• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Transient study of droplet oscillation characteristics driven by an electric field

    2023-12-15 11:48:20YanFeiGao高燕飛WeiFengHe何緯峰AdamAbdalazeemQiLeShi施其樂JiRongZhang張繼榮PengFeiSu蘇鵬飛SiYongYu俞思涌ZhaoHuiYao姚照輝andDongHan韓東
    Chinese Physics B 2023年12期
    關(guān)鍵詞:韓東鵬飛

    Yan-Fei Gao(高燕飛),Wei-Feng He(何緯峰),?,Adam Abdalazeem,Qi-Le Shi(施其樂), Ji-Rong Zhang(張繼榮),Peng-Fei Su(蘇鵬飛), Si-Yong Yu(俞思涌), Zhao-Hui Yao(姚照輝), and Dong Han(韓東)

    1Advanced Energy Conservation Research Group(AECRG),College of Energy and Power Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

    2Dongfang Turbine Co.,Ltd,Deyang 618000,China

    Keywords: electrowetting,dynamic contact angle,level set model,droplet oscillation

    1.Introduction

    As widespread phenomena in various industrial fields(such as electrostatic spraying,[1]electric demulsification[2]and microfluidics[3]), droplet deformation, breakage and movement in an electric field have always been important areas of research.In particular, the wettability of droplets on solid surfaces has attracted much attention in the fields of microfluidics and heat transfer.

    The deformation, movement and wettability of droplets in an electric field are affected by many factors such as droplet location, quantity, diameter, electric field intensity,electric field frequency, fluid physical properties, surfactant and fluid type.[4]The wettability of droplets on a solid surface changes under the electric field; this is called the electrowetting phenomenon.[5]After years of development, electrowetting has been able to realize the transport of droplets between the control electrodes,[6]the directional transport of droplets in the oil phase[7]and the directional transport of underwater oil droplets.[8]Through electrowetting, droplet drive can be realized on a changing two-dimensional array electrode or surface, for example, separation, merging, mixing and transportation.Due to the advantages of in situ control, fast response, flexible manipulation and low energy consumption,electrowetting technology has been widely used in fields of microfluidics such as optics,displays,chip laboratories,printing and separation.[9]

    Some scholars have conducted many experiments and theoretical studies on electrowetting to understand how droplets interact with a solid surface under the influence of electric fields.Moreover, in recent years the study of electrowetting phenomena has begun to shift from surface characteristics to the internal mechanism.Zhanget al.[10]used a DC piezoelectric voltage to drive an electrowetting system to reduce the sliding resistance at a solid-liquid interface.The friction and slip behavior of the solid-liquid interface on a rough surface under the applied voltage was investigated.The results showed that the unstable region of rough slip behavior of droplets on the surface cannot be explained by the electrowetting equation.Heet al.[11]studied the wetting and dewetting behavior of nanodroplets with different molecular numbers on the surface of a nano-column array.The scale effect was tested by molecular dynamics (MD) simulation with or without an applied electric field.Ahmadet al.[12]reported numerical simulations and experiments on electrowetting-induced oscillatory droplets under different hydrophobic conditions,a phasefield based code with a dynamic contact angle model was used to study the droplet dynamics.Hydrophobicity of the substrate intensified the deformation and internal flow structures of the oscillating droplet.It also influenced the phase difference between the contact angle and the contact radius,producing three different phase regimes.The amplitude and frequency of the droplet oscillation change differently with the surface wettability in different phase regimes.Koet al.[13]observed hydrodynamic flow in droplets using an AC voltage from a configuration with air as the ambient phase.The flow was observed using a laser sheet and fluorescent tracers,and a toroidal vortex flow was reported.Furthermore,droplet oscillations were simultaneously observed and it was explained that the toroidal flow originates from such oscillations.Zhanget al.[14]used a DC piezoswing voltage to drive the electrowetting system to reduce the slip resistance of the solid-liquid interface.The results of experimental and theoretical analysis showed that with increase in the piezoswing rate,the slip amplitude of the contact line under electrowetting greatly increased while the corresponding slip frequency decreased.Kanget al.[15]found that under probe-type electrowetting there is vortex flow in the droplet, and this vortex flow changes direction with the frequency of applied voltage.Zhanget al.[16]conducted an MD simulation to study the static and dynamic wetting of water nanodroplets on the surface of nanostructures in the presence of a vertical electric field.Andreaset al.[17]studied the influence of parameters such as density, viscosity and mass on the electrowetting oscillation process and gave the simulation results; it turned out that only electrical grounding from below leads to utilizable oscillations.Markodimitrakiset al.[18]used experiments to prove and calculate the influence of the elasticity and thickness of the medium on the beginning of antenna saturation.The results show that the elastic effect is very important,especially when the thickness of the dielectric layer is less than 10 μm; for thicknesses greater than 20 μm the elastic effect is negligible.They attributed this finding to the effect of dielectric thickness on the electric field as well as the distribution of induced electrical stress near the threephase contact line(TCL).Malket al.[19]dealt with a characteristic hydrodynamic flow appearing in droplets actuated by electrowetting-on-dielectric(EWOD)with an AC voltage.In the coplanar electrode configuration,two pairs of vortex flows were observed to form in a droplet centered on the electrode gap.At the same time, droplet oscillations induced by AC EWOD were also revealed under stroboscopic lighting.These experiments show that vortex location can be controlled by frequency actuation with a fair degree of reproducibility.

