Apparent and Microscopic Contact Angles

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We analyse an image volume of diameter approximately 4. This work provides a rapid method to provide an accurate characterization of pore-scale wettability, which is important for the design and assessment of hydrocarbon recovery and carbon dioxide storage. Dependency of the apparent contact angle on nonisothermal conditions.

The dynamic behavior of liquids in partly filled containers is influenced to a large extend by the angle between the gas-liquid phase boundary and the solid container wall at the contact line. This contact angle in turn is influenced by nonisothermal conditions. In the case of a cold liquid meniscus spreading over a hot solid wall, the contact angle apparently becomes significantly larger. In this paper we want to establish a quantitative equation for this enlargement, both from experimental and numerical data. Our findings can be used to build a subgrid model for computations, where the resolution is not sufficient to resolve the boundary layers.

This might be the case for large containers which are exposed to low accelerations and where the contact angle boundary condition determines the position of the free surface. These types of computation are performed, for example, to solve propellant management problems in launcher and satellite tanks. In this application, the knowledge of the position of the free surface is very important for the withdrawal of liquid and the calculation of heat and mass transfer.

The familiar Young contact angle measurement of a liquid at equilibrium on a solid is a fundamental aspect of capillary phenomena. But in the real world it is not so easy to observe it. What can be easily…. Drop shape visualization and contact angle measurement on curved surfaces. The shape and contact angles of drops on curved surfaces is experimentally investigated.

Image processing, spline fitting and numerical integration are used to extract the drop contour in a number of cross-sections. The three-dimensional surfaces which describe the surface-air and drop-air interfaces can be visualized and a simple procedure to determine the equilibrium contact angle starting from measurements on curved surfaces is proposed.

Contact angles on flat surfaces serve as a reference term and a procedure to measure them is proposed. Such procedure is not as accurate as the axisymmetric drop shape analysis algorithms, but it has the advantage of requiring only a side view of the drop-surface couple and no further information. It can therefore be used also for fluids with unknown surface tension and there is no need to measure the drop volume. Examples of application of the proposed techniques for distilled water drops on gemstones confirm that they can be useful for drop shape analysis and contact angle measurement on three-dimensional sculptured surfaces.

Contact angles of wetting and water stability of soil structure. Kholodov, V. From the soddy-podzolic soils and typical chernozems of different texture and land use, dry mm aggregates were isolated and sieved in water. As a result, water-stable aggregates and water-unstable particles composing dry mm aggregates were obtained. These preparations were ground, and contact angles of wetting were determined by the static sessile drop method.

In most cases, the values of the angles for the water-stable aggregates significantly exceeded those for the water-unstable components. In terms of carbon content in structural units, there was no correlation between these parameters. When analyzing the soil varieties separately, the significant positive correlation between the carbon content and contact angle of aggregates was revealed only for the loamy-clayey typical chernozem.

Based on the multivariate analysis of variance, the value of contact wetting angle was shown to be determined by the structural units belonging to water-stable or water-unstable components of macroaggregates and by the land use type. In addition, along with these parameters, the texture has an indirect effect. Dynamic contact angle of water-based titanium oxide nanofluid.

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This paper presents an investigation into spreading dynamics and dynamic contact angle of TiO2-deionized water nanofluids. Two mechanisms of energy dissipation, 1 contact line friction and 2 wedge film viscosity, govern the dynamics of contact line motion. The primary stage of spreading has the contact line friction as the dominant dissipative mechanism. At the secondary stage of spreading, the wedge film viscosity is the dominant dissipative mechanism. A theoretical model based on combination of molecular kinetic theory and hydrodynamic theory which incorporates non-Newtonian viscosity of solutions is used.


The model agreement with experimental data is reasonable. Complex interparticle interactions, local pinning of the contact line, and variations in solid—liquid interfacial tension are attributed to errors. Croell, A. Franklin Technical Monitor. Precise knowledge of material parameters is more and more important for improving crystal growth processes. Two important parameters are the contact wetting angle and the surface tension, determining meniscus shapes and surface-tension driven flows in a variety of methods Czochralski, EFG, floating-zone, detached Bridgman growth.

