Gradient Estimate of Solutions to a Class of Mean Curvature Equations with Prescribed Contact Angle Boundary Problem

This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained.

Effects of Steam Heat Treatment on the Surface Contact Angle of Chinese Fir

The aim of this study was investigate the effects of heat treatment on the contact angle of Chinese fir, and the indicators affecting the change of contact an-gle change. It was determined that the duration of treatment had significant effect on the change curves of contact angle of Chinese fir wood due to the change curves of contact angle became more centralized and orderly after the specimens heat treated at 180 ℃. Compared with the untreated wood, the contact angle in-creased from 51＆#176; to 124＆#176; after 4 h treatment, and hydroxyl absorbance of hy-drophilic functional groups decreased from 2.08 to 1.63, while carbonyl absorbance from 0.92 to 0.62. The surface roughness has not significant influence on the con-tact angle. Heat treatment of the Chinese fir caused surface morphological change, which produced hol owed-out phenomenon. The increased surface contact angle caused by heat treatment can be used for outdoor and sauna facilities.

Influence of Warm Oxide Layer on Wettability and Contact Angle for Heat Transport Devices

Recently, high heat density has become a problem in electronic devices. Therefore, high heat-transfer efficiency is required in copper heat exchangers. Improvement ofwettability is reported to improve the heat-transfer efficiency. In previous studies, copper oxide layer improves the wettability. In this study, we focus on a copper oxide layer produced under warm conditions （from 200 to 300 ℃）, which are suitable oxidation conditions for improving wettability. Experimental results showed that the surface of the specimens was covered by the oxidation layer and took on a black color. Furthermore, the wettability was improved by the warm copper oxide layer. While, the surface roughness was approximately constant to each warm oxidized specimen. Whereat, the warm oxide layer was observed by SEM （sanning electron microscope）. The results from SEM observations showed that the warm copper oxide layer consisted of stacks and combinations of nanoscopic warm oxidation particles. Thus, the warm oxidation layer has nanoscopic surface asperities. It is seemed that these nanoscopic asperities improved the wettability.

Modeling Superhydrophobic Contact Angles and Wetting Transition

It is well known that surface roughness has a very important effect on superhydrophobicity.The Wenzel and Cassie-Baxter models,which correspond to the homogeneous and heterogeneous wetting respectively,are currently primary instructions for designing superhydrophobic surfaces.However,the particular drop shape that a drop exhibits might depend on how it is formed. A water drop can occupy multiple equilibrium states,which relate to different local minimal energy.In some cases,both equilibrium states can even co-exist on a same substrate.Thus the apparent contact angles may vary and have different values.We discuss how the Wenzel and Cassie-Baxter equations determine the homogeneous and heterogeneous wetting theoretically. Contact angle analysis on hierarchical surface structure and contact angle hysteresis has been put specific attention.In particular, we study the energy barrier of transition from Cassie-Baxter state to Wenzel state,based on existing achievement by previous researchers,to determine the possibility of the transition and how it can be interpreted.It has been demonstrated that surface roughness and geometry will influence the energy required for a drop to get into equilibrium,no matter it is homogeneous or heterogeneous wetting.

Contact Angle Hysteresis and Hysteresis Tension on Rough Solid Surface

Observation and measurement were conducted to investigate contact angle andits hysteresis on rough surface. The experimental results indicate that the increase in solidsurface roughness enlarges advancing contact angle and decreases receding contact angle, resultingin enhanced hysteresis. It was observed that when Young''s contact angle θ_Y 【 90°, as theroughness of solid surface increased the extent of the decrease in receding contact angle exceededthat of the increase in advancing contact angle. Based on the experimental observations, the conceptof hysteresis tension was introduced to describe the contact angle hysteresis behavior on roughsolid surface. The model provides a thoughtful understanding of the physical nature of contact anglehysteresis, in particular an instructive description of the influence of surface roughness on thehysteresis. The prediction of the model is found in quite good agreement with the experimentalobservation and measurement.

Machine Vision Based Measurement of Dynamic Contact Angles in Microchannel Flows

When characterizing flows in miniaturized channels, the determination of the dynamic contact angle is important. By measuring the dynamic contact angle, the flow properties of the flowing liquid and the effect of material properties on the flow can be characterized. A machine vision based system to measure the contact angle of front or rear menisci of a moving liquid plug is described in this article. In this research, transparent flow channels fabricated on thermoplastic polymer and sealed with an adhesive tape are used. The transparency of the channels enables image based monitoring and measurement of flow variables, including the dynamic contact angle. It is shown that the dynamic angle can be measured from a liquid flow in a channel using the image based measurement system. An image processing algorithm has been developed in a MATLAB environment. Images are taken using a CCD camera and the channels are illuminated using a custom made ring light. Two fitting methods, a circle and two parabolas, are experimented and the results are compared in the measurement of the dynamic contact angles.

