Function Of Contact Angle Research Articles

The shape of an axisymmetric meniscus in a static liquid pool: effective implementation of the Euler transformation

Abstract We examine the classical problem of the height of a static liquid interface that forms on the outside of a solid vertical cylinder in an unbounded stagnant pool exposed to air. Gravitational and surface tension forces compete to affect the interface shape as characterized by the Bond number. Here, we provide a convergent power series solution for interface shapes that rise above or fall below the horizontal pool as a function of contact angle and Bond number. We find that the power series solution expressed in terms of the radial distance from the wall is divergent, and thus rewrite the divergent series as a new power series expressed as powers of an Euler transformed variable; this series is modified to match the large distance asymptotic behaviour of the meniscus. The Euler transformation maps non-physical singularities to locations that do not restrict series convergence in the physical domain, while the asymptotic modification increases the rate of convergence of the series overall. We demonstrate that when the divergent series coefficients are used to implement the Euler transformation, finite precision errors are incurred, even for a relatively small number of terms. To avoid such errors, the independent variable in the governing differential equation is changed to that of the Euler transform, and the power series is developed directly without using the divergent series. The resulting power series solution is validated by comparison with a numerical solution of the interface shape and the small Bond number matched asymptotic solution for the height of the interface along the cylinder developed by Lo (1983, J. Fluid Mech., 132, p.65-78). The convergent power series expansion has the ability to exceed the accuracy of the matched asymptotic solution for any Bond number given enough terms, and the recursive nature of the solution makes it straightforward to implement.

Inclined colloidal drops: Evaporation kinetics and pattern formation

The drying of solute-laden drops is ubiquitous in everyday life, from paints and printers to the raindrops drying on our windows. Nonetheless, scientific interest has primarily focused on understanding the evaporation kinetics on flat surface, with the key parameter of substrate inclination only recently started being addressed. This work focuses on the influence of moderate substrate inclinations at 20° and 40° on the evaporation kinetics and associated deposit patterns of colloidal drops. Inclination altered the shape of the drops which formed a lower contact angle at the upper side of the drop (rear edge) and larger contact angle at the lower side (front edge). As evaporation rate is a function of contact angle, which in turn is a function of inclination, the evaporation lifetime was extended by 43% and 61% for 20° and 40°, respectively, compared to a flat drop. A theoretical approximation of the evaporative flux across the liquid-vapour interface of the drops showed the contribution of each edge to the evaporation kinetics. These differences in the evaporative fluxes altered the internal flows within the drop and in turn the coffee-ring formation mechanism. The particle deposit shape at the two edges for each drop was visualised which combined with the theoretical arguments allowed the proposition of the particle deposition mechanism in inclined drops: inclination added a gravitationally-driven velocity flow component within the drops, which is perpendicular and hence negligible in flat drops. This additional flow hindered or enhanced the number of particles arriving at the rear and front edges of the inclined drops, respectively, and hence influenced the dimensions of the coffee-ring patterns. Eventually, the particle deposits grew sufficiently tall to effectively stagnate the outward flow which resulted in enhanced particle accumulation at the interior of the drops as inclination increased.

О результатах исследования КПД шариковинтовых передач с сепаратором

Extensive use of ball screws with separators is due to manufacturing simplicity and increased reliability as compared to ball screws with recirculating rolling elements. The issues of determining the efficiency of such mechanisms have not been sufficiently studied. The paper presents analytically derived primary dimension ratios for parts of ball screws with separators, taking into account those tolerances that should be observed to ensure that the mechanism assembly is guaranteed and the preloads affecting the breakaway forces and the mechanism efficiency are prevented. We provide guidelines for designing parts of ball screws with separators. We plotted the interacting forces in the parts constituting ball screws with separators and analytically determined the efficiency of such mechanisms as a function of contact angles and lead angles. The experimental investigation results concerning electro-mechanical drive prototypes based on ball screws confirm the analytical expressions obtained. Adhering to the dimension ratios proposed for parts of ball screws with separators reveals that the analytically and experimentally determined efficiency values converge. Using the efficiency plots presented for ball screws with separators while designing electromechanical drives is appropriate to assess energy losses in mechanical transmissions

Response surface methodology and artificial neural network modeling of work of adhesion on plasma-treated polyester–cotton-woven fabrics