The sessile drop technique allows the measurement of both parameters simultaneously and has been used to measure the contact angles and the surface tension of Ge 1-x Si x 0 less than or equal to x less than or equal to 1. In addition, the effect of different cleaning procedures and surface treatments on the wetting behavior were investigated.

Measurements were performed both under dynamic vacuum and gas atmospheres argon or forming gas , with temperatures up to C. The highest wetting angles were found for pBN substrates with angles around deg. The temperature dependence of the surface tension showed similar values for Ge 1-x Si x , around The pore radius i. The most common method to determine these two parameters is through measurement of the capillary pressure generated by a reference liquid i.

The rate of rise technique, commonly used to determine the capillary pressure, results in significant uncertainties. In this study, we utilize a recently developed technique for independently measuring the capillary pressure and permeability to determine the equivalent minimum capillary radii and contact angle of water within micropillar wick structures.

In this method, the experimentally measured dryout threshold of a wick structure at different wicking lengths is fit to Darcy's law to extract the maximum capillary pressure generated by the test liquid. The equivalent minimum capillary radii of different wick geometries are determined by measuring the maximum capillary pressures generated using n-hexane as the working fluid. It is found that the equivalent minimum capillary radius is dependent on the diameter of pillars and the spacing between pillars.

The equivalent capillary radii of micropillar wicks determined using the new method are found to be up to 7 times greater than the current geometry-based first-order estimates. The contact angle subtended by water at the walls of the micropillars is determined by measuring the capillary pressure generated by water within the arrays and the measured capillary radii for the different geometries. This mean contact angle of water is determined to be The classical Lucas-Washburn-Rideal LWR equation, using the equilibrium contact angle , predicts a faster capillary rise process than experiments in many cases.

The major contributor to the faster prediction is believed to be the velocity dependent dynamic contact angle. In this work, we investigated the dynamic contact angle models for their ability to correct the dynamic contact angle effect in the capillary rise process. We conducted capillary rise experiments of various wetting liquids in borosilicate glass capillaries and compared the model predictions with our experimental data.

The results show that the LWR equations modified by the molecular kinetic theory and hydrodynamic model provide good predictions on the capillary rise of all the testing liquids with fitting parameters, while the one modified by Joos' empirical equation works for specific liquids, such as silicone oils. The LWR equation modified by molecular self-layering model predicts well the capillary rise of carbon tetrachloride, octamethylcyclotetrasiloxane, and n-alkanes with the molecular diameter or measured solvation force data.

The molecular self-layering model modified LWR equation also has good predictions on the capillary rise of silicone oils covering a wide range of bulk viscosities with the same key parameter W 0 , which results from the molecular self-layering. The advantage of the molecular self-layering model over the other models reveals the importance of the layered molecularly thin wetting film ahead of the main meniscus in the energy dissipation associated with dynamic contact angle. The analysis of the capillary rise of silicone oils with a wide range of bulk viscosities provides new insights into the capillary dynamics of polymer melts.

Contact angle change during evaporation of near-critical liquids. An unexpected change of the dynamic contact angle was recently observed in a near-critical liquid-gas system in a space experiment. We propose an explanation for this phenomenon by taking into account vapor recoil due to evaporation motion of the vapor from the free liquid surface.

This force is normal to the vapor-liquid interface and is directed towards the liquid. It increases sharply near the triple contact line. Near the critical point, where the surface tension force is very weak, the vapor recoil force can be important enough to change the apparent contact angle.

A similar effect can also explain the drying of a heater during boiling at high heat flux. The drying greatly reduces the heat transfer to the liquid causing the heater to melt. We report the preliminary results of the numerical simulation of the liquid evaporation by the Boundary Element method. Eccentricity effect of micropatterned surface on contact angle.

This article experimentally shows that the wetting property of a micropatterned surface is a function of the center-to-center offset distance between successive pillars in a column, referred to here as eccentricity. Measurement results of the static as well as the dynamic contact angles on these surfaces revealed that the contact angle decreases with increasing eccentricity and increasing relative spacing between the pillars. In general, the maximum obtainable hydrophobicity corresponds to micropillars with zero eccentricity.