Mechanism of contact angle saturation and an energy-based model for electrowetting

Electrowetting,as a well-known approach to increasing droplet wettability on a solid surface by electrical bias,has broad applications.However,it is limited by contact angle saturation at large voltage.Although several debated hypotheses have been proposed to describe it,the physical origin of contact angle saturation still remains obscure.In this work,the physical factors responsible for the onset of contact angle saturation are explored,and the correlated theoretical models are established to characterize electrowetting behavior.Combination of the proper 3-phase system employed succeeds in dropping the saturating contact angle below 25？,and validates that the contact angle saturation is not a result of devicerelated imperfection.

Effect of contact angle and helix angle on slide-roll ratio under the accelerated motion state of ball screw mechanism

To study the effect of the contact angle and helix angle on slide-roll ratio at the ball contact points under the accelerated motion state of ball screw mechanisrm(B S M),the curve theory in differential geometry a d the homogeneous transformation matrix ae used to establish the acceleration kinematics model of BSM.The model can be used to describe the accelerated motion relationships among the screw,balls and nut,calculate the acceleration of relative motion at the contact points between the balls and raceways,and analyze five accelerated motion rules between the balls and raceways.It also conducts a simulation analysis of the slide-roll ratio relationship between the accelerations at the ball center and the contact point of ball under different contact angles and helix angles.As shownby the analysis,with the increase in the BSM’s contact angle,the slide-roll ratio at the contact points decreases,and the contact angle has a relatively significant effect on the slide-roll ratio.However,with the decrease in the BSM’helix angle,the slide-roll ratio at the contact points decreases,and the helix angle has a relatively insignificant effect on the slide-roll ratio.By measuring the accelerations of both the screw and nut under the accelerated motion state,it also verifies the existence of the slide-roll mixed motion at the ball contact point A between the ball and the screw racewayand pure rolling at the ball contact point B between the ball and the nut raceway during the accelerated motion.

Prediction of curved oil–water interface in horizontal pipes using modified model with dynamic contact angle

In this study,interface shapes of horizontal oil–water two-phase flow are predicted by using Young-Laplace equation model and minimum energy model.Meanwhile,the interface shapes of horizontal oil–water twophase flow in a 20 mm inner diameter pipe are measured by a novel conductance parallel-wire array probe(CPAP).It is found that,for flow conditions with low water holdup,there is a large deviation between the model-predicted interface shape and the experimentally measured one.Since the variation of pipe wetting characteristics in the process of fluid flow can lead to the changes of the contact angle between the fluid and the pipe wall,the models mentioned above are modified by considering dynamic contact angle.The results indicate that the interface shapes predicted by the modified models present a good consistence with the ones measured by CPAP.

Effects of hysteresis of static contact angle (HSCA) and boundary slip on the hydrodynamics of water striders

It is known that contact lines keep relatively still on solids until static contact angles exceed an interval of hysteresis of static contact angle (HSCA), and contact angles keep changing as contact lines relatively slide on the solid. Here, the effects of HSCA and boundary slip were first distinguished on the micro-curvature force (MCF) on the seta. Hence, the total MCF is partitioned into static and dynamic MCFs correspondingly. The static MCF was found proportional to the HSCA and related with the asymmetry of the micro-meniscus near the seta. The dynamic MCF, exerting on the relatively sliding contact line, is aroused by the boundary slip. Based on the Blake-Haynes mechanism, the dynamic MCF was proved important for water walking insects with legs slower than the minimum wave speed . As insects brush the water by laterally swinging legs backwards, setae on the front side of the leg are pulled and the ones on the back side are pushed to cooperatively propel bodies forward. If they pierce the water surface by vertically swinging legs downwards, setae on the upside of the legs are pulled, and the ones on the downside are pushed to cooperatively obtain a jumping force. Based on the dependency between the slip length and shear rate, the dynamic MCF was found correlated with the leg speed U, as , where and are determined by the dimple depth. Discrete points on this curve could give fitted relations as (Suter et al., J. Exp. Biol. 200, 2523-2538, 1997). Finally, the axial torque on the inclined and partially submerged seta was found determined by the surface tension, contact angle, HSCA, seta width, and tilt angle. The torque direction coincides with the orientation of the spiral grooves of the seta, which encourages us to surmise it is a mechanical incentive for the formation of the spiral morphology of the setae of water striders.