    Based on the droplet dynamics, we can conclude that revealing the dynamic contact behavior and internal flow mechanism of the electrowetting process is essential for the performance prediction and design of advanced electrowetting devices.The effects of droplet physical characteristics,[17]electric field magnitude,[17,18]polarity[10,14]and wall hydrophobicity[12,13]on the electrowetting phenomenon under DC or AC electric fields have been extensively studied.However,the internal flow field mechanism of droplets under alternating current electrowetting(ACEW),as well as the effects of voltage frequency and initial phase angle on the dynamic contact behavior of droplets,have not been thoroughly and completely investigated.Meanwhile,the connection between physical parameters such as pressure,kinetic energy and force on droplets under ACEW and the oscillation process has not been looked at so far.To better simulate the variation of droplet contact angle,an axisymmetric model and dynamic contact angle theory are introduced in this paper.In addition, a transient numerical model of the force on the droplet is also proposed, and the variation of the droplet surface pressure is obtained.The dynamic contact behavior of droplets and the mechanism of variation of the internal flow field are first looked at from a new perspective by analyzing the force and pressure variation on droplets.Furthermore,the intrinsic connection between change in droplet kinetic energy and droplet oscillation is investigated,and the relationship between droplet velocity,energy and kinetic energy is analyzed.The proposed dynamic contact behavior and internal flow field changes of droplets under different environments provide theoretical support for the subsequent electrowetting research.

    2.Numerical models and solution methods

    2.1.Dynamic contact angle model

    The present work explores the electrowetting effect of a sessile droplet on a solid surface coated with a hydrophobic dielectric material.The basic principle of electrowetting on a medium is shown in Fig.1.In the electrowetting process the surface of the plate is usually coated with a dielectric layer to prevent electrolysis of the droplet under high voltage.In the same way a hydrophobic layer is applied to the dielectric layer to increase the hydrophobicity of the wall surface,[20]in order to increase the ability to change the contact angle:θs,OFFis the contact angle when no electric field is applied andθs,ONis the contact angle when an electric field is applied.The surface tensions between solid/liquid,liquid/gas and solid/gas are denoted byσSL,σLGandσSG,respectively.

    The surface tension between solid/liquid can be expressed by the Young equation

    whereε0,εdanddare the vacuum dielectric constant,dielectric constant and dielectric layer thickness, respectively.Formula (3) represents the contact angle of the droplet under an electric field with applied voltage(θs,ON).

    In electrowetting, an electric field force (Fe=ε0εdV2/(2d))drives the droplet along the TCL,friction resistance(Ff)and packing medium resistance(FD)as forward resistance.Considering a droplet as an unbounded sphere moving in air, its drag force is calculated asFD=0.5CDADρfU2,whereCD,AD,ρfandUdenote the drag coefficient,projected area,air density and droplet velocity,respectively.[13]According to the observation of Oprinset al.,[22]it is found that when air is the filling medium the resistance can be ignored.

    Fig.1.Schematic diagram of the principle of electrowetting on a medium.

    The imbalance of electric field force and friction force will cause acceleration on the contact line.Since the mass near the contact line is very small, the force generated by acceleration is not considered in deriving the dynamic contact angle.Thus,the resultant force(Fnet)of the oscillating droplet along the TCL direction can be written as

    Thus, the final expression for the instantaneous dynamic contact angle under electrowetting with voltageVcan be written as[14]

    Due to the singularity of the droplet at the contact line,obtaining an accurate contact linear velocityUcl(t) is a challenge.If the wall is set as a no-slip boundary, the contact line cannot move.In reality, however, the contact line does move,resulting in infinite viscous shear forces and divergent drag on the wall.To avoid this,the Navier sliding boundary condition(uslip=β?u/?y) is introduced to represent the contact line motion as a slip, whereβis the slip length, i.e., the distance from the boundary, where the velocity of linear extrapolation will reach zero.In addition, since the model is an axisymmetric regular geometry model, the contact linear velocity in Eq.(6) can be estimated as the rate of change of the droplet contact radius,which is given by[23]

    whereRis the radius of the droplet-wetting area.

    Moreover,when the friction law on the contact line is linear, the friction coefficientfcldepends on the tension interaction on the contact line, which has the same units as the viscosity and can be measured from experiments or molecular dynamics simulations.Meanwhile, Chenget al.[24]showed that the larger the slip length,the smaller the obstruction effect of the wall on the fluid.The wall resistance characteristics can be changed by adjusting the slip length.

    2.2.Numerical model

    2.2.1.Computational domain and boundary conditions

    In this paper, the numerical research is carried out in a two-dimensional axisymmetric computational domain.As shown in Fig.2(a),the droplet is assumed to be deionized water,the ambient medium is air and both the droplet and air are incompressible fluids.Layer 1 is the dielectric layer with a hydrophobic layer;layer 2 is the negative electrode and the probe is the positive electrode.Since the probe is very thin,it has little influence on the droplet flow field and is ignored in the calculation domain.After a voltage is applied, negative charges accumulate on the surface of layer 2 and positive charges accumulate on the surface of layer 1 inside the droplet; the closer to the TCL, the greater the density of positive charges accumulated on the surface of layer 2.An electric field is formed between the positive and negative charges,which disturbs the droplet.At the initial time, the droplet velocity is 0, and the air condition outside the droplet is atmospheric pressure.The droplet interface is tracked by the level set variable(φ),where the droplet has a value ofφequal to 1 and the surrounding air has a value ofφequal to 0.In addition,the numerical calculations are based on the following assumptions:

    (a)The shape of the droplet is assumed to be a spherical cap.

    (b) The voltage drop along the working fluid is ignored,thus,the droplet is assumed to be a conductor.

    (c)The effect of surfactants or any other foreign particles on deionized water is not considered.

    The mathematical model assumes that the fluid is laminar and incompressible.The laminar Navier-Stokes equations are established for droplet and air, respectively, and the effect of surface tension of the droplet is considered.[25]

    In the simulation of axisymmetric droplet diffusion,several boundary conditions are set to restore the actual scenario.S1 is the symmetric boundary,S2 is set as the wetted wall and S3 is set as the open boundary,so that the model converges by changing the system pressure release when the droplet moves.To accurately capture the influence of the stress tensor on the droplet, the mesh and wetting wall boundary near the droplet surface are specially refined,as shown in Fig.2(b).The final calculation results pass the grid independence numerical test,and the total number of grids is 14412.

    Fig.2.Geometric model for electrowetting simulation: (a) computational domains and boundary conditions;(b)finite element meshing of the model geometry.

    2.2.2.Governing equation

    The governing equations in this paper include continuity and momentum equations of level set variables.The details are as follows:

    whereg,pandFstare gravity, pressure and surface tension,respectively.

