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.

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.

Numerical Stability and Accuracy of Contact Angle Schemes in Pseudopotential Lattice Boltzmann Model for Simulating Static Wetting and Dynamic Wetting

There are five most widely used contact angle schemes in the pseudopotential lattice Boltzmann(LB)model for simulating the wetting phenomenon:The pseudopotential-based scheme(PB scheme),the improved virtualdensity scheme(IVD scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the fluid layer density above the wall(MPB-C scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the weighted average density of surrounding fluid nodes(MPB-W scheme)and the geometric formulation scheme(GF scheme).But the numerical stability and accuracy of the schemes for wetting simulation remain unclear in the past.In this paper,the numerical stability and accuracy of these schemes are clarified for the first time,by applying the five widely used contact angle schemes to simulate a two-dimensional(2D)sessile droplet on wall and capillary imbibition in a 2D channel as the examples of static wetting and dynamic wetting simulations respectively.(i)It is shown that the simulated contact angles by the GF scheme are consistent at different density ratios for the same prescribed contact angle,but the simulated contact angles by the PB scheme,IVD scheme,MPB-C scheme and MPB-W scheme change with density ratios for the same fluid-solid interaction strength.The PB scheme is found to be the most unstable scheme for simulating static wetting at increased density ratios.(ii)Although the spurious velocity increases with the increased liquid/vapor density ratio for all the contact angle schemes,the magnitude of the spurious velocity in the PB scheme,IVD scheme and GF scheme are smaller than that in the MPB-C scheme and MPB-W scheme.(iii)The fluid density variation near the wall in the PB scheme is the most significant,and the variation can be diminished in the IVD scheme,MPB-C scheme andMPBWscheme.The variation totally disappeared in the GF scheme.(iv)For the simulation of capillary imbibition,the MPB-C scheme,MPB-Wscheme and GF scheme simulate the dynamics of the liquid-vapor interface well,with the GF scheme being the most accurate.The accuracy of the IVD scheme is low at a small contact angle(44 degrees)but gets high at a large contact angle(60 degrees).However,the PB scheme is the most inaccurate in simulating the dynamics of the liquid-vapor interface.As a whole,it is most suggested to apply the GF scheme to simulate static wetting or dynamic wetting,while it is the least suggested to use the PB scheme to simulate static wetting or dynamic wetting.

Automatic measurement of three-phase contact angles in pore throats based on digital images

With the help of digital image processing technology, an automatic measurement method for the three-phase contact angles in the pore throats of the microfluidic model was established using the microfluidic water flooding experiment videos as the data source. The results of the new method were verified through comparing with the manual measurement data.On this basis, the dynamic changes of the three-phase contact angles under flow conditions were clarified by the contact angles probability density curve and mean value change curve. The results show that, for water-wetting rocks, the mean value of the contact angles is acute angle during the early stage of the water flooding process, and it increases with the displacement time and becomes obtuse angle in the middle-late stage of displacement as the dominant force of oil phase gradually changes from viscous force to capillary force. The droplet flow in the remaining oil occurs in the central part of the pore throats, without three-phase contact angle. The contact angles for the porous flow and the columnar flow change slightly during the displacement and present as obtuse angles in view of mean values, which makes the remaining oil poorly movable and thus hard to be recovered. The mean value of the contact angle for the cluster flow tends to increase in the flooding process, which makes the remaining oil more difficult to be recovered. The contact angles for the membrane flow are mainly obtuse angles and reach the highest mean value in the late stage of displacement, which makes the remaining oil most difficult to be recovered. After displacement, the remaining oils under different flow regimes are just subjected to capillary force, with obtuse contact angles, and the wettability of the pore throat walls in the microfluidic model tends to be oil-wet under the action of crude oil.

A new model for the formation of contact angle and contact angle hysteresis

The formation mechanism of the contact angle and the sliding angle for a liquid drop on a solid surface plays an important role in producing hydrophobic surfaces. A new half soakage model is established in this paper as a substitute for Wenzel （complete soakage） and Cassie （no soakage） models. The model is suited to many solid surfaces, whether they are hydrophilic or hydrophobic, or even superhydrophobic. Based on the half soakage model, we analyse two surfaces resembling lotus, i.e. taper-like surface and corona-like surface. Furthermore, this new model is used to establish a quantitative relationship between the sliding angle and the parameters of surface morphology.

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.

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.

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.

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.

Water contact angles on charged surfaces in aerosols

Interactions between water and solid substrates are of fundamental importance to various processes in nature and industry.Electric control is widely used to modify interfacial water,where the influence of surface charges is inevitable.Here we obtain positively and negatively charged surfaces using Li Ta O_(3) crystals and observe that a large net surface charge up to 0.1 C/m;can nominally change the contact angles of pure water droplets comparing to the same uncharged surface.However,even a small amount of surface charge can efficiently increase the water contact angle in the presence of aerosols.Our results indicate that such surface charges can hardly affect the structure of interfacial water molecular layers and the morphology of the macroscopic droplet,while adsorption of a small amount of organic contaminants from aerosols with the help of Coulomb attraction can notably decrease the wettability of solid surface.Our results not only provide a fundamental understanding of the interactions between charged surfaces and water,but also help to develop new techniques on electric control of wettability and microfluidics in real aerosol environments.

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.

