基于格子Boltzmann方法的液滴撞击具有不同润湿性孔板的研究

基于格子Boltzmann方法,对液滴撞击不同湿润性节流孔板表面进行了数值模拟.主要研究了在液滴撞击过程中,Weber数(We)、孔板表面湿润性和孔板尺寸对液滴通过孔板时不同状态的影响.数值模拟结果表明:孔板为亲水特性时,在较低We下,液滴不会与孔板表面脱离,而是附着在孔板下表面,并且在毛细作用下液滴会在孔道中上升一段...     

具有蒸发液滴两相介质近壁流动的数学分析

在双连续介质理论框架下，采用匹配渐进展开方法导出并求解了具有蒸发液滴的汽雾流中层流边界层方程，给出了控制汽雾流的相似判据。对于沿曲面的流动，边界层方程的形式取决于是否存在液滴的惯性沉积。给出了热钝体驻点附近蒸汽－液滴边界层的数值计算结果。它们表明：由于蒸发，在边界层内近壁处形成了一个无液滴区域；在该区上边界处，液滴半径趋于零而液滴数密度急剧增高。液滴蒸发及聚集的联合效应造成了表面热流的显著增加，甚至在自由来流中液滴质量浓度很低时此效应依然存在。     

Contact angle effects on microdroplet deformation using CFD

In this paper we use computational fluid dynamics (CFD) to study the effect of contact angle on droplet shape as it moves through a contraction. A new non-dimensional number is proposed in order to predict situations where the deformed droplet will form a slug in the contraction and thus have the opportunity to interact with the channel wall. It is proposed that droplet flow into a contraction is a useful method to ensure that a droplet will wet a channel surface without a trapped lubrication film, and thus help ensure that a slug will remain attached to the wall downstream of the contraction. We demonstrate that when a droplet is larger than a contraction, capillary and Reynolds numbers, and fluid properties may not be sufficient to fully describe the droplet dynamics through a contraction. We show that, with everything else constant, droplet shape and breakup can be controlled simply by changing the wetting properties of the channel wall. CFD simulations with contact angles ranging from 30° to 150° show that lower contact angles can induce droplet breakup while higher contact angles can form slugs with contact angle dependent shape.     

On the Crenation of a Compound Liquid Droplet

The dynamic response of a small, very viscous liquid droplet composed of a core fluid surrounded by a thin fluid shell is examined as additional fluid is deposited into this incompressible shell. At early times, the shell incorporates the extra mass by ruffling its external surface, and a number of crenations form. These protuberances decrease in size and number over a longer time period, and eventually the droplet again becomes spherical, with an increased radius. This sequence of events and its dependence on the rheological properties of the fluids are studied. These effects compare well qualitatively with those obtained using a surface fluid rather than a finite thickness shell of fluid. The possible implications of this fluid model for the surface ruffling effects observed in cell biology are discussed.     

On the Wetting of a Surface by a Very Viscous Fluid

The movement of a small viscous droplet on a flat surface is considered in self-spreading, in roundup, and as a result of an adhesion gradient. Edge conditions based on the dynamic contact angle are discussed within the context of lubrication theory. Tangential slip at the contact line is shown to be small compared to the normal velocity. The shapes of the droplet and its contact line are calculated, and nonlinear and inertial effects assessed.     

On the Crenation of Coated Droplets

The dynamic response of a small, very viscous, coated droplet is examined as additional fluid is deposited into a compressible surface layer. At early times, the surface material behaves like an incompressible fluid and a number of crenations form. These protuberances decrease in size and in number as the compressibility of the coating takes effect, until finally, the droplet again becomes spherical. This sequence of events and its dependence on the compressibility and rheological properties of the fluids are studied. Similar ruffling effects are observed in cell biology, and some of the possible implications of the fluid dynamical model are discussed.     

乙醇液滴撞击高温壁面蒸发过程的模拟预测研究北大核心CSCD

采用CLSVOF方法,引入描述壁面润湿特性的动态接触角,建立了乙醇液滴撞击高温壁面的数值模型,对乙醇液滴撞击高温壁面后的沸腾蒸发过程展开了研究,并与实验数据进行了对比验证.研究表明:在相同液滴温度下,壁面温度越高,亲水性越强,乙醇液滴的撞击速度越快,液滴的沸腾时间越早,蒸发完成所用时间也越短.在此研究基础上,基于机器学习算法,建立了液滴蒸发预测模型,对乙醇液滴撞击高温壁面后蒸发剩余量随时间的变化进行了预测研究,并通过将不同机器学习算法的预测结果与模拟结果对比,选出最优预测模型.     

