairs, from macroscale to nanoscale friction. Nano-sized friction behavior is different from macroscopic friction behavior due to discreteness of atoms. Taking α-Fe as paradigm material, single-asperity friction molecular dynamics (MD) simulations are conducted. The MD results show that the multi-slip phenomenon exists during the tangential loading process of nano-sized single asperity. Meanwhile, the macroscopic friction coefficient model is not suitable for nano-sized friction, while the macroscopic Kogut-Etsion (KE) contact radius model can approximately describe nano-sized contact radius. Besides, the Mindlin model can hardly describe the initial tangential stiffness under large normal loadings due to the neglect of plastic deformation. Therefore, it is suggested to modify the macroscopic friction models by considering the plastic deformation mechanism and asperity size effect to improve the full-scale description ability.

Air entrapment of a neutral drop impacting onto a flat solid surface in electric fields

When a charge neutral drop impacts on a flat solid substrate, a small air bubble is always trapped underneath due to the lubrication pressure coming from the viscous stress in the squeezed air film. Herein we find experimentally and numerically that the process of the air entrapment and the initial contact state of the drop with the substrate can be profoundly altered via an external electric field. In an electric field, the induced electric stresses at the bottom of the drop increase drastically right before the drop contacts the substrate, which acts against the lubrication pressure, resulting in reduced initial contact radius and air bubble size. When the external electric field reaches a critical value, the electrical stress accelerates the flow near the bottom of the drop and generates a conical tip quickly instead of a dimple, resulting in a centre contact and eliminating the air bubble entrapment. Based on the dipole mirror charge model, we find the dimensionless strength of critical electric field scales with the square root of capillary number based on the air viscosity. This scaling law of the critical electric field for eliminating the air bubble entrapment is verified experimentally and numerically. This work may offer a new way to mitigate defects caused by air bubble entrapment for inkjet printing and droplet-based additive manufacturing.

Effect of modeling parameters on the mechanical response of macroscopic crushing of agglomerate

The discrete element method is widely used in agricultural engineering and is especially for analyzing the crushing of agricultural materials. However, research on agglomerate mode parameters is relatively limited. Therefore, it is necessary to investigate the impact of agglomeration model parameters on the macroscopic mechanical reaction of crushing. In this paper, agglomerate models of corn kernels were built based on the Bonded Particle Model, and the crushing behavior of the agglomerate was simulated by the compression test. The results show that the particle filling method, particle size, and particle bonding contact radius all have a significant impact on the network force chain structure within the agglomerate, which affects the mechanical properties of the agglomerate. There is a DoseResp function relationship between the average coordination number of particles and the crushing resistance of agglomerates. The research results can provide some theory references for constructing the agglomerate model. • Models of corn kernel agglomerates with different modeling methods based on BPM. • The effect of model parameters on agglomerate mechanical properties. • The effect of fill rate and bonded radius on the average coordination number. • Effect of average coordination number on the crushing resistance of agglomerates. • A relationship between the average coordination number and the bond's intact rate.

Modeling the microscale contact status in chemical mechanical polishing process

The micro-scale contact status between pad and workpiece surface plays one of the most significant roles in determining the material removal rate (MRR) during the chemical mechanical polishing (CMP) process. To evaluate the contribution of random contact status to the material removal process, the paper proposed a novel concept of “effective contact spots”. It represents the probability of randomly distributed pad asperities sliding across a given coordinate point on the workpiece surface. Furthermore, mechanical removal capacity parameter γ and chemical reaction capacity parameter β were defined to mathematically model the material removal process from a micro-scale chemical-mechanical synergistic perspective. To validate the model, a series of CMP tests (with in-situ conditioning) were conducted on three types of materials (BK7 glass, fused silica, and Si). The real contact status was also measured and analyzed statistically after being conditioned with two types of conditioners. Experimental observations and theoretical analysis results indicated that the chemical-mechanical synergism was the fundamental mechanism for the contribution of the micro-scale contact status to the material removal process. Resulting in the fact that the real contact ratio, radius, and spacing of the real contact spots play different dominant roles on MRR for different materials. Moreover, solution strategies in this study can provide the knowledge needed for improving the material removal stability, and further enable predictive control on the polishing or conditioning recipe before a non-ideal contact status result in an unexpected material removal rate.

Elucidating the Multi‐Scale Temperature Evolution and Densification Mechanisms of Amorphous Powders During Spark Plasma Sintering: Experiments and Modeling

This work investigates amorphous powders’ temperature distribution and densification mechanism at macroscopic and particle scales during spark plasma sintering. The evolution of contact necks between powders is studied by quasi‐in situ microstructure examination. Amorphous powders’ contact mode changes from point contact to surface contact as sintering proceeds. The high current density concentration leads to local overheating at the particle necks. As the contact radius ratio increases, the temperature gap between the necks and the interior of the particles becomes less noticeable. In the early stage, localized high temperature and high stress around the necks significantly reduce the densification onset temperature of amorphous powders. As the relative density increases, the uneven temperature field at the particle scale disappears, while the macroscopic temperature gradient increases. The dominant densification mechanism of amorphous powders has transitioned from particle‐scale to macroscopic temperature. The sample temperature is significantly higher than the nominal sintering temperature, promoting the contribution of viscous flow to porosity elimination. This work can provide new insights into the evolution of multi‐scale temperature distribution during spark plasma sintering and its impact on the densification behavior of amorphous powders.