EFFECT OF CONTACT ANGLE HYSTERESIS ON DROPLET BEHAVIORS:TWO-PHASE LATTICE BOLTZMANN SIMULATION

An approach of dealing with contact angle hysteresis in lattice Boltzmann method is introduced in detail.The approach is also used to investigate droplet behaviors on surfaces of chemical inhomogeneities or roughness(non-ideal surfaces).Droplet slipping on surfaces under gravity or in shear flows,and droplet impacting on surfaces are numerically simulated.It is found that the present approach is suitable to model droplet motions on non-ideal surfaces and the contact angle hysteresis has an obvious effect on the motion of droplets.

Contact angle hysteresis in electrowetting on dielectric

Contact angle hysteresis(CAH) is one of the significant physical phenomena in electrowetting on dielectric(EWOD).In this work, a theoretical model is proposed to characterize electrowetting evolution on substrates with CAH, and the relationship among apparent contact angle, potential, and some other parameters is quantified. And this theory is also validated experimentally. The results indicate that our theory and equation based on energy balance succeed in describing the electrowetting response of potential with significant contact angle hysteresis. The CAH in EWOD, ranging from 0° to about 20° in electrowetting cycle, increases with the increase of voltage and climbs up to about 20° when voltage is increased to about 38 V, and then decreases to zero with the further increase of voltage.

Comparative study of two lattice Boltzmann multiphase models for simulating wetting phenomena: implementing static contact angles based on the geometric formulation

Wetting phenomena are widespread in nature and industrial applications. In general, systems concerning wetting phenomena are typical multicomponent/multiphase complex fluid systems. Simulating the behavior of such systems is important to both scientific research and practical applications. It is challenging due to the complexity of the phenomena and difficulties in choosing an appropriate numerical method. To provide some detailed guidelines for selecting a suitable multiphase lattice Boltzmann model, two kinds of lattice Boltzmann multiphase models, the modified S-C model and the H-C-Z model, are used in this paper to investigate the static contact angle on solid surfaces with different wettability combined with the geometric formulation(Ding, H. and Spelt, P.D. M. Wetting condition in diffuse interface simulations of contact line motion. Physical Review E, 75(4), 046708(2007)). The specific characteristics and computational performance of these two lattice Boltzmann method(LBM) multiphase models are analyzed including relationship between surface tension and the control parameters, the achievable range of the static contact angle, the maximum magnitude of the spurious currents(MMSC), and most importantly, the convergence rate of the two models on simulating the static contact angle. The results show that a wide range of static contact angles from wetting to non-wetting can be realized for both models. MMSC mainly depends on the surface tension. With the numerical parameters used in this work, the maximum magnitudes of the spurious currents of the two models are on the same order of magnitude. MMSC of the S-C model is universally larger than that of the H-C-Z model. The convergence rate of the S-C model is much faster than that of the H-C-Z model. The major foci in this work are the frequently-omitted important details in simulating wetting phenomena. Thus, the major findings in this work can provide suggestions for simulating wetting phenomena with LBM multiphase models along with the geometric formulation.

Modified smoothed particle hydrodynamics approach for modelling dynamic contact angle hysteresis

Dynamic wetting plays an important role in the physics of multiphase flow, and has a significant influence on many industrial and geotechnical applications. In this work, a modified smoothed particle hydrodynamics (SPH) model is employed to simulate surface tension, contact angle and dynamic wetting effects at meso-scale. The wetting and dewetting phenomena are simulated in a capillary tube, where the liquid particles are raised or withdrawn by a shifting substrate. The SPH model is modified by introducing a newly developed viscous force formulation at the liquid-solid interface to reproduce the rate-dependent behaviour of the moving contact line. Dynamic contact angle simulations with the interfacial viscous force are conducted to verify the effectiveness and accuracy of this new formulation. In addition, the influence of interfacial viscous forces with different magnitude on the contact angle dynamics is examined by empirical power-law correlations;the derived constants suggest that the dynamic contact angle changes monotonically with the interfacial viscous force. The simulation results are consistent with experimental observations and theoretical predictions, implying that the interfacial viscous force can be associated with the slip length of flow and the microscopic surface roughness. This work demonstrates that the modified SPH model can successfully account for the rate-dependent effects of a moving contact line, and can be used for realistic multiphase flow simulations under dynamic conditions.

