Contact Radius Research Articles

Drying behaviour of nanofluid sessile droplets on self-affine vis-à-vis corrugated nanorough surfaces.

In recent years, evaporative self-assembly of sessile droplets has gained considerable attention owing to its wide applicability in many areas. While the phenomenon is well studied for smooth and isotropically rough (self-affine) surfaces, investigations comparing the outcomes on self-affine vis-à-vis corrugated surfaces remains to be done. In this experimental work, we compare the wetting and evaporation dynamics of nano-colloidal microlitre droplets on self-affine and corrugated nanorough surfaces having identical roughnesses and interface properties. The coupled influence of particle size, concentration, and surface structuring has been explored. Differences in wettability and evaporation dynamics are observed, which are explained via the interaction between wetting fluid and anisotropic surface roughness. Our findings exhibit different temporal behaviour of contact radius and angle in the evaporation process of the droplets. Further, the corrugated surface exhibits anisotropic wettability with a monotonic change in droplet shape as evaporation proceeds, finally giving rise to irregular dried patterns. The scaled rim width and crack spacing of the particulate deposits are examined. Our results can inspire fabrication of surfaces that can facilitate direction-dependent droplet motion for specific applications.

Edge effect and indentation depth-dependent contact behavior in contact of an elastic quarter-space

The edge effect in contact of an elastic quarter-space is numerically studied in this work. The extension of Hetényi’s approach of overlapping two elastic half-spaces is implemented in the boundary element method to obtain the solution of an elastic quarter-space whose top and side surfaces could be both loaded. In the study on the indentation test of a rigid sphere on an elastic quarter-space, the dependencies of the normal force, mean contact radius, and pressure distribution in contact area as well as the internal von Mises stress in relation to the position of the sphere from the side edge are obtained numerically and expressed by fitting the numerical results. These equations can be also used to interpret the indentation depth-dependent contact behavior: from Hertzian contact at the beginning of the indentation to the non-circular contact at large indentation depth.In addition, the results are compared with a contact case of a quarter-space in which the side surface of the quarter-space is not completely free: shear stresses on the side surface vanish but normal stress exists. The latter case generates very similar results, especially the contact area, but its solutions are much easier to achieve by applying a symmetrical loading on an elastic half-space, offering an effective way to approximate the solution of a quarter-space.

Radius of Contact During Friction Surfacing of Stainless Steel 304L: Effect of Spindle Speed and Rod Diameter

Abstract The “radius of contact” or the “real-rotational contact plane,” has been increasingly mentioned terminology in friction surfacing. However, the fundamental understanding of the flow dynamics behind this phenomenon is still very limited. The goal of this study was to understand the influence of spindle speed and consumable rod diameter on the flow dynamics and the radius of contact during friction surfacing of 304L stainless steel over a substrate of the same material. Friction surfacing was performed using consumable rods with diameters of 4.76 mm, 9.52 mm, and 12.7 mm while using spindle speeds from 1500 rpm to 20,000 rpm. The impact of spindle speed on deposition morphology, including the radius of contact, was studied. The radius of contact was calculated empirically and was found to be inversely proportional to the tangential velocity of the rod. The coupling between flow stresses and localized forces is hypothesized to be the key factor behind the variation of the radius of contact with processing conditions.

Transients of Marangoni and Stefan advection dynamics during generic sessile droplet evaporation