    The level set variable (φ) is used to track two phases,

    whereφ= 1 represents the secondary phase (i.e., droplet)andφ=0 represents the primary phase(i.e., air).Therefore,φ=0.5 denotes the droplet interface,where the level set variable(φ)can be calculated using the following equation:

    whereεis the interface thickness parameter andγis the reinitialization parameter, and for numerical calculations the appropriate choice isε=h,wherehis the grid cell size.

    The surface tension in Eq.(9)acting on the interface can be calculated by the normal vector of the interface and the curvature of the interface,as shown below:[23]

    Theδfunction is approximately a smoothing function

    whereσrepresents the surface tension coefficient,nrepresents the unit normal vector at the interface,krepresents the curvature of the fluid interface andδrepresents the Dirac function.

    In addition,the fluid domain is divided into two materials by the interface, and in each subdomain the material properties are constant.However, the density and viscosity are discontinuous throughout the solution domain.To simplify the calculation so that the values of density,viscosity and surface tension can continuously transition from the air to the droplet,the following formula is used:[25]

    where the subscripts g and l represent the gas and liquid,μlandμgindicate the dynamic viscosity of droplet and air, andρlandρgindicate the density of droplet and air,respectively.

    2.3.Model validation

    The friction coefficientfclcan be measured by fitting molecular dynamics simulation data to experimental data.In general, when contact angle hysteresis is not considered, it is found that the larger values (fcl= 0.2-0.4 N·s·m-2) fit the experimental data well,[26-28]otherwise a smaller value(fcl=0.18 N·s·m-2) is more suitable.[29,30]In order to verify the correctness and accuracy of the model constructed in this paper,other materials have the same characteristics under the same voltage(32 V DC)(see Table 1).In the simulation in this article,fcl=0.1 N·s·m-2andfcl=0.15 N·s·m-2are used,as shown in Fig.3.Whenβ=0.3μm andfcl=0.1 N·s·m-2,molecular dynamics simulation results data more accurately predict the experimental data of Chenget al.[24]The data obtained from the numerical simulation are basically consistent with the experimental data, and the error of the data is very small, which indicates the correctness of the model.Therefore this article choosesβ=0.3μm andfcl=0.1 N·s·m-2for subsequent simulation.

    Table 1.Material properties of liquids/substrates used in direct current electrowetting experiments and simulations.

    Fig.3.Comparison of experimental and numerical results at different times when the static contact angle is 118?.

    2.4.Force analysis model

    By analyzing the force balance of the droplet under electrowetting,the relationship between the force change and other parameters of the droplet can be obtained.Chenget al.[24]observed that viscous dissipation is not obvious in droplet oscillation dynamics with an AC electric field.In addition,Ahmadet al.[14]observed that the viscous force is negligible compared with the applied electricity and friction.Therefore, the influence of viscous force is ignored in this model.In the process of droplet oscillation,the friction forceFf=fclUclon the contact line during the oscillation of the droplet is the main part of the resistance.Therefore,Ffacts as a resistance to the electric field force in the mechanical analysis.In the process of droplet oscillation under electrowetting, droplet motion starts from the TCL.Therefore, in the force balance analysis, the dominant force along the TCL ignores other forces in the vertical direction.

    The applied sinusoidal waveform voltage(V)is given by

    whereK=ε0εd/(2d).

    3.Results and analysis

    In the simulation calculation,the droplet volume is 5μl.The initial shape of the droplet is a spherical crown, and the initial contact angle is 110?.The total thickness of the dielectric and hydrophobic layerd=2.5 μm and the total effective relative dielectric constantεd= 2.8, The droplet is deionized water,withρ=997 kg·m-3and kinematic viscosityμ=1.01×10-3Pa·s.The ambient gas is air,and the droplet is in an equilibrium state before the voltage is applied(t=0 ms).

    3.1.Dynamic contact characteristics of droplets under ACEW

    Figure 4 shows the variation of droplet contact radius with time,whereRwis the wetting radius of the droplet.The amplitude of the droplet is the displacement of the droplet contact line moving forward along the wall during diffusion,and is represented by the symbolAm.After completion of the first oscillation,the droplet maintains a new contact radius higher than the initial contact radius and continues to oscillate with the maximum possible diffusion; then, the time it takes to return to the original contact radius during a certain period of oscillation is called the stable oscillation periodT.As can be seen from Fig.4, the variation of the displacementRwof the droplet contact line tends to be a sinusoidal waveform.The AC amplitude is kept constant,and its magnitude is 75 V.When the AC frequency increases from 50 Hz to 500 Hz,the oscillating wave amplitudes after the droplet stabilization are 0.036 mm,0.016 mm,0.013 mm and 0.002 mm,respectively,and the oscillation periodsTof the droplet wetting radius are 11 ms, 4 ms, 2 ms and 1 ms, respectively.It can be seen that with the increase in AC frequency, the stable oscillation period of the droplet decreases stepwise,and the amplitude of the stable waveform after oscillation also decreases stepwise.It can be seen from the analysis that the surface of the droplet under stimulation with different frequencies presents different surface waves,which causes the movement of the contact line.In fact, there is a delay between the movement of the droplet contact line and the change in the electric field force.The higher the AC frequency is, the faster the rate of change the electric field force will be: if the electric field force changes too fast, it will hinder the process of droplet contact wire movement, which shows that the larger the AC frequency is,the smaller the oscillation amplitude of the droplet is.It can be seen from Fig.4(a)that whenf=500 Hz,the droplet oscillation amplitude is very small, which is similar to the variation trend of droplet wetting radius under direct current electrowetting(the DC voltage is the effective value corresponding to the AC amplitude).

    Fig.4.Dynamics of droplets under ACEW with time.(a)Variation of droplet wetting radius with time at different frequencies.(b)Oscillation period of droplet wetting radius at different frequencies.