As the pillar relative spacing decreases, the effect of eccentricity on hydrophobicity becomes more pronounced. The dependence of the wettability conditions of the micropatterned surface on the pillar eccentricity is attributed to the contact line deformation resulting from the changed orientation of the pillars. This finding provides additional insights in design and fabrication of efficient micropatterned surfaces with controlled wetting properties.

Edge contact angle and modified Kelvin equation for condensation in open pores. We consider capillary condensation transitions occurring in open slits of width L and finite height H immersed in a reservoir of vapor. Similar results apply for condensation in cylindrical pores of finite length. We test these predictions against numerical results obtained using a microscopic density-functional model where the presence of an edge contact angle characterizing the shape of the menisci is clearly visible from the density profiles.

Effect of contact angle hysteresis on moving liquid film integrity. A study was made of the formation and breakdown of a water film moving over solid surfaces teflon, lucite, stainless steel, and copper. The flow rate associated with film formation was found to be higher than the flow rate at which film breakdown occurred. The difference in the flow rates for film formation and film breakdown was attributed to contact angle hysteresis.

Analysis and experiment, which are in good agreement, indicated that film formation and film breakdown are functions of the advancing and receding angles , respectively. Anomalous contact angle hysteresis of a captive bubble: advancing contact line pinning. Receding pinning is generally attributed to localized defects that are more wettable than the rest of the surface.

However, the defect model cannot explain advancing pinning of liquid phase invasion driven by a deflating bubble and continuous retreat of liquid phase driven by the inflating bubble. A simple thermodynamic model based on adhesion hysteresis is proposed to explain anomalous contact angle hysteresis of a captive bubble quantitatively. Our analytical analysis indicates that contact line pinning represents frustration in surface free energy, and the equilibrium shape corresponds to a nondifferential minimum instead of a local minimum.

On the basis of our thermodynamic model, Surface Evolver simulations are performed to reproduce both advancing and receding behavior associated with a captive bubble on the acrylic glass. Gunshot residue patterns on skin in angled contact and near contact gunshot wounds.

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The goal of this study was the reproduction of shape and pattern of gunshot residues in near contact and contact gunshot wounds by a series of experimental gunshots on a skin and soft tissue model. The aim was to investigate the shape and direction of soot deposits with regard to the muzzle according to different muzzle-target angles , firing distances, type of ammunition and weapon and barrel length.

Based on a review of the literature and on the results of the experiments the authors could make the following statements of gunshot residues in angled contact and close contact gunshot: 1 gunshot residues on the target surface can be differentiated in a "inner" and "outer powder soot zone"; 2 the outer powder soot zone is much less visible than the inner powder soot zone and may lack on human skin; 3 with increasing muzzle target distance both inner and outer powder soot halo increase in size and decrease in density; 4 in angled shots the inner powder soot halo shows an eccentric, elliptic shape which points towards the muzzle, regardless of ammunition, calibre and barrel length; 5 the outer powder soot points away from the muzzle in angled contact and close contact shots.

Effect of contact angle and contact angle hysteresis on the floatability of spheres at the air-water interface. The floatability of solid particles on the water surface governs many natural phenomena and industrial processes including film flotation and froth flotation separation of coal and valuable minerals. For many years, the contact angle CA has been postulated as the key factor in determining the particle floatability. Indeed, the maximum force tenacity supporting the flotation of fine spheres was conjectured to occur when the apical angle of the contact circle is equal to the contact angle.

In this paper, the model predictions are reviewed and compared with experimental results. It is shown that CA can be affected by many physical and chemical factors such as surface roughness and chemical heterogeneity and can have a range of values known as the CA hysteresis. This multiple-valued CA invalidates the available theories on the floatability of spheres.

Even the intuitive replacement of CA by the advancing maximum CA in the classical theories can be wrong. A few new examples are also reviewed and analyzed to demonstrate the significance of CA variation in controlling the particle floatability.

They include the pinning of the contact line at the sharp edge, known as the Gibbs inequality condition, and the nearby interaction among floating particles, known as lateral inter-particle interaction. It is concluded that our quantitative understanding of the floatability of real particles being irregular and heterogeneous both morphologically and chemically is still far from being satisfactory.