We probe the transient evolution of Marangoni thermo-hydrodynamics in the liquid domain and the Stefan advection in the gaseous domain during evaporation of sessile droplets with generic contact line dynamics [both constant contact radius (CCR) and constant contact angle (CCA) modes]. A transient arbitrary Lagrangian–Eulerian framework was considered to computationally model the evaporation phenomenon over the droplet lifetime. The governing equations corresponding to the transport processes in both liquid and gaseous domains are simulated in a fully coupled manner, while precisely tracing the liquid–vapor interface and three phase contact line. The effects of the wetting state and contact line dynamics during CCR and CCA modes were explored, and good agreement with experimental observations is noted. The results show that the non-uniformity in an internal temperature field due to evaporation leads to formation of multi-vortex Marangoni patterns in the flow field at initial periods. At the quasi-stable state, the temperature variation becomes monotonic, thereby resulting in a single recirculation vortex in both liquid and gaseous domains. For the CCR mode, the strength of these advection fields is solely governed by a critical contact angle of ∼32°, which is determined to correspond to the critical Marangoni number. Beyond this critical point, viscous action becomes significant, and the fluid motion mitigates progressively with the formation of twin vortices at final stages due to localized heat advection near the contact line. For the CCA mode, the strength of initial vortices augments with progressing time due to amplified evaporative fluxes at smaller contact radius. The internal thermofluidic patterns and evaporative modes in turn modulate the external Stefan flow fields and neighborhood temperature fields. These findings may hold strong implications for efficient functioning of practical droplet based processes involving transport, mixing, and deposition of dissolved particles.

Joint effect of air flow and substrate wettability on evaporation of a sessile droplet on a solid surface

We study the evaporation of microliter droplets of water on hydrophilic, hydrophobic, and superhydrophobic substrates subjected to airflow around them. While there is a large body of literature on diffusion-limited evaporation, evaporation in the presence of external convection is not fully-explored. We use side-view imaging and a custom-built flow channel to record the evaporating droplets from the side and develop an analytical model for evaporation in the presence of convection. Based on the droplet’s inlet flow velocity and wetted diameter, the maximum Reynolds number is 203. We quantify the time-variation of droplet volume, wetted diameter, and dynamic contact angle as a function of substrate wettability and airflow velocity. We found that the droplet lifetime decreases with the airflow, which is explained by the larger contribution of the convective mass loss rate compared to the diffusive mass flow rate computed by the model. Interestingly, the droplet lifetime is longer on a hydrophobic substrate due to the smallest area of liquid-gas interface among the three substrates for a given airflow. In general, evaporation occurs at constant contact radius (CCR) mode for hydrophilic surface in case of without flow and for all cases of airflow velocity. The CCR followed by constant contact angle (CCA) mode is observed for hydrophobic surface, and CCA followed by mixed mode is reported for superhydrophobic surface. The theoretical model reasonably predicts the measurements of different cases of airflow velocity and substrate wettability.

Fabrication of Superhydrophobic Water-Pinning Surfaces through Integration of Silica Colloids into Cellulose Nanocrystals.

The water-pinning effect is a phenomenon in which water droplets adhere to a surface and do not roll off, even when the surface is tilted or turned upside down. This effect holds great potential for applications in various areas, such as dew collection in arid regions, anti-drip function for a greenhouse, and liquid transport and control. However, creating surfaces that exhibit this effect poses challenges, necessitating materials with both hydrophobicity and high adhesive force along with a scalable, cost-effective method to produce the essential geometries that have not yet been established. To address these challenges, we propose a straightforward coating approach involving silica nanoparticles (SiO2) and cellulose nanocrystals (CNCs) to fabricate artificial water-pinning surfaces. We assessed the water-pinning ability of the coated surface through measurements of the contact angle, contact radius, and hysteresis. Remarkably, the coated surface exhibited a contact angle of approximately 153.87° and a contact radius of around 0.89 mm when a 10 μL water droplet was applied, demonstrating its resistance to rolling off, even at a tilting angle of 90°. The droplet only began to fall when its volume reached approximately 33 μL, requiring a substantial water pinning force of 323.4 μN. We also investigated the physicochemical characteristics of the SiO2@CNC coating surface, including morphology, chemical composition, and chemical structure, to unravel the underlying mechanism behind its water-pinning ability. Our proposed fabrication method offers a promising avenue for the development of functional biopolymer-based surfaces capable of precisely manipulating water droplets.

