Theoretical analysis of droplet transition from Cassie to Wenzel state

Whether droplets transit from the Cassie to the Wenzel state(C–W) on a textured surface is the touchstone that the superhydrophobicity of the surface is still maintained. However, the C–W transition mechanism, especially the spontaneous transition of small droplets, is still not very clear to date. The interface free energy gradient of a small droplet is firstly proposed and derived as the driving force for its C–W evolution in this study based on the energy and gradient analysis.Then the physical and mathematical model of the C–W transition is found after the C–W driving force or transition pressure,the resistance, and the parameters of the meniscus beneath the droplet are formulated. The results show that the micro/nano structural parameters significantly affect the C–W driving force and resistance. The smaller the pillar diameter and pitch,the minor the C–W transition pressure, and the larger the resistance. Consequently, the C–W transition is difficult to be completed for the droplets on nano-textured surfaces. Meanwhile if the posts are too short, the front of the curved liquid–air interface below the droplet will touch the structural substrate easily even though the three phase contact line(TPCL) has not depinned. When the posts are high enough, the TPCL beneath the drop must move firstly before the meniscus can reach the substrate. As a result, the droplet on a textured surface with short pillars is easy to complete its C–W evolution. On the other hand, the smaller the droplet, the easier the C–W shift, since the transition pressure becomes larger, which well explains why an evaporating drop will collapse spontaneously from composite to Wenzel state. Besides, both intrinsic and advancing contact angles affect the C–W transition as well. The greater the two angles, the harder the C–W transition. In the end, the C–W transition parameters and the critical conditions measured in literatures are calculated and compared, and the calculations accord well with the experimental results.     

Analysis of meniscus beneath metastable droplets and wetting transition on micro/nano textured surfaces

The expressions of interface free energy(IFE) of composite droplets with meniscal liquid–air interface in metastable state on micro/nano textured surfaces were formulated. Then the parameters to describe the meniscus were determined based on the principle of minimum IFE. Furthermore, the IFE barriers and the necessary and sufficient conditions of drop wetting transition from Cassie to Wenzel were analyzed and the corresponding criteria were formulated. The results show that the liquid–air interface below a composite droplet is flat when the post pitches are relatively small, but in a shape of curved meniscus when the piteches are comparatively large and the curvature depends on structural parameters. The angle between meniscus and pillar wall is just equal to the supplementary angle of intrinsic contact angle of post material. The calculations also illustrate that Cassie droplets will transform to Wenzel state when post pitch is large enough or when drop volume is sufficiently small. The opposite transition from Wenzel to Cassie state, however, is unable to take place spontaneously because the energy barrier is always positive. Finally, the calculation results of this model are well consistent with the experimental observations in literatures for the wetting transition of droplets from Cassie to Wenzel state.     

A multicomponent multiphase lattice Boltzmann model with large liquid–gas density ratios for simulations of wetting phenomena

A multicomponent multiphase(MCMP) pseudopotential lattice Boltzmann(LB) model with large liquid–gas density ratios is proposed for simulating the wetting phenomena. In the proposed model, two layers of neighboring nodes are adopted to calculate the fluid–fluid cohesion force with higher isotropy order. In addition, the different-time-step method is employed to calculate the processes of particle propagation and collision for the two fluid components with a large pseudoparticle mass contrast. It is found that the spurious current is remarkably reduced by employing the higher isotropy order calculation of the fluid–fluid cohesion force. The maximum spurious current appearing at the phase interfaces is evidently influenced by the magnitudes of fluid–fluid and fluid–solid interaction strengths, but weakly affected by the time step ratio.The density ratio analyses show that the liquid–gas density ratio is dependent on both the fluid–fluid interaction strength and the time step ratio. For the liquid–gas flow simulations without solid phase, the maximum liquid–gas density ratio achieved by the present model is higher than 1000:1. However, the obtainable maximum liquid–gas density ratio in the solid–liquid–gas system is lower. Wetting phenomena of droplets contacting smooth/rough solid surfaces and the dynamic process of liquid movement in a capillary tube are simulated to validate the proposed model in different solid–liquid–gas coexisting systems. It is shown that the simulated intrinsic contact angles of droplets on smooth surfaces are in good agreement with those predicted by the constructed LB formula that is related to Young's equation. The apparent contact angles of droplets on rough surfaces compare reasonably well with the predictions of Cassie's law. For the simulation of liquid movement in a capillary tube, the linear relation between the liquid–gas interface position and simulation time is observed, which is identical to the analytical prediction. The simulation results regarding the wetting phenomena of droplets on smooth/rough surfaces and the dynamic process of liquid movement in the capillary tube demonstrate the quantitative capability of the proposed model.     