This paper aimed to study the effects of plasma treatment parameters on polyester–cotton of woven fabric surfaces through the work of adhesion test using artificial neural network (ANN) and response surface methodology (RSM). This study used plasma treatment parameters, such as electrode distance, voltage, and plasma exposure time, as inputs for the models. We used surface tension as a function of contact angle (θ) to measure the work of adhesion ( the model's output. Results showed that adhesion is closely related to the selected input variables. In addition, the development of artificial neural networks and response surface methodology could predict the experimental data with the coefficient of determination results were 0.902 and 0.719, and the root-mean-square error (RMSE) values were 2.135138 and 3.685359, respectively. Based on this research, compared with SRM, ANN has higher accuracy in calculating the work of adhesion. We concluded that ANN is expected to be a valuable quantitative method to predict and understand the adhesion effect of plasma treatment on the surface modification of polyester–cotton woven fabrics. The novelty of this study is that we used both ANN and RSM for the first time to predict the work of adhesion of polyester–cotton woven fabric treated with corona plasma. The use of the artificial neural network to simulate and predict the effect of plasma treatment on improving the work of adhesion is another novelty of this research.

Aggregation patterns of copper sulphate salt via droplet drying: mediation by surface hydrophobicity and salt concentration.

Patterns in drying droplets formed from colloidal solution of copper sulphate and gelatin are investigated with respect to variation of substrate hydrophobicity and salt concentration. Hydrophilic substrates as (i) glass, (ii) quartz and hydrophobic substrate as (iii) polypropylene (PP) have been used. It is observed that the dry residue pattern of salt crystals shows curved branches of crystalline aggregate growth about droplet centre for hydrophilic substrates, while thick, light and dark concentric bands of aggregates are observed for hydrophobic substrates. The geometry and topology of the patterns have been characterized through an analysis of fractal dimension and the topological measure, Euler characteristic. The fractal dimension of the deposit increases substantially with salt concentration for hydrophilic substrates, but decreases with concentration for hydrophobic substrate. Our analysis leads us to propose that an optimal viscosity contrast that facilitates prominent viscous fingers is a function of contact angle and salt concentration. We propose that substrate hydrophobicity and salt concentration together are responsible for DLA-like aggregation in evaporating droplets.

The response of a 2D droplet on a wall executing small sinusoidal vibrations

This study concerns a two-dimensional liquid drop surrounded by gas and attached to a sinusoidally vibrating wall. Gravity is neglected and the moving contact lines are modelled using a Navier-type boundary condition at the wall and a prescribed contact angle, θ¯, which can take any value in the range 0<θ¯<π. The vibration amplitude, and hence the departure from equilibrium of the drop, is assumed sufficiently small that the problem can be linearized. Wall vibration can have components both normal and tangential to the wall. The solution of the linear problem can be expressed as the sum of two decoupled components corresponding to the response to purely normal and purely tangential vibration, which are respectively symmetric and antisymmetric with respect to reflection in the symmetry plane of the equilibrium drop. Asymptotic analysis of the drop oscillations for small Ohnesorge number, Oh, brings out two distinct damping mechanisms, both of which are accounted for. One, arising from viscous dissipation in the regions near the contact lines, is characterized by a parameter β. The other comes from the boundary layer at the wall and is of order Oh1/2. The small-Oh problem has been implemented numerically. As expected, lightly damped normal modes are found to have resonant response close to their inviscid oscillation frequencies. Damping coefficients for each of the two damping mechanisms and lightly damped modes are determined as a function of contact angle. The relative importance of boundary-layer and contact-line damping is quantified and found to depend both on the contact angle and on β/Oh1/2. Cases can be found in which the two damping mechanisms have comparable effects, as well as others for which one or other of the mechanisms is dominant. Comparison with DNS, which allows for nonlinear effects and has the same contact-line model, shows agreement for a particular case having small Oh and small wall displacement amplitude.

Role of anisotropic pinning and liquid properties during partial rebound of droplets on unidirectionally structured hydrophobic surfaces

Droplet impact dynamics on super-hydrophobic micro-structured surfaces is vital in a multitude of processes such as spray coating, cooling, and inkjet printing etc. Majority of the research has been focused on the rebound phenomena while partial rebound is relatively underreported. Recent studies indicate that partial rebound is encountered where transition of wetting state may take place on super-hydrophobic surfaces. Herein, we report that satellite drops are formed during partial rebound of droplets even on hydrophobic surfaces with unidirectional topography created using a mask-less and stamp-less fabrication process. The simultaneous capillary driven retraction along the wrinkles and the strong contact line pinning across these anisotropic substrates leads to formation of satellite drops on hydrophobic surfaces. Excess rebound energy has been evaluated as functions of contact angle, contact angle hysteresis and the maximum spreading diameter to explain partial rebound on such surfaces with potential applications in the design of novel, functional surfaces.