A lattice Boltzmann investigation of liquid viscosity effects on the evolution of a cavitation bubble attached to chemically patterned walls

The thermal lattice Boltzmann model is applied to explore liquid viscosity effects on a single cavitation bubble attached to chemically patterned walls. A conversion method based on the surface tension and the non-ideal equation of state parameters is proposed. According to the force analysis, it is found that the local pressure difference and the unbalanced Young's force are two main controlling factors for contactpoint dynamics. The dynamic contact angle is larger than the equilibrium contact angle throughout the evolution process for a hydrophilic wall, which results in a hysteresis effect in the bubble growth process due to the unbalanced Young's force and accelerates the contact point retraction velocity in the collapse stage. For hydrophobic walls, the unbalanced Young's force accelerates the contact radius expanding, resulting in a larger maximum contact radius than for a bubble attached to a hydrophilic wall. The hysteresis effects caused by the unbalanced Young's force slow down the contact points retraction in the early collapse stage and accelerate the retraction later because of dramatic interface deformation. The bubble is punctured over a larger volume with a hydrophilic wall than with a hydrophilic wall, resulting in a smaller collapse intensity. An exponential relationship between the micro-jet volume and the cosine function of the equilibrium contact angle at the collapse point is found. Furthermore, the jet volume before bubble collapse decreases, and the collapse time delays with the increase in viscosity.

Properties of Ag-GNP silver-graphene composites and finite element analysis of electrical contact coupling field

By using powder metallurgy, new electrical contact materials of Ag-GNP with mass fractions of 0.2%–3% were created. The mechanical and electrical properties of the materials were studied, and the force-thermal-electric coupling fields of the electrical contact process were calculated using the finite element method. The findings demonstrate that GNP can greatly boost the material’s mechanical strength while also increasing its resistivity; nevertheless, concentration levels of less than 3 weight percent do not appreciably impair the silver matrix’s electrical conductivity. The finite element simulation gives the stress field, current density distribution, and temperature field during contact. A comparison of the theoretically calculated contact radius and the simulation results show the same trend of variation. Both the stress field and temperature field are enhanced with increasing GNP content. The temperature rise of the contact may be unfavorable when the GNP content is greater than 1 wt.%.

Investigation of Droplet Dynamics Under Shear Flow

The dynamics of droplet under shear flow was investigated in normal gravity and microgravity. Drop under shear flow has many applications in aerospace such as aircraft de-icing and environmental control and life support system in space station. Shape analysis of the droplet showed that drop in microgravity have a greater contact angle and height, but a smaller contact radius, than that in normal gravity. The difference between advancing and receding contact angle θa-θr is greater in microgravity than that in normal gravity under the same wind speed. The effect of airflow on the droplet is mainly dependent on the We number and the dimensionless number k′, which characterizes the ratio of wind force and adhesion force. the k’ in microgravity is larger than that in normal gravity. The droplet exposed to airflow from static to motion state can be divided into three regimes.

Conditions of enhanced evaporation for nanofluids droplet and inhibition of coffee-ring effect under buoyancy and Marangoni convection

Evaporation of nanofluid droplets whose size is larger than capillary length is common in industrial processes, but there is currently a lack of research on the evaporation kinetics and more complex deposition patterns under the combined effects of buoyancy and Marangoni convection of large evaporating droplet. Experimental investigations on evaporation of Al2O3H2O nanofluid sessile droplet with initial contact line diameter of 4 mm on heating PTFE coating substrate are reported. The variation in contact angle, contact radius, and droplet volume over time under different conditions were obtained through experiments. The average evaporation rate is calculated. Internal flow characteristics are inferred through the surface temperature distribution detected by the top view infrared camera. The constant contact radius mode takes place at the beginning of evaporation. Then mixed evaporation mode and stick slip mode may occur for different substrate temperature, nanoparticle mass concentration and nanoparticle size. Increasing nanoparticle size causes a decrease in average evaporation rate. Whether the use of nanofluids can improve evaporation rate and heat transfer or not depends on multiple factors. Convection cells exist, and three kinds of deposition patterns are formed due to the underlying coupled transport phenomena. Under the combined effect of buoyancy and Marangoni convection in this article, the most common coffee-ring pattern does not appear. The deposition patterns are directly affected by the pinning stability, which decrease at higher temperature.