Temperature-Dependent Effect of Near-Interface Traps on SiC MOS Capacitance

A two-dimensional electrical SiC MOS interface model including interface and near-interface traps is established based on the relevant tunneling and interface Shockley–Read–Hall model. The consistency between simulation results and measured data in the different temperatures shows that this interface model can accurately describe the capture and emission performance for near-interface oxide traps, and can well explain the hysteresis-voltage response with increasing temperature, which is intensified by the interaction between deep oxide traps and shallow oxide traps. This also indicates that the near-interface traps result in an increase of threshold-voltage shift in SiC MOSFET with increasing temperature.     

Analogue correction method of errors and its application to numerical weather prediction

In this paper, an analogue correction method of errors (ACE) based on a complicated atmospheric model is further developed and applied to numerical weather prediction (NWP). The analysis shows that the ACE can effectively reduce model errors by combining the statistical analogue method with the dynamical model together in order that the information of plenty of historical data is utilized in the current complicated NWP model. Furthermore, in the ACE, the differences of the similarities between different historical analogues and the current initial state are considered as the weights for estimating model errors. The results of daily, decad and monthly prediction experiments on a complicated T63 atmospheric model show that the performance of the ACE by correcting model errors based on the estimation of the errors of 4 historical analogue predictions is not only better than that of the scheme of only introducing the correction of the errors of every single analogue prediction, but is also better than that of the T63 model.     

Lubricant film flow and depletion characteristics at head/disk storage interface

The characteristics of lubricant film at head/disk interface(HDI) are essential to the stability of hard disk drives. In this study, the theoretical models of the lubricant flow and depletion are deduced based on Navier–Stokes(NS) and continuity equations. The air bearing pressure on the surface of the lubrication film is solved by the modified Reynolds equation based on Fukui and Kaneko(FK) model. Then the lubricant film deformations for a plane slider and double-track slider are obtained. The equation of lubricant film thickness is deduced with the consideration of van der Waals force, the air bearing pressure, the surface tension, and the external stresses. The lubricant depletion under heat source is simulated and the effects of different working conditions including initial thickness, flying height and the speed of the disk on lubricant depletion are discussed. The main factors that cause the lubricant flow and depletion are analyzed and the ways to reduce the film thickness deformation are proposed. The simulation results indicate that the shearing stress is the most important factor that causes the thickness deformation and other terms listed in the equation have little influence. The thickness deformation is dependent on the working parameter, and the thermal condition evaporation is the most important factor.     

Molecular simulation study of the adhesion work for water droplets on water monolayer at room temperature

The wetting phenomenon of water droplets coexisting with the ordered water monolayer termed an unexpected phenomenon of "water that does not wet a water monolayer" at room temperature has been found on several solid surfaces.Although the hydrogen bond saturation inside the monolayer can qualitatively describe this phenomenon, whether the Young–Dupré equation still holds under this unconventional wetting framework is still not answered. In this work, we have calculated the contact angle values of the droplets as well as the work of adhesion between the droplets and the monolayer based on an extended phantom-wall method. The results show that similar to the conventional solid–liquid interface,classical Young–Dupré equation is also applicable for the interface of liquid water and ordered water monolayer.     

Water droplet impact on superhydrophobic surfaces with microstructures and hierarchical roughness

Quantitative correlation between the critical impact velocity of droplet and geometry of superhydrophobic surfaces with microstructures is systematically studied.Experimental data shows that the critical impact velocity induced wetting transition of droplet on the superhydrophobic surfaces is strongly determined by the perimeter of single micropillar,the space between the repeat pillars and the advancing contact angle of the sidewall of the micropillars.The proposed model agrees well with the experimental results,and clarifies that the underlying mechanism which is responsible for the superhydrophobic surface with hierarchical roughness could sustain a higher liquid pressure than the surfaces with microstructures.     

Contact resistance asymmetry of amorphous indium–gallium–zinc–oxide thin-film transistors by scanning Kelvin probe microscopy

In this work, a method based on scanning Kelvin probe microscopy is proposed to separately extract source/drain(S/D) series resistance in operating amorphous indium–gallium–zinc–oxide(a-IGZO) thin-film transistors. The asymmetry behavior of S/D contact resistance is deduced and the underlying physics is discussed. The present results suggest that the asymmetry of S/D contact resistance is caused by the difference in bias conditions of the Schottky-like junction at the contact interface induced by the parasitic reaction between contact metal and a-IGZO. The overall contact resistance should be determined by both the bulk channel resistance of the contact region and the interface properties of the metalsemiconductor junction.     