    Figure 5 shows the time variation of different forces(electric field forceFe,contact line frictionFfand net forceFnet)on the droplet atV0=75 V,f=50 Hz and?=0?.As shown in Fig.5, the line of contact frictionFf=fclUcl, the line of contact friction force and the direction depend on the value of the linear velocity.The speed changes along the sine wave,so the line of contact friction also presents a sinusoidal waveform change, with the positive and negative friction corresponding to expanding and contracting behavior of the contact wires.As shown in Fig.4(a), withint=0-6 ms, the droplet amplitude rapidly increases to a peak,and aftert=6 ms,the droplet amplitude presents a waveform oscillation, corresponding to Fig.5.The droplet velocity reaches its maximum at the initial time, the contact line friction reaches its maximum and then the droplet size presents waveform fluctuation.As Ahmadet al.[12]mentioned, the magnitude and direction of friction depend on the speed of the contact line.The positive and negative values of friction represent the diffusion stage and the contraction stage, respectively.Friction increases with time,and reaches a maximum when the electric field force reaches a peak.At the same time,it is accompanied by the maximum change in diffusion radius.In addition,the staticFnetsize near the droplet contact line in Fig.5 also changes with a waveform oscillation, which further explains that the variation curve of stable droplet oscillation amplitude under the action of electrowetting is a sinusoidal waveform.

    Fig.5.Change of force on the contact line with time (V0 = 75 V,f =50 Hz,? =0?).

    Figure 6 shows the change in droplet contact behavior over time when the AC voltage is the same and the initial phase angle is different.As can be seen from Fig.6, when the initial phase angle is 0?, 45?or 90?there is no significant difference in the droplet wetting radius,indicating that the initial phase angle does not affect the change in the droplet wetting radius.However,the initial phase angle is related to the initial phase angle of the droplet oscillation curve.For?=45?, 0?and 90?,the droplet reaches stable oscillation successively and then continues to move with the same stable oscillation period.

    Fig.6.Change of droplet contact radius under different phase angles.

    3.2.Droplet internal flow under ACEW

    Fig.7.Change of average pressure at the gas-liquid interface with time.

    Fig.8.The change of droplet morphology with different frequency.(a)Internal flow field variation.(b)Vortex and wave crest relationship diagram.

    Under the action of an electric field force, the contact angle of stationary droplets changes, as shown in Fig.4(a).The droplet presents a sinusoidal oscillation motion along the wall.It can be seen that under the effect of electrowetting,the static internal flow of the droplet is changed into an internal eddy current under the stimulation of an electric field.Figure 7 shows the changes in the average pressure at the gas-liquid surface with time at different frequencies.It can be seen from Fig.7 that under AC stimulation, the pressure at the interface rapidly increases from close to atmospheric pressure to the maximum pressure value, and then the interface pressure changes to show waveforms.The reason for the pressure change can be obtained by referring to the change in the droplet contact radius over time in Fig.4(a).In the initial deformation stage of the droplet, the force balance of the droplet is broken under the stimulation of the electric field force,and a certain kinetic energy is accumulated,which eventually leads to the accumulation of pressure at the edge of the droplet.Under the action of pressure,the droplet reciprocates,resulting in the accelerated retreat of the contact line and oscillation of the wetting radius.At the same time,since the voltage applied to the droplet constantly changes with time,the pressure near the droplet contact line will also constantly change with the trend of voltage variation.In addition,the larger the frequencyfis, the smaller the accumulated pressure oscillation amplitude at the interface will be.The reason for this is that the pressure change has a delay compared with the voltage change.The larger the voltage frequency is,the faster the voltage change will be, so the change of electric field force will also be accelerated.Therefore,an electric field force that changes too quickly will interfere with the pressure accumulation process at the interface.The larger the frequencyfis,the stronger the interference will be,and the smaller the eventual change of the interface pressure will be.

    Figure 8 shows the change of droplet morphology over time with different frequencies.Figure 8(a)shows the velocity vector field and pressure distribution inside the droplet at different frequencies.In this figure,half an oscillation period is selected for modesP2andP4and one oscillation period is selected for modesP8.In the process of droplet oscillation,each peak value of droplet oscillation corresponds to a resonance modePn(n=2,4,...), and the value ofndepends on the number of wave peaks at the droplet interface.As can be seen from Fig.4, the higher the resonance mode is, the smaller the droplet oscillation amplitude is.In addition, the recirculating eddies can be identified from the streamline profile and the number of eddies matches their resonance modes.For example, two vortices can be observed inP2mode, four inP4mode and eight inP8mode,and most of the vortex centers are located on or near the free surface.It is also noted that the oscillation amplitude of the droplet decreases continuously as the frequencyfincreases from 50 Hz to 250 Hz.As can be seen from Fig.8(a), the oscillation process of the droplet decreases continuously as the oscillation mode of the droplet changes from modeP2to modeP8, and the size of the vortex at the interface also decreases continuously.As mentioned by Yiet al.,[23]when a droplet is actuated under ACEW,the droplet exhibits time-harmonic shape oscillations.The oscillation amplitude is found to decrease with increasing actuation frequency due to the dominant effect of inertia over other forces.The surface wave propagates with a similar phase velocity to capillary waves.

    The connection between the droplet surface pressure and the resonance mode can be investigated through Figs.7 and 8.Whenf=50 Hz,the pressure changes slowly,so the droplet surface forces change more slowly and can be seen as a more stable oscillation.Due to the slow change of droplet surface perturbation, there are fewer wave peaks and vortices on the surface.At the same time,whenf=250 Hz the rate of pressure change is accelerated,so the force balance on the droplet surface changes dramatically.Due to the strong change in perturbation on the droplet surface,the wave and vortex currents on the surface also increase.In addition, the pressure amplitude becomes smaller fromf=50 Hz to 250 Hz and the intensity of droplet surface perturbation decreases,resulting in a reduction in the size of wave crests and vortices.

    Figure 8(b) shows the quantitative correlation between the number of vorticesnon the droplet surface and the number of wave peakswat the interface during the oscillation.Resonance modes areP2corresponding to one wave,P4to two waves,P8to four waves andP12to six waves.It can be concluded from Fig.8(b) thatw=z/2, namely, the number of vortices on the droplet surfacezis always twice the number of wave peaks, and the interface wave peaks caused by droplet oscillation are always symmetric along the center line.The largerfis, the more frequently the interface is disturbed, but the intensity of the disturbance of the electric field force is decreasing.Therefore, under voltage stimulation, the larger frequency of the droplet the more surface crests and vortices there are and the smaller the size of ripples generated by the droplet surface is.