Super gas wet and gas wet rock surface: State of the art evaluation through contact angle analysis

Recently,super gas wet and gas wet surfaces have been extensively attended in petroleum industry,as supported by the increasing number of publications in the last decade related to wettability alteration in gas condensate reservoirs.In many cases,contact angle measurement has been employed to assess the wettability alteration.Even though contact angle measurement seems to be a straightforward approach,there exist many misuses of this technique and consequently misinterpretation of the corresponding results.In this regard,a critical inspection of the most recent updated concepts and the intervening parameters in the contact angle based wettability evaluation of liquid-solid-gas systems could aid to provide some remediation to alleviate this problem.To this end,this work presents a survey on the accurate terms and rigorous protocols based on the community of surface science and chemistry.As a preliminary step,advancing,receding,static,and the most stable contact angle terminology are defined.The study is followed by the definition of the contact angle hysteresis effect.The application of surface free energy in the selection of the best gas wet agent is then analyzed.Afterward,the impact of the size-dependent behavior of drop on contact angle is discussed.Finally,a sessile drop experiment is explained to achieve the defined parameters.For future contributions to petroleum industry journals,like this journal,this work could offer an easy use of the conceptual framework for analyzing the results and comparative evaluations in chemical wettability modifier agents.

A Simple Method to Measure the Contact Angle of Metal Droplets on Graphite

The determination of solid–liquid interfacial tension plays an important role in science and technology.Here,we propose a simple method to directly measure the contact angle between metal droplets and a graphite substrate for the determination of metal–graphite interfacial tension.The proposed method involves the synthesis of micro-and nanosized metal droplets on graphite by arc melting.Owing to its small volume,the rapid cooling of the prepared metal droplets on the graphite substrate leads to the freezing of equilibrium contact confguration after solidifcation.We observe that the measured contact angle between micro-and nanosized Au(or Ag)particles and the graphite substrate is almost size independent,even though the size of the particles synthesized herein is 1–3 orders of magnitude smaller than that studied in previous works.In addition,the interfacial tensions of Au and Ag on the step edges(edge plane)of graphite are found to be larger than that on the(0001)plane(basal plane).The proposed method provides a simple approach to determine the solid–liquid interfacial tension and may be efective in the study of interface related science and technology.

NUMERICAL STUDY OF THE RELATIONSHIP BETWEEN APPARENT SLIP LENGTH AND CONTACT ANGLE BY LATTICE BOLTZMANN METHOD

The apparent slip between solid wall and liquid is studied by using the Lattice Boltzmann Method （LBM） and the Shan-Chen multiphase model in this paper. With a no-slip bounce-back scheme applied to the interface, flow regimes under different wall wettabilities are investigated. Because of the wall wettability, liquid apparent slip is observed. Slip lengths for different wall wettabilities are found to collapse nearly onto a single curve as a function of the static contact angle, and thereby a relationship between apparent slip length and contact angle is suggested. Our results also show that the wall wettability leads to the formation of a low-density layer between solid wall and liquid, which produced apparent slip in the micro-scale.

Spontaneous Imbibition of Water and Determination of Effective Contact Angles in the Eagle Ford Shale Formation Using Neutron Imaging

Understanding of fundamental processes and prediction of optimal parameters during the horizontal drilling and hydraulic fracturing process results in economically effective improvement of oil and natural gas extraction. Although modern analytical and computational models can capture fracture growth, there is a lack of experimental data on spontaneous imbibition and wettability in oil and gas reservoirs for the validation of further model development. In this work, we used neutron im- aging to measure the spontaneous imbibition of water into fractures of Eagle Ford shale with known geometries and fracture orientations. An analytical solution for a set of nonlinear second-order diffe- rential equations was applied to the measured imbibition data to determine effective contact angles. The analytical solution fit the measured imbibition data reasonably well and determined effective con- tact angles that were slightly higher than static contact angles due to effects of in-situ changes in veloci- ty, surface roughness, and heterogeneity of mineral surfaces on the fracture surface. Additionally, small fracture widths may have retarded imbibition and affected model fits, which suggests that aver- age fracture widths are not satisfactory for modeling imbibition in natural systems.

Effect of Open Porosity of Y2O3 Ceramic on the Apparent Contact Angles and Interactions Between Ti47Al Alloys and Y2O3 Ceramic

The effect of open porosity of Y2O3ceramic on the apparent contact angle and interaction between molten Ti47 Al alloy and Y2O3ceramic substrates under pure Ar was investigated by using a sessile drop method at 1600 °C. As the open porosity increased from 9.6% to 30.3%, the spreading rate of molten Ti47 Al alloys on Y2O3ceramic substrates reduced from 2.3 to 1.1°/s; meanwhile, the final equilibrium contact angles increased from 55.8° to 63.6°. The microstructure observations revealed that with increasing the open porosity of the Y2O3substrates, the thickness of sand adhesion at the interfaces of the alloy droplets increased from 5.4 to 15.7 lm, and ceramic particles in the alloy matrix increased as well. The increasing contact area between the molten alloy and the substrate played a dominant role in determining the interaction on Ti Al/Y2O3interface.

Contact Angle Determination in Multicomponent Lattice Boltzmann Simulations

Droplets on hydrophobic surfaces are ubiquitous in microfluidic applications and there exists a number of commonly used multicomponent and multiphase lattice Boltzmann schemes to study such systems.In this paper we focus on a popular implementation of a multicomponent model as introduced by Shan and Chen.Here,interactions between different components are implemented as repulsive forces whose strength is determined by model parameters.In this paper we present simulations of a droplet on a hydrophobic surface.We investigate the dependence of the contact angle on the simulation parameters and quantitatively compare different approaches to determine it.Results show that the method is capable of modelling the whole range of contact angles.We find that the a priori determination of the contact angle is depending on the simulation parameters with an uncertainty of 10%to 20%.