Large area optical mapping of surface contact angle. Top-down contact angle measurements have been validated and confirmed to be as good if not more reliable than side-based measurements. A range of samples, including industrially relevant materials for roofing and printing, has been compared. Using the top-down approach, mapping in both 1-D and 2-D has been demonstrated. The method was applied to study the change in contact angle as a function of change in silver Ag nanoparticle size controlled by thermal evaporation. Large area mapping reveals good uniformity for commercial Aspen paper coated with black laser printer ink.

A demonstration of the forensic and chemical analysis potential in 2-D is shown by uncovering the hidden CsF initials made with mineral oil on the coated Aspen paper. The method promises to revolutionize nanoscale characterization and industrial monitoring as well as chemical analyses by allowing rapid contact angle measurements over large areas or large numbers of samples in ways and times that have not been possible before. Many physical phenomena and industrial applications involve multiphase fluid flows and hence it is of high importance to be able to simulate various aspects of these flows accurately.

In the past few decades, many mathematical models were developed for predicting the contact angles of the inter-face with the wall boundary under various flow conditions. In the current thesis, a simple approach to incorporate the static and dynamic contact angle boundary conditions using the level set method is developed and implemented in multiphase CFD codes, LIT Level set Interface Tracking Herrmann and NGA flow solver Desjardins et al Various DCA models and associated boundary conditions are reviewed.

In addition, numerical aspects such as the occurrence of a stress singularity at the contact lines and grid convergence of macroscopic interface shape are dealt with in the context of the level set approach. Correlating contact line capillarity and dynamic contact angle hysteresis in surfactant-nanoparticle based complex fluids. Dynamic wettability and contact angle hysteresis can be correlated to shed insight onto any solid-liquid interaction.

Complex fluids are capable of altering the expected hysteresis and dynamic wetting behavior due to interfacial interactions. We report the effect of capillary number on the dynamic advancing and receding contact angles of surfactant-based nanocolloidal solutions on hydrophilic, near hydrophobic, and superhydrophobic surfaces by performing forced wetting and de-wetting experiments by employing the embedded needle method. A segregated study is performed to infer the contributing effects of the constituents and effects of particle morphology.

The static contact angle hysteresis is found to be a function of particle and surfactant concentrations and greatly depends on the nature of the morphology of the particles. An order of estimate of line energy and a dynamic flow parameter called spreading factor and the transient variations of these parameters are explored which sheds light on the dynamics of contact line movement and response to perturbation of three-phase contact.

The Cox-Voinov-Tanner law was found to hold for hydrophilic and a weak dependency on superhydrophobic surfaces with capillary number, and even for the complex fluids, with a varying degree of dependency for different fluids. Surface tension and contact angles : Molecular origins and associated microstructure. Gradient theory converts the molecular theory of inhomogeneous fluid into nonlinear boundary value problems for density and stress distributions in fluid interfaces, contact line regions, nuclei and microdroplets, and other fluid microstructures.

The relationship between the basic patterns of fluid phase behavior and the occurrence and stability of fluid microstructures was clearly established by the theory. All the inputs of the theory have molecular expressions which are computable from simple models. On another level, the theory becomes a phenomenological framework in which the equation of state of homogeneous fluid and sets of influence parameters of inhomogeneous fluids are the inputs and the structures, stress tensions and contact angles of menisci are the outputs. These outputs, which find applications in the science and technology of drops and bubbles, are discussed.

Contact angle hysteresis on doubly periodic smooth rough surfaces in Wenzel's regime: The role of the contact line depinning mechanism. We report here on the contact angle hysteresis, appearing when a liquid meniscus is in contact with doubly sinusoidal wavelike patterned surfaces in Wenzel's wetting regime. Using the full capillary model we obtain numerically the contact angle hysteresis as a function of the surface roughness factor and the equilibrium contact angle for a block case and a kink case contact line depinning mechanism.

We find that the dependencies of the contact angle hysteresis on the surface roughness factor are different for the different contact line depinning mechanisms. These dependencies are different also for the two types of rough surfaces we studied. The relations between advancing, receding, and equilibrium contact angles are investigated. A comparison with the existing asymptotical, numerical, and experimental results is carried out. We consider the phase equilibria of a fluid confined in a deep capillary groove of width L with identical side walls and a bottom made of a different material.