    4.Conclusions

    Based on our numerical simulation, the dynamic contact process and internal flow field of droplets under electrowetting are studied in this paper.The following conclusions are drawn.

    1.The dynamic contact angle model is used to simulate and predict the electrowetting process more reasonably, and the change in droplet contact radius under different frequencies and initial phase angles is studied.When the AC frequency increases from 50 Hz to 500 Hz, the oscillating wave amplitudes of droplet stabilization are 0.036 mm, 0.016 mm,0.013 mm and 0.002 mm,respectively,and the oscillation periodsTof the droplet wetting radius are 11 ms, 4 ms, 2 ms and 1 ms, respectively.With increase in frequency, the stable oscillation period of the droplet decreases stepwise, and the amplitude of the stable waveform after oscillation also decreases stepwise.In addition, when the initial phase angle is 0?,45?or 90?,there is no significant difference in the droplet wetting radius,indicating that the initial phase angle does not affect the change in the droplet wetting radius.

    2.A model of droplet force variation in the electrowetting process is proposed, and it is concluded that the friction of the contact line presents sinusoidal waveform changes.The positive and negative friction forces, respectively, correspond to the expansion and contraction behaviors of the contact line.The staticFnetnear the droplet contact line also changes as a waveform oscillation, which further explains why the fluctuation curve of stable droplet oscillation amplitude under the action of electrowetting is a sinusoidal waveform.

    3.In the case of ACEW, the droplet interface will show velocity vortices and oscillating ripples corresponding to the frequency.As the frequencyfincreases from 50 Hz to 250 Hz the oscillation amplitude of the droplet decreases continuously, and the oscillation mode of the droplet changes fromP2toP8mode.The oscillation process of the droplet decreases continuously,and the vortex size at the interface also decreases continuously.

    Acknowledgements

    The authors expressed their sincere gratitude to the Natural Science Foundation of Jiangsu Province (Grant No.BK2020194), the Basic Research Fund of Central University (Grant No.NS2022026), and the Graduate Research and Practice Innovation Program(Grant No.xcxjh20220215).