Self-consistent approximations for the tangential-displacement correction to the incremental indentation stiffness

An axisymmetric problem of unilateral frictionless contact between a paraboloidal or conical indenter and a transversely isotropic elastic half-space is considered in the refined formulation by accounting for the tangential (radial) displacements of the surface points of the elastic body. Using the idea of self-consistent approximation, a system of two coupled relations for the main contact variables (contact force, indenter displacement, and contact radius) is derived. The concept of the true contact radius is discussed, and it has been argued that the incremental stiffness relation should be expressed in its terms. Correction factors for the force–displacement relation and the incremental indentation stiffness (as a function of the true contact radius) are evaluated in explicit form.

Static Wetting of a Liquid Droplet on a Soft Elastic Substrate

Abstract A refined spherical cap model, combined with an elastic foundation model for the elastic substrate, is proposed to study the static wetting of a liquid droplet on a soft elastic substrate. The strain energy of the substrate is evaluated by the Johnson–Kendall–Roberts (JKR) model, and the increase of the surface energy of the substrate outside the contact zone is calculated based on the elastic foundation model. The total potential energy of the droplet-substrate system is given in terms of four geometrical parameters: the contact radius, the contact angle of the droplet, the deflection angle inside the contact zone, and the maximum downward displacement of the substrate surface at the contact zone center. The equilibrium state is determined based on the stationary condition of total potential energy. The present model reduces to the Young’s equation for a rigid substrate and to the Neumann’s triangle for a liquid-like substrate. Three equations are given to determine the liquid droplet shape in terms of surface energies and substrate’s elastic modulus. Reasonable agreement with existing experimental data and simulation results shows that the present model with derived formulas has the potential to catch the role of substrate’s elastic deformation on static wetting and fill the gap between the Young’s equation and the Neumann’s triangle for a soft elastic substrate.

Surface Effect in Nano-Scale Fretting Contact Problems

Abstract The fretting contact behavior of nanostructured materials is significantly influenced by the surface effect. A model of fretting contact between a nano-sized rigid cylindrical indenter and an elastic half-plane is established based on Gurtin–Murdoch (G–M) surface elasticity theory, with which the surface effects on the stress and displacement distributions and the size of stick region (no-slip region) in the contact zone are systematically studied. It is found that the surface effect induces an additional traction besides the external force applied by punch, which could help to smoothen the stress and displacement distributions. The normal surface-induced traction related to the residual surface stress is opposite to the externally applied compression, which results in a material stiffening in the contact zone so that the contact radius, normal displacement, and normal stress decrease compared with their classical counterparts. The tangential surface-induced traction is also opposite to the externally applied frictional stress, consequently leading to reductions of the shear stress and tangential displacement induced by friction in the contact zone. More interestingly, the surface effect leads to three possible states in the contact zone, including complete slip, partial slip, and complete stick, instead of the solely partial slip state in classical fretting contact models without surface effect. Among them, the complete stick due to the action of surface residual stress is more beneficial for inhibiting the wear of contact devices, which can be realized by reducing the indenter size. The present research does not only help one to better understand the physical mechanism in nano-scale fretting contact problems, but should also guide the anti-wear design in nano-electro-mechanical (NEMs) systems.

Flexural strains in a toughened glass panel generated by impact of an ice sphere

An analytical model for predicting flexural strains on a toughened glass panel generated by the impact of ice is presented in this paper. The time-history of the generated surface tensile strains can be used to predict the fracture probability of glass in a projected hailstorm scenario. As demonstrated in this article, the strain intensity is insensitive to changes in the panel size, positions of impact, and boundary conditions. The development of flexural strain at the point of contact is controlled purely by the initial generation of waves. This wave-controlled phenomenon can be explained by the early occurrence of the maximum flexural strain at the point of impact in advance of the arrival of reflected waves from the plate boundary. Thus, only the size of the ice sphere, impact velocity, temperature, and panel thickness are relevant to the prediction. The model for predicting flexural strain utilises considerably less computation time than numerical models. The derivation of expressions for predicting maximum strains involved investigations into the change in contact force and radius of the contact area with time. Integrating these relationships gave predictions of the maximum curvature and surface strains on the glass panel. The model has been validated by comparison of the simulated and measured quantities.