All walls are completely wet by the liquid. This alters the capillary condensation transition which is now first order; this would be continuous in a capped capillary made wholly of either type of material. These occur as the width i becomes macroscopically large, and ii is reduced to a microscopic value determined by the difference in Hamaker constants.

This second wetting transition is characterized by large scale fluctuations and essential critical singularities arising from marginal interfacial interactions. Interpreting contact angle results under air, water and oil for the same surfaces. Under-water and under-oil superhydropobicity and superhydrophilicity have gained significant attention over the last few years. In this study, contact angles on five flat surfaces polypropylene, poly methyl methacrylate , polycarbonate, TEFLON-FEP and glass slide were measured in water drop-in-air, air bubble-under-water, oil drop-in-air, air bubble-under-oil, oil drop-under-water and water drop-under-oil conditions.

Heptane, octane, nonane, decane, dodecane, and hexadecane hydrocarbons were used as oils. These pairs were used in the two-liquid contact angle measurements. However, it was determined that there are large deviations from this rule in practical cases and these deviations depend on surface free energies of solids. Three complementary cases of water-in-air with air bubble-under-water ; oil-in-air with air bubble-under-oil ; and oil-under-water with water-under-oil were investigated in particular to determine the deviations from ideality. It was experimentally determined that.

Nanobubbles in confined solution: Generation, contact angle , and stability. The formation of gas bubbles presents a frequent challenge to microfluidic operations, for which fluids are geometrically confined to a microscale space. Here, to understand the mechanism of nucleating gas bubbles in microfluidic devices, we investigate the formation and stability of nanobubbles in confined solutions. Our molecular dynamics simulations show that while pinning of the contact line is a prerequisite for the stability of surface nanobubbles in open systems that can exchange gas with surrounding environment, in confined solutions, stable nanobubbles can exist even without pinning.

In supersaturated condition, stable bubbles can be found in confined solutions with acute or obtuse contact angle , depending on the substrate hydrophobicity. We also demonstrate that when open to the bulk solution, the stable nanobubbles in closed systems would become unstable unless both supersaturation and pinning of the contact line are satisfied. Our results not only shed light on the design of novel heterogeneous surfaces for generating nanobubbles in confined space with controllable shape and stability but also address the crucial effect of gas exchange with the surroundings in determining the stability of nanobubbles.

The three-phase contact line of a droplet on a smooth surface can be characterized by the Young equation. On the mesoscale, wettability is modeled by a film-height-dependent wetting energy f h. Here, we derive a similar consistency condition for the case of a liquid covered by an insoluble surfactant. We derive macroscopic and mesoscopic descriptions of a contact line at equilibrium and show that they are consistent only if a particular dependence of the wetting energy on the surfactant concentration is imposed.

This is illustrated by a simple example of dilute surfactants, for which we show excellent agreement between theory and time-dependent numerical simulations. In situ assessment of the contact angles of nanoparticles adsorbed at fluid interfaces by multiple angle of incidence ellipsometry. Here multiple angle of incidence ellipsometry was successfully applied to in situ assess the contact angle and surface coverage of gold nanoparticles as small as 18 nm, coated with stimuli-responsive polymers, at water-oil and water-air interfaces in the presence of NaCl and NaOH, respectively.

The interfacial adsorption of the nanoparticles was found to be very slow and took days to reach a fairly low surface coverage. For water-oil interfaces, in situ nanoparticle contact angles agree with the macroscopic equilibrium contact angles of planar gold surfaces with the same polymer coatings, whilst for water-air interfaces, significant differences have been observed. Diminution of contact angle hysteresis under the influence of an oscillating force. We suggest a simple quantitative model for the diminution of contact angle hysteresis under the influence of an oscillatory force invoked by thermal fluctuations, substrate vibrations, acoustic waves, or oscillating electric fields.

Employing force balance rather than the usual description of contact angle hysteresis in terms of Gibbs energy, we highlight that a wetting system, such as a sessile drop or a bubble adhered to a solid substrate, appears at long times to be partially or fully independent of contact angle hysteresis and thus independent of static friction forces, as a result of contact line pinning. We verify this theory by studying several well-known experimental observations such as the approach of an arbitrary contact angle toward the Young contact angle and the apparent decrease or increase in an advancing or a receding contact angle under the influence of an external oscillating force.