Gate-modulated generation–recombination current in n-type metal–oxide–semiconductor field-effect transistor

Gate-modulated generation–recombination（GMGR） current IGMGRinduced by the interface traps in an n-type metal–oxide–semiconductor field-effect transistor（n MOSFET） is investigated. The generation current is found to expand rightwards with increasing the reversed drain PN junction bias, and the recombination current is enhanced as the forward drain bias increases. The variations of IGMGRcurves are ascribed to the changes of the electron density and hole density at the interface, NSand PS, under the different drain bias voltages. Based on an analysis of the physical mechanism, the IGMGR model is set up by introducing two coefficients（m and t）. The coefficients m and t can modulate the curves widths and peak values. The simulated results under reverse mode and forward mode are obviously in agreement with the experimental results. This proves that this model can be applicable for generation current and recombination current and that the theory behind the model is reasonable. The details of the relevant mechanism are given in the paper.     

Phase-field modeling droplet dynamics with soluble surfactants

Using lattice Boltzmann approach, a phase-field model is proposed for simulating droplet motion with soluble surfactants. The model can recover the Langmuir and Frumkin adsorption isotherms in equilibrium. From the equilibrium equation of state, we can determine the interfacial tension lowering scale according to the interface surfactant concentration. The model is able to capture short-time and long-time adsorption dynamics of surfactants. We apply the model to examine the effect of soluble surfactants on droplet deformation, breakup and coalescence. The increase of surfactant concentration and attractive lateral interaction can enhance droplet deformation, promote droplet breakup, and inhibit droplet coalescence. We also demonstrate that the Marangoni stresses can reduce the interface mobility and slow down the film drainage process, thus acting as an additional repulsive force to prevent the droplet coalescence.     

壁面静止水滴冻结过程形状变化

低温表面上的液滴冻结时会形成具有尖顶的形状。针对这一现象开展了理论与实验研究,建立了新的动态曲形相界面模型用来模拟水滴冻结过程中的形状变化。模型考虑重力和成核再辉效应的影响,将冻结过程中的冰水相界面近似为球冠形曲面,并在三相点处引入动态生长角和直角关系。对壁面上20μL静止水滴进行了冻结实验,记录水滴三相点高度的演化过程,以此拟合得到了其随时间变化的关联式,基于该关联式求解理论模型,得到了水滴最终冻结形状。模拟结果与实验结果在水滴初始轮廓、成核再辉轮廓和最终冻结轮廓以及冻结时间上均吻合良好。曲面模型的计算结果表明,固液相界面上不同位置处的冻结速率不同;随着相界面向上推移,冻结速率逐渐减小。     

Electro-hydrodynamic behavior and interface instability of double emulsion droplets under high electric field

Dynamics of multiphase flow under high voltage has attracted extensive research interests due to its wide industrial applications. In this paper, numerical solution of electro-hydrodynamic behavior and interface instability of double emulsion droplet is presented. Level set method and leaky dielectric model coupled with Navier-Stokes equation are used to solve the electro-hydrodynamic problem. The method is validated against the theoretical analysis and the simulation results of the other researchers. Double emulsion droplet with inner droplet (core) and outer droplet (shell) phases immersed in continuous phase is subjected to high electric field. Shell/continuous and core/shell interfaces of the droplet undergo prolate-oblate or oblate-prolate deformation depending on the extent of the penetration of electric potential and sense of charge distribution at the interfaces. The deformation of the shell deviates from theory at larger volume fraction of core for oblate-prolate case whereas it follows theory for prolate-oblate case. The interfaces showing oblate-prolate deformation split at the poles whereas, for prolate-oblate, they split away along the equator. The re-union of the interfaces under high electric field results with production of daughter droplet at the core. The large decrease in critical electric field for oblate-prolate case shows their less interface stability at larger volume fraction of core. When the core is eccentric, the electric field drives it towards the shell center or to the shell/continuous interface depending on electrical parameters. The study is beneficial in understanding the electro-hydrodynamic behavior of emulsion droplets and efficient design of related industrial processes.     