Asymmetric droplet evaporation on inclined surfaces

A computational model based on disjoining pressure is developed to study the asymmetric evaporation of droplets on an inclined substrate. In the proposed formulation, the disjoining pressure is combined with the arbitrary Lagrange-Euler method (ALE) to describe the solid-liquid interaction and investigate the contact angle hysteresis during evaporation. This model can be used to simulate the droplet evaporation modes of constant contact radius (CCR), constant contact angle (CCA) and “Stick-Slip” (mix evaporation mode), while the results are in good agreement with the experimental data. The obtained droplet shape for different inclined angles shows an asymmetric variation in contact angle at the front and rear ends, with the mean contact angle decreasing as the tilt angle increases. The evaporation flux is symmetric in the case of a horizontal substrate, however, when the substrate is tilted, the front and rear contact angles are modified, which leads to a larger evaporation flux on the rear contact line. Moreover, the asymmetric droplet morphology leads to asymmetric temperature field and vortex in the initial stage of evaporation; as evaporation proceeds, however, the flow and temperature fields within the droplet exhibit a gradual convergence towards symmetry. Moreover, when droplets evaporate on a pair of substrates with complementary tilt angles, their lifetimes exhibit a remarkable similarity. From the evaporation rate evolution, it yields that the larger the percentage of pinning time on the contact line, the faster the evaporation rate of the droplet. The evaporation rate of droplets was 14.76% higher at a tilt angle of α=0° than the case of α=45°.

Magnetic regulation on evaporation behavior of ferrofluid sessile droplets.

Active magnetic regulation is an emerging subject due to the special and programmable wettability of the sessile ferrofluid droplet. The interaction between liquid and externally applied magnetic field gives rise to controllable spreading and thus evaporation. This work reports the experimental and numerical results of the natural evaporation of a ferrofluid droplet under the effect of a nonuniform magnetic field. The evaporation process of droplets is described into two stages in terms of the geometric distortion and the appearance of the deposition pattern. The presence of the magnetic field leads to a transition of droplet drying from the disk shape with a ring to multiple peaks. A numerical model is established to simulate the evaporation process of ferrofluid droplets with the arbitrary Lagrangian-Eulerian method for tracking droplet deformation. The increasing magnetic flux could effectively enlarge the contact radius and enhance the internal flow of the ferrofluid droplet, thus promoting the evaporation process. The numerical results are verified by comparing the droplet geometry deformation with the experimental results. In both the numerical and experimental investigations, the externally applied magnetic field shortens the process of ferrofluid droplet evaporation. The design and optimization of the magnetic field play an important role in regulating ferrofluid droplet evaporation, which in turn facilitates technological advances in industries such as evaporative cooling and inkjet printing.

Comparison of the theoretical and experimental coefficient of friction for the brake disc-brake pad system

Contact between the automotive brake pad and the disc is mathematically modelled to estimate the coefficient of friction (COF). The mathematical model is proposed for the prognosis of the COF of brake pad material, by considering the contact mechanics between the interfacing surface and their material properties. The Greenwood-Williamson contact model is applied for rough contact surfaces for the estimation of the real contact radius. A MATLAB program has been formulated for generating the surface of brake pad material by considering its material properties which aid in the analytical evaluation of the COF. The proposed model is further validated with experimentation on pin-on-disc apparatus, as it is considered suitable for friction pad product testing according to previous research. The 25 pins were fabricated as per the ASTM G99 test for testing under varying loads and speeds. The obtained results showed that the range of COF has been between 0.2 and 0.4. The investigation presents an analytical approach for estimating COF and contact radius for brake disc and brake pad, which can be used to design an efficient automotive brake disc-brake pad system under the given load and rotational speed. The artificial neural network (ANN) is modelled for predicting the values of the COF for brake disc-brake pad systems, which can be further used for determining the tribological properties of new friction materials and their compatibility for efficient brake systems.