Behaviour of sessile drops revealed in ‘car crash’ like impact

This study reports the effect of impact forces on the behaviour of sessile drops when their rapid horizontal displacement is abruptly abrogated. The experimental setup is akin to “car crash” simulation, wherein an object is moved linearly at a predetermined speed and then brought to a complete stop by colliding with a stationary obstacle. The mechanical translator used allowed drops to attain consistent speeds prior to imposition of an impact force. In investigations on binary mixtures comprising glycerol-water (0–100% vv) and polyvinyl alcohol – water (0–10% vv), it was found that the positions as well as the contact angles of the advancing and receding contact lines could alter in tandem. The trajectories from a new phase-space representation for binary mixtures of varied compositions indicated that drop behaviour as a function of contact angle and positional displacement differed between the advancing and receding contact lines in order to dissipate the impact energy applied. The experimental results scaled well with Ohnesorge numbers but not Bond or Weber numbers, indicating a dominant effect played by viscosity. The approach here offers new vistas in viscosity determination of fluids, and in the study of drops subjected to evaporation and freezing conditions.

Investigation of modified Water chemistry for improved oil recovery: Application of DLVO theory and surface complexation model

It is widely accepted that oil recovery during waterflooding can be improved by modifying the composition of the injected brine. A typical approach is diluting the formation water to a specific lower salinity. However, recent experimental studies report the adverse effect of formation water dilution on oil recovery for specific oil/brine/rock systems. The adverse effect depends on the interactions within the system and is more pronounced in carbonates. In this study, we investigated the effect of water composition on the performance of low salinity water injection by considering the complex interaction of oil, brine, and rock system.A surface complexation model (SCM) is developed to calculate the zeta-potential at oil and rock surfaces. Considering a water film between oil and rock and using DLVO theory, attractive/repulsive forces between oil/brine and brine/rock interfaces are calculated. Contact angle is predicted employing the augmented Young-Laplace equation. Our zeta potential calculations based on the SCM reproduced the experimental data of oil/brine and brine/calcite zeta potential measurements. Our contact angle calculations using the DLVO theory and the augmented Young-Laplace equation accurately estimated the dynamic trend of contact angle during low salinity flood. Modeling wettability alteration as a function of contact angle was sufficient to predict the low salinity effect. The developed model is implemented in a comprehensive compositional reactive transport simulator to validate the proposed approach.

A rapid method for interfacial tension calculation between rock plug and crude oil based on contact angles, application for EOR

ABSTRACTInterfacial tension and contact angle are two specific important parameters to take decisions for enhanced oil recovery, for instance, proper chemicals to use for surface tension reduction, expected wettability of solids, interaction between crude oil and rock. For this purpose, the article presents a method for easy calculation of the solid-liquid interfacial tension based on contact angle measurements applying Neumann's correlation and Young's equation. The main idea stands on the calculation of the rock parameters, like wettability, with known substances and extend these results to crude oils. It was possible, based on the results obtained, to establish a relationship between solid-liquid interfacial tension and contact angle for the crude oil – rock system, which can definitively be used for the calculation of interfacial tension of any other fluid spread out on the same kind of rock. A linear regression was obtained with an accuracy as good as R2 = 0.9989. Viscosity as a function of contact angle could also be obtained for the studied crude oils in the same kind of rock.

Model of spontaneous evaporating droplet on solid horizontal substrate

Free evaporation of sessile liquid non-isothermal drop on solid substrate is analyzed. Exact formulae for temperature and concentration fields are found out as functions of dimensionless parameters. The non-uniform temperature distribution at the drop surface creates the thermocapillar Marangonni forces that change their direction in the vicinity of stagnation points. Direction of the forces and disposition of the stagnation points are derived as function of contact angle and thermodynamic parameters of model. Conditions for the stagnation points to appear are found out. Moreover, maximal value of contact angle corresponding to presence of stagnation points in droplet is calculated as a function of the thermal conductivity ratio.

Effect of electrode surface properties on enhanced electron transfer activity in microbial fuel cells.

The influence of electrode surface chemistry over biofilm growth was evaluated for photo-bioelectrocatalytic fuel cell. A consortium of photosynthetic bacteria was grown onto different electrodes designed with polyethylenimine (PEI) and multiwall carbon nanotubes as hydrophilic and hydrophobic modifier, respectively. The designed electrodes were loaded with 0.08, 0.17, and 0.33μg/cm2 of PEI to change the hydrophilicity. However, 0.56, 0.72, and 0.83mg/cm2 of multiwall carbon nanotubes were used to alter the hydrophobicity of the electrodes. The surface chemistry of electrode and bio-interaction was evaluated as a function of contact angle and biofilm formation. The results were compared with those obtained with a carbon paper electrode. The contact angle on the untreated electrode (carbon paper) was 118°, whereas for hydrophobic and hydrophilic electrodes, the maximum and minimum contact angles were 170° and 0°, respectively. Interestingly, the maximum biofilm growth (0.2275g, wet basis) was observed on highly hydrophobic surface; however, the maximum electrochemical performance (246mV) was shown by the most hydrophilic electrode surface. PEI-based electrode with good biofilm formation showed comparatively higher electrogenic activity.