    猜你喜歡
    韓東鵬飛
    一匹馬
    詩林(2022年2期)2022-04-13 08:38:49
    可愛的敘事者——讀韓東短篇小說《素素與李蕓》
    都市(2022年1期)2022-03-08 02:23:34
    Quality Control for Traditional Medicines - Chinese Crude Drugs
    為了避嫌
    雜文月刊(2019年18期)2019-12-04 08:30:40
    懲“前”毖“后”
    21世紀(jì)(2019年10期)2019-11-02 03:17:02
    執(zhí)“迷”不悟
    21世紀(jì)(2019年10期)2019-11-02 03:17:02
    舉賢
    21世紀(jì)(2019年9期)2019-10-12 06:33:44
    重新做人
    詩潮(2017年4期)2017-12-05 10:16:18
    落后的家鄉(xiāng)
    上海故事(2017年4期)2017-04-18 16:30:59
    迷信的老爸
    三月三(2016年7期)2016-08-23 10:18:59
    波多野结衣高清无吗| 国产精品二区激情视频| 老司机靠b影院| 黄色成人免费大全| 日日夜夜操网爽| 国产精品 欧美亚洲| 成人国语在线视频| 别揉我奶头~嗯~啊~动态视频| 欧美黑人巨大hd| a级毛片a级免费在线| 国产欧美日韩精品亚洲av| 国产男靠女视频免费网站| av电影中文网址| 久久午夜亚洲精品久久| 亚洲无线在线观看| 美女高潮喷水抽搐中文字幕| 丰满的人妻完整版| 人人妻,人人澡人人爽秒播| 精品一区二区三区视频在线观看免费| 国产高清视频在线播放一区| 一本大道久久a久久精品| 很黄的视频免费| 亚洲成av人片免费观看| a级毛片在线看网站| 成人亚洲精品一区在线观看| 久久久久久久久久黄片| 欧美午夜高清在线| 美女午夜性视频免费| 久久久国产欧美日韩av| 国内少妇人妻偷人精品xxx网站 | 一a级毛片在线观看| 丝袜在线中文字幕| 国产亚洲精品久久久久久毛片| 亚洲va日本ⅴa欧美va伊人久久| 黑人操中国人逼视频| 亚洲av中文字字幕乱码综合 | 神马国产精品三级电影在线观看 | 国产黄片美女视频| 窝窝影院91人妻| 波多野结衣巨乳人妻| 国产精品电影一区二区三区| 国产99久久九九免费精品| 怎么达到女性高潮| 男男h啪啪无遮挡| 久久 成人 亚洲| 中文字幕最新亚洲高清| 一本精品99久久精品77| 亚洲精品国产一区二区精华液| 国产成人一区二区三区免费视频网站| 色播亚洲综合网| 国产一区二区在线av高清观看| av中文乱码字幕在线| 99久久久亚洲精品蜜臀av| 免费在线观看影片大全网站| 日韩中文字幕欧美一区二区| 久久精品91蜜桃| 国产精品免费视频内射| 日韩精品中文字幕看吧| 婷婷精品国产亚洲av| 无限看片的www在线观看| 精品卡一卡二卡四卡免费| 黄色毛片三级朝国网站| 国产激情欧美一区二区| 黄色毛片三级朝国网站| 亚洲国产欧美网| 久久精品亚洲精品国产色婷小说| 国产亚洲精品综合一区在线观看 | 99久久无色码亚洲精品果冻| 成在线人永久免费视频| 国产高清激情床上av| www日本黄色视频网| 日本 av在线| 久久久国产欧美日韩av| 每晚都被弄得嗷嗷叫到高潮| 欧美+亚洲+日韩+国产| 久久精品91蜜桃| 亚洲精品在线美女| 亚洲色图av天堂| 国语自产精品视频在线第100页| 老熟妇乱子伦视频在线观看| 国产成+人综合+亚洲专区| 久久 成人 亚洲| 欧美日本视频| 99久久99久久久精品蜜桃| 搡老熟女国产l中国老女人| 一级毛片精品| 久久久久久久久中文| 波多野结衣巨乳人妻| 色综合婷婷激情| 色综合婷婷激情| 久久精品国产综合久久久| 黄色毛片三级朝国网站| 日本在线视频免费播放| 日本三级黄在线观看| 成人亚洲精品av一区二区| 成人手机av| 美国免费a级毛片| av欧美777| 久久精品国产亚洲av高清一级| 国产精品野战在线观看| 桃色一区二区三区在线观看| av视频在线观看入口| 久久久久久大精品| 精品国产美女av久久久久小说| 巨乳人妻的诱惑在线观看| 男女午夜视频在线观看| 99国产极品粉嫩在线观看| 国产一级毛片七仙女欲春2 | 午夜福利高清视频| 国产精品电影一区二区三区| 一本精品99久久精品77| 日本三级黄在线观看| 91麻豆av在线| 精品久久蜜臀av无| 亚洲成人久久爱视频| 别揉我奶头~嗯~啊~动态视频| 欧美乱妇无乱码| 成年人黄色毛片网站| 91国产中文字幕| 麻豆av在线久日| 亚洲欧美一区二区三区黑人| 日韩av在线大香蕉| 夜夜爽天天搞| 精品欧美国产一区二区三| 黄片大片在线免费观看| 亚洲精品久久国产高清桃花| 长腿黑丝高跟| 国产私拍福利视频在线观看| 国产蜜桃级精品一区二区三区| 日本 av在线| 亚洲av美国av| 99精品欧美一区二区三区四区| 深夜精品福利| 女生性感内裤真人,穿戴方法视频| 久久香蕉国产精品| 老汉色av国产亚洲站长工具| 久久香蕉国产精品| 欧美激情 高清一区二区三区| 啦啦啦免费观看视频1| 好男人电影高清在线观看| 亚洲 国产 在线| 一区二区三区高清视频在线| 午夜视频精品福利| 少妇粗大呻吟视频| 最好的美女福利视频网| 一区福利在线观看| 99在线人妻在线中文字幕| 变态另类丝袜制服| 日韩欧美免费精品| 又大又爽又粗| 欧美日韩一级在线毛片| 可以在线观看的亚洲视频| 欧美中文日本在线观看视频| 成人亚洲精品av一区二区| 人人澡人人妻人| 好看av亚洲va欧美ⅴa在| 手机成人av网站| 欧美性长视频在线观看| 老司机在亚洲福利影院| 女同久久另类99精品国产91| 每晚都被弄得嗷嗷叫到高潮| 亚洲精品在线观看二区| 一a级毛片在线观看| 亚洲av美国av| 美女高潮到喷水免费观看| 露出奶头的视频| 免费人成视频x8x8入口观看| 视频在线观看一区二区三区| 国产真实乱freesex| 国产麻豆成人av免费视频| 亚洲成a人片在线一区二区| 日本三级黄在线观看| 啦啦啦观看免费观看视频高清| 国产伦一二天堂av在线观看| 搞女人的毛片| 熟女电影av网| 神马国产精品三级电影在线观看 | 国产成人av激情在线播放| 成人精品一区二区免费| 欧美不卡视频在线免费观看 | 亚洲专区国产一区二区| 久久婷婷成人综合色麻豆| 91成人精品电影| 免费在线观看完整版高清| 在线天堂中文资源库| 天天添夜夜摸| 大香蕉久久成人网| 特大巨黑吊av在线直播 | 精品一区二区三区视频在线观看免费| 自线自在国产av| 99re在线观看精品视频| 1024香蕉在线观看| 久久久精品欧美日韩精品| 免费人成视频x8x8入口观看| 国产真实乱freesex| 欧美一级毛片孕妇| www.