Shear-induced anisotropy of effective thermal conductivity in granular packings

This work explores shear-induced anisotropy of the effective thermal conductivity (ETC) in granular packings when subjected to quasistatic shear deformation. The discrete element method is adopted to track the position, force, and contact condition of every particle in the packing during the shear process. The ETC of the packing at different shear strains is evaluated using the particle-resolved finite element method. The simulation results show that the anisotropy ratio of the ETC can reach 40% as the shear strain increases to 0.11. The increase of the anisotropy mainly results from the variation of the network formed by the contacts that exist in two consecutive shear steps. It is also proved that contacts with large contact radius and strong thermal conductance are preferentially aligned with the direction of the applied deformation. The non-uniform distribution of the contact radius and the preferential orientation of the contacts contribute to the anisotropy of the thermal conductivity. Finally, by grouping the contacts in a packing into sub-networks with either weak or strong contact, it is shown that the thermal conductivity anisotropy of a packing is mainly caused by strong contacts.

Selective evaporation and contact line motions of evaporating ethylene glycol–water mixture droplets

The evaporation of sessile binary mixture droplets with different volatile liquids is essential in various applications such as ink-jet printing, evaporators, fuel combustion, and medical diagnosis. The present study examined the evaporating characteristics of ethylene glycol–water binary mixture droplets (EGWBMDs) used for patterning the functional materials in inkjet printing. In particular, the study focused on selective evaporation and dynamic contact line motion. To this end, surface plasmon resonance and shadowgraph imaging methods were employed to measure the temporal ethylene glycol concentrations and droplet shapes, respectively. The results revealed that EGWBMDs evaporated in the depinning mode following the constant contact radius mode. The ethylene glycol concentrations increased with time; evaporation of water was dominant throughout concentration measurement, showing selective evaporation. In addition, there was a non-linear change in the volume of EGWBMDs due to the different volatility of each component. In particular, the volume variation changed rapidly at the initial stage. Next, the evaporation rates of water and ethylene glycol were quantitatively calculated based on the ethylene glycol concentration and droplet shape measurement. The evaporation rate obtained from the experiment was found to be consistent with the predictions obtained using a diffusion model, with maximum and average error rates of 6.14 and 2.56%, respectively.

A force–displacement relation based on the JKR theory for DEM simulations of adhesive particles

Studying the collective behavior of adhesive particles with the discrete element method (DEM) requires well-founded force–displacement relations (force models). While the Johnson–Kendall–Roberts (JKR) theory reliably predicts the dependence of the contact radius a on the force F, it has remained a challenge in this framework to obtain a straightforward force–displacement relation F(δ) with physically meaningful parameters to calculate the force F from the displacement δ. We derive a novel force–displacement relation from the JKR theory as a composition of functions F(δ)=(F∘a∘λ)(δ), with the intermediate functions contact radius a(λ) and effective adhesive contact radius λ(δ). We also analyze contact geometry errors in the Hertz and JKR models, derive the exact contact centroid to accurately calculate contact torques and relative tangential velocities, and propose a smoothed JKR model to avoid discontinuities in force and energy. We find that incorrect torques and relative tangential velocities are obtained when the stiffness quotient is neglected because it affects the exact location of the contact centroid. We also find that contact geometry errors can become non-negligible for nanoparticles due to their large relative contact size. In addition, we show from bouncing ball simulations that the JKR models with a nominal coefficient of restitution derived for the Hertz model result in higher damping and thus reduced actual coefficients of restitution. Our analysis serves as a foundation for contact-mechanics-based force models for DEM simulations of adhesive particles to investigate their collective behavior in the future.