Non-contact angle measurement based on parallel multiplex laser feedback interferometry

We present a novel precise angle measurement scheme based on parallel multiplex laser feedback interferometry （PLFI）, which outputs two parallel laser beams and thus their displacement difference reflects the angle variation of the target. Due to its ultrahigh sensitivity to the feedback light, PLFI realizes the direct non-contact measurement of non- cooperative targets. Experimental results show that PLFI has an accuracy of 8＂ within a range of 1400＂. The yaw of a guide is also measured and the experimental results agree with those of the dual-frequency laser interferometer Agilent 5529A.

Application of Laser Ultrasonic Technique for Non-contact Detection of Angled Surface Defects

Based on the finite element method,the angled surface defects have been investigated by using the laser generated surface acoustic wave(SAW).The feature of laser generated SAW interaction with the angled defect is analyzed in time and frequency domains.An increase in the amplitude of SAW at the edge of the defect is observed,and the spectral feature is angle dependent.With the angle decreasing from 120°to 30°,the maximum amplitude of frequency spectrum of SAW increases gradually.The corresponding experimental results verify the feasibility of numerical analyses and reach a good agreement with simulation results.

Contact pressure distribution and support angle optimization of kiln tyre

According to the shearing force character and the deformation coordination condition of shell at the station of supports, the mathematical models to calculate contact angle and contact pressure distribution between tyre and shell were set up, the formulae of bending moment and bending stress of tyre were obtained. Taking the maximum of tyre fatigue life as the optimal objective, the optimization model of tyre support angle was built. The computational results show that when tyre support angle is 30°, tyre life is far less than that when tyre support angle is optimal, which is 35.6°, and it is unsuitable to stipulate tyre support angle to be 30° in traditional design. The larger the load, the less the nominal stress amplitude increment of tyre, the more favorable the tyre fatigue life when tyre support angle is optimal.

Contact Angle Prediction Model for Underwater Oleophobic Surfaces Based on Multifractal Theory

Traditional microstructure scale parameters have difficulty describing the structure and distribution of a roughmaterial’s surface morphology comprehensively and quantitatively. This study constructs hydrophilic and underwateroleophobic surfaces based on polyvinylidene fluoride (PVDF) using a chemical modification method, and the fractaldimension and multifractal spectrum are used to quantitatively characterize the microscopic morphology. A new contactangle prediction model for underwater oleophobic surfaces is established. The results show that the fractal dimension ofthe PVDF surface first increases and then decreases with the reaction time. The uniformity characterized by the multifractalspectrum was generally consistent with scanning electron microscope observations. The contact angle of water droplets onthe PVDF surface is negatively correlated with the fractal dimension, and oil droplets in water are positively correlated.When the fractal dimension is 2.0975, the new contact angle prediction model has higher prediction accuracy. Themaximum and minimum relative deviations of the contact angle between the theoretical and measured data are 18.20%and 0.72%, respectively. For water ring transportation, the larger the fractal dimension and spectral width of the materialsurface, the smaller the absolute value of the spectral difference, the stronger the hydrophilic and oleophobic properties, andthe better the water ring transportation stability.

Simple Hydrostatic Model of Contact Angle Hysteresis of a Sessile Drop on Rough Surface

The phenomenon of hysteresis of contact angle is an important topic subject to a long time of argument.A simple hydrostatic model of sessile drops under the gravity in combination with an ideal surface roughness model is used to interpret the process of drop volume increase or decrease of a planar sessile drop and to shed light on the contact angle hysteresis and its relationship with the solid surface roughness. With this model, the advancing and receding contact angles are conceptually explained in terms of equilibrium contact angle and surface roughness only,without invoking the thermodynamic multiplicity. The model is found to be qualitatively consistent to experimental observations on contact angle hysteresis and it suggests a possible way to approach the hysteresis of three-dimensional sessile drops.

Improved contact angle measurement in multiphase lattice Boltzmann

Contact angle is an essential parameter to characterize substrate wettability.The measurement of contact angle in experiment and simulation is a complex and time-consuming task.In this paper,an improved method of measuring contact angle in multiphase lattice Boltzmann simulations is proposed,which can accurately obtain the real-time contact angle at a low temperature and larger density ratio.The three-phase contact point is determined by an extrapolation,and its position is not affected by the local deformation of flow field in the three-phase contact region.A series of simulations confirms that the present method has high accuracy and gird-independence.The contact angle keeps an excellent linear relationship with the chemical potential of the surface,so that it is very convenient to specify the wettability of a surface.The real-time contact angle measurement enables us to obtain the dynamic contact angle hysteresis on chemically heterogeneous surface,while the mechanical analyses can be effectively implemented at the moving contact line.