Forefoot angle at initial contact determines the amplitude of forefoot and rearfoot eversion during running. Clinically, foot structures are assessed intrinsically - relation of forefoot to rearfoot and rearfoot to leg. We have argued that, from a biomechanical perspective, the interaction of the foot with the ground may influence forces and torques that are propagated through the lower extremity. We proposed that a more appropriate measure is an extrinsic one that may predict the angle the foot makes with ground at contact.

The purposes of this study were to determine if the proposed measure predicts contact angles of the forefoot and rearfoot and assess if the magnitude of those angles influences amplitude and duration of foot eversion during running. With the individual in prone, extrinsic clinical forefoot and rearfoot angles were measured relative to the caudal edge of the examination table. Participants ran over ground while frontal plane forefoot and rearfoot contact angles , forefoot and rearfoot eversion amplitude and duration were measured. Participants were grouped twice, once based on forefoot contact inversion angle moderate median and once based on rearfoot contact inversion angle moderate median.

The forefoot and rearfoot extrinsic clinical angles predicted, respectively, the forefoot and rearfoot angles at ground contact. Large forefoot contact angles were associated with greater amplitudes but not durations of forefoot and rearfoot eversion during stance. Rearfoot contact angles , however, were associated with neither amplitudes nor durations of forefoot and rearfoot eversion.

Possible mechanisms for the increased risk of running injuries associated with large forefoot angles are discussed. Beyond Cassie equation: Local structure of heterogeneous surfaces determines the contact angles of microdroplets. The application of Cassie equation to microscopic droplets is recently under intense debate because the microdroplet dimension is often of the same order of magnitude as the characteristic size of substrate heterogeneities, and the mechanism to describe the contact angle of microdroplets is not clear.

By representing real surfaces statistically as an ensemble of patterned surfaces with randomly or regularly distributed heterogeneities patches , lattice Boltzmann simulations here show that the contact angle of microdroplets has a wide distribution, either continuous or discrete, depending on the patch size. The origin of multiple contact angles observed is ascribed to the contact line pinning effect induced by substrate heterogeneities.

We demonstrate that the local feature of substrate structure near the contact line determines the range of contact angles that can be stabilized, while the certain contact angle observed is closely related to the contact line width. A method to measure internal contact angle in opaque systems by magnetic resonance imaging.

Internal contact angle is an important parameter for internal wettability characterization. However, due to the limitation of optical imaging, methods available for contact angle measurement are only suitable for transparent or open systems. For most of the practical situations that require contact angle measurement in opaque or enclosed systems, the traditional methods are not effective.

Based upon the requirement, a method suitable for contact angle measurement in nontransparent systems is developed by employing MRI technology. In the Article, the method is demonstrated by measuring internal contact angles in opaque cylindrical tubes. It proves that the method also shows great feasibility in transparent situations and opaque capillary systems. By using the method, contact angle in opaque systems could be measured successfully, which is significant in understanding the wetting behaviors in nontransparent systems and calculating interfacial parameters in enclosed systems.

To study the effects of surfactants on wettability of excipients, the contact angles of six types of surfactants on the surface of two common excipients and mixture of three surfactants with excipients were measured using hypsometry method. The results demonstrated that contact angle of water on the surface of excipients was associated with hydrophilcity of excipients.

Contact angle was lowered with increase in hydrophilic groups of excipient molecules. The sequence of contact angle from small to large was starch contact angle of excipients, and their abilities to lower contact angle varied. The results of the present study offer a guideline in the formulation design of tablets. Influence of spin creepage and contact angle on curve squeal: A numerical approach. Curve squeal is a loud tonal sound that may arise when a railway vehicle negotiates a tight curve. Due to the nonlinear nature of squeal, time-domain models provide a higher degree of accuracy in comparison to frequency-domain models and also enable the determination of squeal amplitudes.

In the present paper, a previously developed engineering time-domain model for curve squeal is extended to include the effects of the contact angle and spin creepage. The extensions enable the evaluation of more realistic squeal cases with the computationally efficient model. The model validation against Kalker's variational contact model shows good agreement between the models.