Wetting behavior of CMSX-4 in V-shaped channels for investment casting of fine features

An analytical model was developed to predict the infiltration of a non-wetting liquid into a sharp-cornered channel with rough walls. The distance from the liquid meniscus to the corner and the liquid radius of curvature predicted by the model are a function of contact angle, corner angle, head height and surface roughness. Measurements of these lengths were made in a model experiment as a function of liquid head height. The results of the experiments suggest that the analytical model accurately predicts the wetting limit of corner sharpness.

Contact Angle Effects on Pore and Corner Arc Menisci in Polygonal Capillary Tubes Studied with the Pseudopotential Multiphase Lattice Boltzmann Model

In porous media, pore geometry and wettability are determinant factors for capillary flow in drainage or imbibition. Pores are often considered as cylindrical tubes in analytical or computational studies. Such simplification prevents the capture of phenomena occurring in pore corners. Considering the corners of pores is crucial to realistically study capillary flow and to accurately estimate liquid distribution, degree of saturation and dynamic liquid behavior in pores and in porous media. In this study, capillary flow in polygonal tubes is studied with the Shan-Chen pseudopotential multiphase lattice Boltzmann model (LBM). The LB model is first validated through a contact angle test and a capillary intrusion test. Then capillary rise in square and triangular tubes is simulated and the pore meniscus height is investigated as a function of contact angle θ. Also, the occurrence of fluid in the tube corners, referred to as corner arc menisci, is studied in terms of curvature versus degree of saturation. In polygonal capillary tubes, the number of sides leads to a critical contact angle θc which is known as a key parameter for the existence of the two configurations. LBM succeeds in simulating the formation of a pore meniscus at θ &gt; θc or the occurrence of corner arc menisci at θ &lt; θc. The curvature of corner arc menisci is known to decrease with increasing saturation and decreasing contact angle as described by the Mayer and Stoewe-Princen (MS-P) theory. We obtain simulation results that are in good qualitative and quantitative agreement with the analytical solutions in terms of height of pore meniscus versus contact angle and curvature of corner arc menisci versus saturation degree. LBM is a suitable and promising tool for a better understanding of the complicated phenomena of multiphase flow in porous media.

Modeling the diffusion-driven growth of a pre-existing gas bubble in molten tin

Finite element method is utilized to solve the diffusion equation and model the diffusion driven growth of a pre-existing spherical gas bubble in molten tin at the solder/substrate interface for reflow time of 120 s and temperature of 250 °C. The gibbs free energy change required for determining the equilibrium concentration at liquid solder/gas bubble boundary was calculated using the thermodynamic polynomial coefficients. The rate of change of radius, as function of concentration flux, is calculated using the lagrangian mesh update methodology. With an initial diameter of 20 μm, the bubble growth is calculated as a function of contact angle. When the wetting angle is varied from a value of 30° to 135°, the numerical calculation has yielded the final sizes for the bubble to change from 62.87 μm to 82.8 μm respectively. The effect of wetting transition in the growth of bubble was studied by the in-situ observation of bubble dynamics through synchrotron radiation imaging technique. The scanning electron microscopy images of the morphologies of intermetallic compounds influenced by growing bubble in Sn/Cu solder joint and bubble pictures obtained through synchrotron radiation are utilized to get the experimental size of the bubble. The mean experimental bubble diameter has been obtained as 76.39 μm. The growing bubble inhibits the growth of intermetallic compound at its vicinity and thereby reduces the strength of solder joints.

Correlation of Contact Angle Hysteresis and Hydrodynamic Lubrication

The strength of molecular adhesion at the lubricant–solid interface plays a key role in determining the load-carrying and film forming capacity of a lubricated system of meso- or microscale. If the liquid molecules gain higher energies than the potential energy barrier for adhesion, slip occurs at the interface. The contact angle of a liquid on a solid surface is related to the intermolecular attractive force. Some studies demonstrated the connection of the contact angle to the lubrication effect. However, there were also studies drawing the opposite conclusion. A theoretical model derived based on thermodynamic principles shows that the potential energy barrier of a surface is not only a function of contact angle, but also of another interfacial parameter, contact angle hysteresis (CAH). This study thus evaluates the two, contact angle and CAH, by conducting thin film hydrodynamic lubrication experiments with surfaces of hydrophilic and hydrophobic (contact angle ranging from 30° to 110°). The lubricating film thickness was measured under different speed–load conditions using optical interferometry with a fixed-incline slider bearing. The paper identifies CAH to be a better interfacial parameter for correlating with the thin film hydrodynamic lubrication effect. Fundamental relation between the potential energy barrier and CAH is discussed, and the experimental results are described using the critical shear stress slip model.