精华液| 久久久久久久精品吃奶| 啦啦啦免费观看视频1| 久久婷婷人人爽人人干人人爱| 久久久久久久久久黄片| 国产一区二区激情短视频| 欧美在线一区亚洲| 俺也久久电影网| 国产精品久久久久久人妻精品电影| 桃红色精品国产亚洲av| 老司机午夜十八禁免费视频| 亚洲成国产人片在线观看| 天堂影院成人在线观看| 亚洲av片天天在线观看| 99国产精品一区二区三区| 一进一出抽搐gif免费好疼| 欧美av亚洲av综合av国产av| 国产精品二区激情视频| а√天堂www在线а√下载| 久久久久九九精品影院| 欧美成狂野欧美在线观看| www国产在线视频色| 精品久久久久久久久久久久久 | 国产精品乱码一区二三区的特点| 亚洲精品在线美女| 韩国精品一区二区三区| 村上凉子中文字幕在线| 国产主播在线观看一区二区| 长腿黑丝高跟| 99久久无色码亚洲精品果冻| 18美女黄网站色大片免费观看| 在线观看日韩欧美| 国产视频内射| 校园春色视频在线观看| 正在播放国产对白刺激| www.熟女人妻精品国产| 国产v大片淫在线免费观看| 精品日产1卡2卡| 亚洲国产精品久久男人天堂| 国产激情偷乱视频一区二区| svipshipincom国产片| 窝窝影院91人妻| 国产免费男女视频| 欧美三级亚洲精品| 日韩欧美国产一区二区入口| 国产高清激情床上av| 天堂√8在线中文| 1024视频免费在线观看| 成人手机av| 亚洲免费av在线视频| 国产片内射在线| 国产成+人综合+亚洲专区| 精品国产超薄肉色丝袜足j| 午夜视频精品福利| 色哟哟哟哟哟哟| 日韩免费av在线播放| 国产99白浆流出| 一级a爱片免费观看的视频| 亚洲国产欧洲综合997久久, | 亚洲avbb在线观看| 99精品在免费线老司机午夜| 国产久久久一区二区三区| 精品国内亚洲2022精品成人| 欧美国产精品va在线观看不卡| 妹子高潮喷水视频| 一进一出抽搐gif免费好疼| 亚洲av成人不卡在线观看播放网| 国产精品香港三级国产av潘金莲| 久久精品影院6| 中亚洲国语对白在线视频| 性欧美人与动物交配| 色尼玛亚洲综合影院| 一级毛片高清免费大全| 欧美+亚洲+日韩+国产| 亚洲片人在线观看| 国产精品爽爽va在线观看网站 | 久久久久国内视频| 99久久国产精品久久久| 国产片内射在线| 久久久久免费精品人妻一区二区 | 在线观看免费视频日本深夜| 精品电影一区二区在线| 美女大奶头视频| 国产精品,欧美在线| 亚洲人成77777在线视频| 国产色视频综合| 日本在线视频免费播放| 色老头精品视频在线观看| 精品人妻1区二区| 国产午夜精品久久久久久| 在线观看免费日韩欧美大片| 可以免费在线观看a视频的电影网站| 成人精品一区二区免费| 999精品在线视频| 国产一区在线观看成人免费| 淫秽高清视频在线观看| 欧美日韩一级在线毛片| 欧美一级毛片孕妇| 韩国av一区二区三区四区| 曰老女人黄片| 亚洲av成人不卡在线观看播放网| 午夜免费观看网址| 一夜夜www| 久久这里只有精品19| 久久热在线av| 国产伦在线观看视频一区| 老熟妇仑乱视频hdxx| 久久香蕉国产精品| 99在线视频只有这里精品首页| 国产激情久久老熟女| 久久久久免费精品人妻一区二区 | 欧美av亚洲av综合av国产av| 日韩三级视频一区二区三区| www.www免费av| 亚洲男人的天堂狠狠| 国产成人精品久久二区二区免费| 一进一出抽搐gif免费好疼| 色综合站精品国产| 国产区一区二久久| 无限看片的www在线观看| 老汉色∧v一级毛片| 亚洲第一青青草原| 精品久久久久久久末码| 国产v大片淫在线免费观看| 亚洲自偷自拍图片 自拍| 免费看a级黄色片| 国产三级黄色录像| 好男人在线观看高清免费视频 | 日韩 欧美 亚洲 中文字幕| 亚洲性夜色夜夜综合| bbb黄色大片| 亚洲av成人一区二区三| 大型黄色视频在线免费观看| 琪琪午夜伦伦电影理论片6080| 成年人黄色毛片网站| 亚洲国产精品久久男人天堂| www日本在线高清视频| 国产真人三级小视频在线观看| 欧美性猛交╳xxx乱大交人| 日韩高清综合在线| 99热这里只有精品一区 | 熟女电影av网| 精品乱码久久久久久99久播| 亚洲国产欧美一区二区综合| 亚洲男人的天堂狠狠| 黑人操中国人逼视频| 久久国产乱子伦精品免费另类| 欧美性猛交黑人性爽| 非洲黑人性xxxx精品又粗又长| 亚洲av片天天在线观看| 日韩欧美国产一区二区入口| 日韩欧美三级三区| 欧美乱妇无乱码| 国产在线精品亚洲第一网站| 亚洲电影在线观看av| 日本 av在线| 久久中文字幕人妻熟女| 国产极品粉嫩免费观看在线| 人人澡人人妻人| 国产精品一区二区精品视频观看| 国产三级在线视频| 美女高潮到喷水免费观看| 国产av又大| 亚洲 欧美一区二区三区| 18禁观看日本| 久久久国产精品麻豆| 久99久视频精品免费| 久久 成人 亚洲| 日韩精品青青久久久久久| 女性生殖器流出的白浆| 免费看日本二区| 日韩精品中文字幕看吧| 欧美一区二区精品小视频在线| 男女做爰动态图高潮gif福利片| 亚洲黑人精品在线| 色av中文字幕| 亚洲五月色婷婷综合| 国产一卡二卡三卡精品| 俺也久久电影网| 一级毛片高清免费大全| 一区二区三区高清视频在线| 深夜精品福利| 桃红色精品国产亚洲av| 日本一本二区三区精品| 老司机靠b影院| 亚洲男人天堂网一区| 可以在线观看的亚洲视频| 窝窝影院91人妻| 久久久国产欧美日韩av| 久久中文字幕一级| 亚洲人成伊人成综合网2020| 黑人操中国人逼视频| 男人舔女人下体高潮全视频| a在线观看视频网站| 亚洲第一电影网av| 亚洲三区欧美一区| 亚洲久久久国产精品| 久久久久国内视频| 法律面前人人平等表现在哪些方面| 亚洲国产精品合色在线| 午夜福利一区二区在线看| 欧美成狂野欧美在线观看| 国产精品电影一区二区三区| 