Results of studies on the influence of spin creepage and contact angle show that the contact angle has a significant influence on the vertical-lateral dynamics coupling and, therefore, influences both squeal amplitude and frequency. Spin creepage mainly influences processes in the contact , therefore influencing the tangential contact force amplitude.

In the combined spin- contact angle study the spin creepage value is kinematically related to the contact angle value. Results indicate that the influence of the contact angle is dominant over the influence of spin creepage. Modeling contact angle hysteresis of a liquid droplet sitting on a cosine wave-like pattern surface.

A liquid droplet sitting on a hydrophobic surface with a cosine wave-like square-array pattern in the Wenzel state is simulated by using the Surface Evolver to determine the contact angle. For a fixed drop volume, multiple metastable states are obtained at two different surface roughnesses. Unusual and non-circular shape of the three-phase contact line of a liquid droplet sitting on the model surface is observed due to corrugation and distortion of the contact line by structure of the roughness. The contact angle varies along the contact line for each metastable state.

The maximum and minimum contact angles among the multiple metastable states at a fixed viewing angle correspond to the advancing and the receding contact angles , respectively. In addition, the receding or advancing contact angles at different viewing angles are determined at different metastable states. The contact angle of minimum energy among the multiple metastable states is defined as the most stable equilibrium contact angle.

(PDF) Apparent and Microscopic Contact Angles | Janusz Laskowski -

The Wenzel model is not able to describe the contact angle along the three-phase contact line. The contact angle hysteresis at different drop volumes is determined. The number of the metastable states increases with increasing drop volume. Drop volume effect on the contact angles is also discussed. Numerical analysis of moving contact line with contact angle hysteresis using feedback deceleration technique. Contact angle CA hysteresis is important in many natural and engineering wetting processes, but predicting it numerically is difficult.

We developed an algorithm that considers CA hysteresis when analyzing the motion of the contact line CL. This algorithm employs feedback control of CA which decelerates CL speed to make the CL stationary in the hysteretic range of CA, and one control coefficient should be heuristically determined depending on characteristic time of the simulated system.

The algorithm requires embedding only a simple additional routine with little modification of a code which considers the dynamic CA. The method is non-iterative and explicit, and also has less computational load than other algorithms. For a drop hanging on a wire, the proposed algorithm accurately predicts the theoretical equilibrium CA. If so, it may have a n The update introduces OxygenOS 10 and will be a staged rollout over the n Although some will be disappointed about the delay of the core Matisse CPU, ot New tip suggests Microsoft Surface device will come with AMD's Ryzen 5 U and Ryzen 7 U processors An interesting tip from a well-known leaker has seemingly revealed which AMD processors could find their way into Microsoft Surface devices in the not too distant future.

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Lloyd,, K. Stika,, L. Stephans,, G. Magallanes,, V. Dimonie,, E. Sudol, and, M. Macromolecules , 33 23 , Semal,, C. Bauthier,, M. Vanden Eynde,, R. Gouttebaron, and, J. De Coninck. The Journal of Physical Chemistry B , 26 , Woodward,, H. Gwin, and, D. Langmuir , 16 6 , Peter S. Swain and, David Andelman.

Lecture 32: Wetting (Contact between three phases)

Langmuir , 15 26 , Wei Chen,, Alexander Y. Langmuir , 15 10 , Scientific Reports , 8 1 DOI: Ludmila Boinovich, Alexandre Emelyanenko. Fatema H. Rajab, Zhu Liu, Lin Li. Production of stable superhydrophilic surfaces on L steel by simultaneous laser texturing and SiO 2 deposition. Applied Surface Science , , Wood, Timothy J. Singler, Congrui Jin. Journal of Membrane Science , , Melanie N. MacGregor-Ramiasa, Krasimir Vasilev. Advanced Materials Interfaces , 5 , Shilo A. Mahoney, Thomas E. Rufford, David Johnson, Anastasia S. The effect of rank, lithotype and roughness on contact angle measurements in coal cleats.

Abraham Marmur. Interfaces at equilibrium: A guide to fundamentals. Advances in Colloid and Interface Science , , Alsu I. Akhmetshina, Olesya R. Gumerova, Artem A. Atlaskin, Anton N. Petukhov, Tatyana S. Sazanova, Nail R. Yanbikov, Alexander V. Nyuchev, Evgeny N. Razov, Ilya V. Permeability and selectivity of acid gases in supported conventional and novel imidazolium-based ionic liquid membranes. Separation and Purification Technology , , Andrea Ehrmann, Tomasz Blachowicz. Hydrophobic and Hydrophilic Textiles.

