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.

INFLUENCE OF TOOL HELIX ANGLE ON STABILITY IN HIGH-SPEED MILLING PROCESS

An integrated dynamic model considering the influence of the helix angle is developed through dividing the cutting process into three cutting processes： uninterrupted, entry, and exit cutting processes. The semi-discretized technique is used to approximate the finite dimensional Floquet transition matrix of the dynamic control equation to determine the stability of milling process. The stability charts for helix mills are obtained. Results show that the helix angle plays an important role in the stability of milling process. The stability regions with helix angle become larger than those without helix angle. Some ＂islands＂ are presented in the stability charts, and ＂island＂ locations are determined by the relation between the axial depth of cut and the helix pitch. The ＂islands＂ are connected by the ＂bridge＂ by the effects of entry and exit cutting processes. The theoretical results are validated by milling experiments.

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.

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.

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.

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.

Dynamic Stability Analysis of Cages in High-Speed Oil-Lubricated Angular Contact Ball Bearings

To investigate the cage stability of high-speed oil-lubricated angular contact ball bearings, a dynamic model of cages is developed on the basis of Gupta’s and Meeks’ work. The model can simulate the cage motion under oil lubrication with all six degrees of freedom. Particularly, the model introduces oil-film damping and hysteresis damping, and deals with the collision contact as imperfect elastic contact. In addition, the effects of inner ring rotational speed, the ratio of pocket clearance to guiding clearance and applied load on the cage stability are investigated by simulating the cage motion with the model. The results can provide a theoretical basis for the design of ball bearing parameters.

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.

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.

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.

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.

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.

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.

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.

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.

Hydraulic support stability control of fully mechanized top coal caving face with steep coal seams based on instable critical angle

Analyzed the support instable mode of sliding,tripping,and so on,and believed the key point of the support stability control of fully mechanized coal caving face with steep coal seams was to maintain that the seam true angle was less than the hydraulic support instability critical angle.Through the layout of oblique face,the improvement of support setting load,the control of mining height and nonskid platform,the group support system of end face,the advance optimization of conveyor and support,and the other control tech- nical measures,the true angle of the seam is reduced and the instable critical angle of the support is increased,the hydraulic support stability of fully mechanized coal caving face with steep coal seams is effectively controlled.

Optimization of Slope Angle and Its Seismic Stability: A Case Study for the Proposed Open Pit Coalmine in Phulbari,NW Bangladesh

The present study reflects upon the results of substantial program of two-dimensional Finite Element Method （FEM） numerical analyses of the open pit that links to slope angle optimization associated with the safety factor of the pit slope of a coal mine in Bangladesh. In the present analyses, two types of models have been presented. The first model estimates safety factor without seismic effect on the overall pit slope of the model; the second model incorporates safety factor with seismic stability of the model. The calculated optimum slope angle of the first model is 31% with a rational safety factor of 1.51, prior to the seismic effect. However, the value is reduced to 0.93, 0.82, and 0.72, after we applies the seismic effect in the second model with M6, M6.5, and M7, respectively. Finally, our modeling results emphasize that for the case of the proposed Phulbari coalmine, there is extremely high prospect for causing massive slope failure along the optimum pit slope angle with 31% if the mine area felt seismic shaking, like the Sikkim （in northern India） earthquake with M6.9 on September 18, 2011.

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.