DEVELOPMENTS ON WETTING EFFECTS IN MICROFLUIDIC SLUG FLOW

Wetting effects form a dimension of fluid dynamics that becomes predominant, precisely controllable, and possibly useful at the micro-scale. Microfluidic multiphase flow patterns, including size, shape, and velocity of fluidic particles, and mass and heat transfer rates are affected by wetting properties of microchannel walls and surface tension forces between fluid phases. The novelty of this field, coupled to difficulties in experimental design and measurements, means that literature results are scarce and scientific understanding is incomplete. Numerical methods developed recently have enabled a shortcut in obtaining results that can be perceived as realistic and that offer insight otherwise not possible. In this work the effect of the contact angle on gas-liquid two-phase flow slug formation in a microchannel T-junction was studied by numerical simulation. The contact angle, varied from 0 to 140 degrees, influenced the interaction of the gas and liquid phases with the channel wall, affecting the shape, size, and velocity of the slugs. The visualisation of the cross-sectional area of gas slugs allowed insight into the existence of liquid flow along rectangular microchannel corners, which was affected by the contact angle and determined the occurrence of velocity slip. The velocity profile within the gas slugs was also found to change as a function of contact angle, with hydrophilic channels inducing greater internal circulation, compared to greater channel wall contact in the case of hydrophobic channels. These effects play a role in heat and mass transfer from channel walls and highlight the value of numeral simulation in microfluidic design. Supplementary materials are available for this article. Go to the publisher's online edition of Journal of Chemical Engineering Communications to view the supplemental file.

Length scale effects of friction in particle compaction using atomistic simulations and a friction scaling model

The objective of this study is to illustrate and quantify the length scale effects related to interparticle friction under compaction. Previous studies have shown as the length scale of a specimen decreases, the strength of a single crystal metal or ceramic increases. The question underlying this research effort continues the thought—If there is a length scale parameter related to the strength of a material, is there a length scale parameter related to friction? To explore the length scale effects of friction, molecular dynamics (MD) simulations using an embedded atom method potential were performed to analyze the compression of two spherical FCC nickel nanoparticles at different contact angles. In the MD model study, we applied a macroscopic plastic contact formulation to determine the normal plastic contact force at the particle interfaces and used the average shear stress from the MD simulations to determine the tangential contact forces. Combining this information with the Coulomb friction law, we quantified the MD interparticle coefficient of friction and showed good agreement with experimental studies and a Discrete Element Method prediction as a function of contact angle. Lastly, we compared our MD simulation friction values to the tribological predictions of Bhushan and Nosonovsky (BN), who developed a friction scaling model based on strain gradient plasticity and dislocation-assisted sliding that included a length scale parameter. The comparison revealed that the BN elastic friction scaling model did a much better job than the BN plastic scaling model of predicting the coefficient of friction values obtained from the MD simulations.

Wetting Behavior of Amorphous and Crystalline Silicon Dioxide in Contact with a Silicate Slag Based on Fayalite

AbstractIn this work the wetting behaviour of amorphous and crystalline silicon dioxide in contact with a silicate slag based on fayalite is demonstrated as a function of contact angles, activation energies of the kinetic stages of wetting. In addition the dynamic adhesion work has been calculated as a function of the inclination angle. The amorphous silicon dioxide in contact with the slag presents lower contact angles accompanied also by higher dynamic adhesion works in comparison to crystalline porous ceramics with the same chemistry.

Advanced characterization of electrowetting retroreflectors

Electrowetting retroreflectors use a simple and scalable construction, and incorporate an electrically tunable liquid lenslet. By electrically modulating the lenslet geometry, the reflection is switched between retroreflection and scattering. In this paper, we report new capability and characterization, including higher index liquids and contrast ratio as a function of contact angle (theta(V)). The reflected intensity is also spatially profiled and reported as a function of view angle. A high contrast ratio of >16X is demonstrated, and methods for further improving performance are discussed. Because the electrowetting retroreflector platform is broad spectrum (VIS-IR), the electrowetting retroreflector may be useful for a large variety of naked eye applications such as safety markings, road-signage, or friend-foe-identification.