Friess, L. Kim, Anupam Kumar. Theoretical consideration of contact angle hysteresis using surface-energy-minimization methods. International Journal of Heat and Mass Transfer , , Yang, Yong-Wei Zhang. Nanostructure Formation by controlled dewetting on patterned substrates: A combined theoretical, modeling and experimental study. Scientific Reports , 6 1 DOI: Eric J. Falde, Stefan T. Yohe, Yolonda L. Colson, Mark W. Superhydrophobic materials for biomedical applications.

Biomaterials , , A numerical study of three-dimensional droplets spreading on chemically patterned surfaces. Modification of epoxy resin, silicon and glass surfaces with alkyl- or fluoroalkylsilanes for hydrophobic properties. Yukihiro Yonemoto, Tomoaki Kunugi. Experimental and theoretical investigation of contact-angle variation for water—ethanol mixture droplets on a low-surface-energy solid. International Journal of Heat and Mass Transfer , 96 , Acta Metallurgica Sinica English Letters , 29 , Sara M. Use of bacterial cellulose in degraded paper restoration. Part I: application on model papers.

Journal of Materials Science , 51 , Ahmed Z. The Journal of Chemical Thermodynamics , 93 , Advances in Materials Science and Engineering , , Mihir M. Shah, Satish G. Water emergence from the land region and water—sidewall interactions in Proton Exchange Membrane Fuel Cell gas channels with microgrooves.

Journal of Power Sources , , Bottiglione, G. Carbone, B. Fluid contact angle on solid surfaces: Role of multiscale surface roughness. The Journal of Chemical Physics , , Boussinot, Efim A. Inhibition of Rayleigh-Plateau instability on a unidirectionally patterned substrate. Chebolu, Nagahanumaiah. Contact angle measurement on micropatterned surface using sessile drop shape fit profile detection. The Imaging Science Journal , 63 , Bertola, M.

Dynamic contact angle of dilute polymer solution drops impacting on a hydrophobic surface. Super Repellency. Guan, F. Luo, G. Lim, M. Hong, H. Zheng, Bojin Qi. Fabrication of metallic surfaces with long-term superhydrophilic property using one-stop laser method. Stetsyshyn, A. Kostruba, K. Harhay, V. Donchak, H. Ohar, V. Savaryn, B. Kulyk, L. Ripak, Yu. Multifunctional cholesterol-based peroxide for modification of amino-terminated surfaces: Synthesis, structure and characterization of grafted layer.

Beattie, Marta Krasowska. Static and dynamic wetting behaviour of ionic liquids. Droplet on a regularly patterned solid. Wu, Xiao Dong Chen. Colloids and Surfaces B: Biointerfaces , , Marta L. Trobo, Ezequiel V. Critical wetting in the two-dimensional Ising ferromagnet confined between inhomogeneous walls. Marcin Dokowicz, Waldemar Nowicki. Morphology of a droplet deposited on a strip and triangular groove.

Surface Innovations , 2 4 , Yildirim Erbil. The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: A review. Surface Science Reports , 69 4 , Superhydrophobic hybrid micro-nanocomposites for non-stick and self-cleaning coatings. Composite Interfaces , 21 , Propagation-of-uncertainty from contact angle and streaming potential measurements to XDLVO model assessments of membrane—colloid interactions.

Apparent and Microscopic Contact Angles Apparent and Microscopic Contact Angles
Apparent and Microscopic Contact Angles Apparent and Microscopic Contact Angles
Apparent and Microscopic Contact Angles Apparent and Microscopic Contact Angles
Apparent and Microscopic Contact Angles Apparent and Microscopic Contact Angles
Apparent and Microscopic Contact Angles Apparent and Microscopic Contact Angles
Apparent and Microscopic Contact Angles Apparent and Microscopic Contact Angles
Apparent and Microscopic Contact Angles Apparent and Microscopic Contact Angles
Apparent and Microscopic Contact Angles Apparent and Microscopic Contact Angles

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