成人av一区二区三区在线看| www.999成人在线观看| 女警被强在线播放| 91在线观看av| 国产蜜桃级精品一区二区三区| 后天国语完整版免费观看| 免费在线观看日本一区| 色在线成人网| 又大又爽又粗| 最近最新中文字幕大全电影3 | 大型黄色视频在线免费观看| 丝袜美腿诱惑在线| 欧美乱妇无乱码| 久久久久免费精品人妻一区二区 | 久久香蕉国产精品| 美女 人体艺术 gogo| 欧美日韩精品网址| 免费在线观看完整版高清| 久久久精品国产亚洲av高清涩受| 激情在线观看视频在线高清| 岛国视频午夜一区免费看| 性欧美人与动物交配| 麻豆成人av在线观看| 久久香蕉国产精品| 久久草成人影院| 国产视频一区二区在线看| 美女高潮到喷水免费观看| 老司机午夜十八禁免费视频| 黑人巨大精品欧美一区二区mp4| 国产黄a三级三级三级人| 成年免费大片在线观看| 成年版毛片免费区| 久久精品国产清高在天天线| 黄色片一级片一级黄色片| 国产精品乱码一区二三区的特点| 亚洲精品国产区一区二| 在线永久观看黄色视频| 国产欧美日韩一区二区精品| 女性被躁到高潮视频| 美女高潮到喷水免费观看| 欧美成人免费av一区二区三区| 国产午夜福利久久久久久| a级毛片a级免费在线| 可以免费在线观看a视频的电影网站| 手机成人av网站| 长腿黑丝高跟| 日本撒尿小便嘘嘘汇集6| 中文亚洲av片在线观看爽| www.999成人在线观看| 精品久久蜜臀av无| 白带黄色成豆腐渣| 男女床上黄色一级片免费看| 久久这里只有精品19| 老熟妇乱子伦视频在线观看| 欧美三级亚洲精品| 精品久久久久久,| 一本久久中文字幕| 韩国av一区二区三区四区| avwww免费| 欧美人与性动交α欧美精品济南到| 女性被躁到高潮视频| 在线免费观看的www视频| 两人在一起打扑克的视频| 亚洲熟女毛片儿| 免费高清在线观看日韩| 在线播放国产精品三级| 久久久久亚洲av毛片大全| 国产精华一区二区三区| 国产亚洲精品一区二区www| 1024香蕉在线观看| 免费在线观看成人毛片| 亚洲欧美精品综合一区二区三区| 成人免费观看视频高清| svipshipincom国产片| 成人av一区二区三区在线看| 免费人成视频x8x8入口观看| 亚洲 欧美一区二区三区| 啦啦啦免费观看视频1| 1024手机看黄色片| 亚洲一区二区三区不卡视频| 亚洲第一青青草原| 亚洲免费av在线视频| 久久精品91蜜桃| 亚洲七黄色美女视频| 日本在线视频免费播放| 日本黄色视频三级网站网址| 日韩视频一区二区在线观看| 久久久久久久久免费视频了| 亚洲自拍偷在线| 国产熟女午夜一区二区三区| 激情在线观看视频在线高清| 女性生殖器流出的白浆| 亚洲精品国产一区二区精华液| 亚洲精品中文字幕在线视频| 免费女性裸体啪啪无遮挡网站| 脱女人内裤的视频| 国产主播在线观看一区二区| 可以免费在线观看a视频的电影网站| 亚洲成人免费电影在线观看| 久久精品国产亚洲av高清一级| 日日摸夜夜添夜夜添小说| 久久婷婷人人爽人人干人人爱| 国产日本99.免费观看| 欧美三级亚洲精品| 亚洲欧美一区二区三区黑人| 一级毛片精品| 波多野结衣av一区二区av| 91成年电影在线观看| 我的亚洲天堂| 久久天堂一区二区三区四区| www国产在线视频色| 亚洲 国产 在线| 18禁裸乳无遮挡免费网站照片 | 身体一侧抽搐| 亚洲国产欧美一区二区综合| 超碰成人久久| 久久久国产精品麻豆| 淫妇啪啪啪对白视频| 日韩 欧美 亚洲 中文字幕| 亚洲免费av在线视频| 少妇粗大呻吟视频| 在线观看午夜福利视频| 亚洲一区中文字幕在线| 免费高清在线观看日韩| 免费观看精品视频网站| 美女免费视频网站| 最新在线观看一区二区三区| 悠悠久久av| 91国产中文字幕| 色老头精品视频在线观看| 听说在线观看完整版免费高清| 窝窝影院91人妻| 天堂动漫精品| 人人澡人人妻人| 在线免费观看的www视频| 午夜福利成人在线免费观看| 人人妻,人人澡人人爽秒播| 国产欧美日韩一区二区精品| 一区二区三区激情视频| 久久亚洲真实| 国产精品乱码一区二三区的特点| 90打野战视频偷拍视频| 久久热在线av| 国产免费av片在线观看野外av| 午夜福利成人在线免费观看| 午夜免费成人在线视频| 国产国语露脸激情在线看| 亚洲中文字幕一区二区三区有码在线看 | www.999成人在线观看| 午夜久久久久精精品| 国产精品香港三级国产av潘金莲| 99久久精品国产亚洲精品| 最好的美女福利视频网| bbb黄色大片| ponron亚洲| 黄色片一级片一级黄色片| 少妇粗大呻吟视频| 久久午夜亚洲精品久久| 国产一区二区三区视频了| 桃红色精品国产亚洲av| 变态另类成人亚洲欧美熟女| 性色av乱码一区二区三区2| 日韩国内少妇激情av| 日韩视频一区二区在线观看| 看片在线看免费视频| 欧美激情极品国产一区二区三区| 国产99久久九九免费精品| 男女床上黄色一级片免费看| 国产高清videossex| 一区二区日韩欧美中文字幕| 色尼玛亚洲综合影院| 香蕉av资源在线| 国产aⅴ精品一区二区三区波| 久久精品aⅴ一区二区三区四区| 校园春色视频在线观看| avwww免费| 欧美中文综合在线视频| 日本 av在线| 99热这里只有精品一区 | 99精品欧美一区二区三区四区| 一本精品99久久精品77| 日韩欧美三级三区| 最新美女视频免费是黄的| 男女床上黄色一级片免费看| 夜夜躁狠狠躁天天躁| 波多野结衣高清作品| 免费在线观看日本一区| 哪里可以看免费的av片| 怎么达到女性高潮| 女生性感内裤真人,穿戴方法视频| 啦啦啦韩国在线观看视频| 久久久水蜜桃国产精品网| 中文字幕av电影在线播放| 99在线人妻在线中文字幕| 亚洲中文日韩欧美视频| 免费观看人在逋| 熟妇人妻久久中文字幕3abv| 51午夜福利影视在线观看| 欧美激情久久久久久爽电影| 啪啪无遮挡十八禁网站| 白带黄色成豆腐渣| 欧美成人一区二区免费高清观看 | 俺也久久电影网| 欧美亚洲日本最大视频资源| 国产熟女午夜一区二区三区| 日本免费一区二区三区高清不卡| x7x7x7水蜜桃| 丁香欧美五月| 日本在线视频免费播放| 午夜免费观看网址| 国产精品一区二区免费欧美| 十八禁网站免费在线| 麻豆一二三区av精品| 成在线人永久免费视频| 免费在线观看视频国产中文字幕亚洲| 亚洲av熟女|