带自由面流体的多体耗散粒子动力学模拟

利用多体耗散粒子动力学(MDPD)方法对介观尺度下液滴动力学进行了模拟分析,探讨了MDPD系统中液气共存界面的形成,并对表面张力进行了模拟研究,研究结果表明,MDPD方法形成的液气共存界面满足Laplace定律,通过改变不同的粒子间保守力作用参数,获得了液滴在固体壁面上不同的接触角,并研究了保守力作用参数与接触角之间的变化规律,进一步模拟了液滴在复杂微通道内的流动,研究结果有助于解释带自由面流体在粗糙表面上的运动行为。     

Droplets breakup via a splitting microchannel

On the basis of a volume of fluid(VOF) liquid/liquid interface tracking method, we apply a two-dimensional model to investigate the dynamic behaviors of droplet breakup through a splitting microchannel. The feasibility and applicability of the theoretical model are experimentally validated. Four flow regimes are observed in the splitting microchannel, that is, breakup with permanent obstruction, breakup with temporary obstruction, breakup with tunnels, and non-breakup. The results indicate that the increase of the capillary number Ca provides considerable upstream pressure to accelerate the droplet deformation, which is favorable for the droplet breakup. The decrease of the droplet size contributes to its shape changing from the plug to the sphere, which results in weakening droplet deformation ability and generating the nonbreakup flow regime.     

液滴在非互溶大黏度比液体表面的铺展特性

利用基于润滑理论的液滴在非互溶液体表面铺展的物理模型,探讨大黏度比情形下黏度比对液滴演化过程和平衡形状的影响,分析液滴厚度、铺展半径等特征参数的变化。结果表明：接触线附近液—液界面的变形受黏度比和表面张力比的影响;提高黏度比将导致铺展速率降低、时间常数减小,进而延长演化历程,但不影响液滴最终稳定形状;铺展半径与时间的关系满足x_max= 1 - 0.2 exp(- βt);大黏度比液滴铺展后期并未出现小黏度比时的惯性振荡现象。     

An analytical study of droplet combustion under microgravity: Quasi-steady transient approach

An analytical model based on an assumption of combined quasi-steady and transient behavior of the process is presented to exemplify the unsteady, sphero-symmetric single droplet combustion under microgravity. The model used in the present study includes an alternative approach of describing the droplet combustion as a process where the diffusion of fuel vapor residing inside the region between the droplet surface and the flame interface experiences quasi-steadiness while the diffusion of oxidizer inside the region between the flame interface and the ambient surrounding experiences unsteadiness. The modeling approach especially focuses on predicting; the variations of droplet and flame diameters with burning time, the effect of vaporization enthalpy on burning behavior, the average burning rates and the effect of change in ambient oxygen concentration on flame structure. The modeling results are compared with a wide range of experimental data available in the literature. It is shown that this simplified quasi-steady transient approach towards droplet combustion yields behavior similar to the classical droplet theory.     

等直径微液滴碰撞过程的改进光滑粒子动力学模拟

运用一种改进光滑粒子动力学(SPH)方法模拟了相溶和不相溶两种情况下的等直径微液滴碰撞动力学过程. 为提高传统SPH方法的数值精度和稳定性, 采用一种不涉及核导数计算的核梯度改进形式; 为处理液滴界面张力采用修正的van der Waals表面张力模型. 通过模拟牛顿液滴碰撞聚并变形过程并与相关文献或试验结果进行对比, 验证了改进SPH 方法模拟微液滴碰撞过程的可靠性. 随后, 研究了基于van der Waals模型相溶聚合物微液滴碰撞聚并变形过程及不相溶微液滴碰撞后的反弹、分离过程, 讨论了碰撞过程中碰撞速度、碰撞角度、密度比等参数对碰撞变形过程的影响, 分析了流体桥、旋转角度等因素的变化情况. 关键词： 光滑粒子动力学 微液滴 聚合物液滴 碰撞     

Anisotropy of the interface tension of the three-dimensional Ising model

We determine the interface tension for the 100, 110 and 111 interface of the simple cubic Ising model with nearest-neighbour interaction using novel simulation methods. To overcome the droplet/strip transition and the droplet nucleation barrier we use a newly developed combination of the multimagnetic algorithm with the parallel tempering method. We investigate a large range of inverse temperatures to study the anisotropy of the interface tension in detail.     

湿蒸汽非平衡态凝结流动的数值方法研究

在欧拉-欧拉、非结构有限体积框架下发展了湿蒸汽非平衡态凝结流动的数值方法。推导了基于真实物性,密度、内能和湿度全耦合的Roe通量。提出了适用于欧拉-欧拉法的三自由度TTSE水蒸气表。使用矩方法(MOM)和积分矩方法(QMOM)模拟水珠半径分布,并就时间推进时QMOM方法的不稳定现象给出了修正方法。通过两个无黏喷管和一个湍流平面叶栅算例进行了验证,表明本文的数值方法能比较准确地捕捉非平衡态凝结现象。