T型微通道内液滴在幂律流体中运动机理的格子Boltzmann方法研究北大核心CSCD

采用非Newton不可压两相流格子Boltzmann模型研究了T型微通道内Newton液滴在非Newton幂律流体中的运动过程.研究了非Newton流体幂律指数n、主管道毛细数Ca、两相流量比Q、两相黏度比M以及主管道壁面润湿性θ对液滴在T型微通道内的形成尺寸、形成时间和变形参数(DI)的影响.研究结果表明:首先,主管道流体幂律指数n从0.4增加到1.6时,液滴的形成尺寸近似呈线性减小,而液滴的形成时间和变形参数先快速减小,然后缓慢减小;其次,黏度比对液滴形成尺寸、液滴形成以及变形参数的影响与幂律指数的影响基本一致;再者,随着Ca和主管道壁面润湿性的增加,形成液滴的尺寸近似呈线性减小,形成液滴的时间和变形参数先快速减小然后缓慢减小,且减小趋势随幂律指数的增加而减缓;最后,研究结果还表明主管道和子管道的流量比Q越大,液滴形成时间越长,液滴形成尺寸和变形参数越小.     

Lattice Boltzmann Study on the Motion of Dual Droplets in Microchannels With Contact Angle Hysteresis北大核心CSCD

接触角滞后表现为流体在非理想固体表面上运动时前进接触角和后退接触角不同,是两相流体在润湿表面上流动的重要现象.该文采用改进的伪势格子Boltzmann(LB)多组分模型,并与几何润湿边界条件相结合,研究了两个液滴在具有接触角滞后性微通道表面上的运动行为,主要研究了通道内特征数、通道表面性质以及液滴初始参数的影响.研究结果表明：毛细数的增大有助于液滴的移动,然而并不利于液滴的排出,且毛细数的增加对上游液滴的影响大于其对下游液滴的影响;另一方面,接触角滞后性窗口越大,液滴运动和形变更迟缓,但形变程度更明显,两液滴更早地发生合并,但更晚地排出管道;液滴间距的增加使液滴的运动行为在不同阶段表现为不同的模式,但都导致通道中残留小液滴,使得液滴排出通道的时间增加.研究结果还表明：上游液滴和下游液滴的相对尺寸差距越大,越不利于液滴排出管道.     

The simulation of micro droplet behavior of molten lead-free solder in inkjet printing process and its experimental validation

Micro droplets of molten lead-free solder were ejected at 230 °C using a piezoelectric inkjet printing process. The effect of the micro droplet formation of molten lead-free solder was investigated on the pulse time of the waveform. In this study, a numerical system for simulating the shape evolution of micro droplet of molten lead-free solder in the inkjet printing process was developed based on a solution algorithm (SOLA) scheme for the solution of velocity and pressure fields. It is coupled with the volume-of-fluid (VOF) and piecewise-linear interface construction (PLIC) techniques for the transport of mass and construction of the interface. For the treatment of surface tension effects, a CSF (continuum surface force) model is employed. The simulation results were validated with experimental observations. The numerical result was used to understand the mechanisms of the extrusion of the liquid column, the contraction of the liquid thread, and the pinch-off of the liquid thread at the nozzle exit.     

Fully discrete energy stable scheme for a phase-field moving contact line model with variable densities and viscosities

In this study, we propose a fully discrete energy stable scheme for the phase-field moving contact line model with variable densities and viscosities. The mathematical model comprises a Cahn–Hilliard equation, Navier–Stokes equation, and the generalized Navier boundary condition for the moving contact line. A scalar auxiliary variable is employed to transform the governing system into an equivalent form, thereby allowing the double well potential to be treated semi-explicitly. A stabilization term is added to balance the explicit nonlinear term originating from the surface energy at the fluid–solid interface. A pressure stabilization method is used to decouple the velocity and pressure computations. Some subtle implicit–explicit treatments are employed to deal with convention and stress terms. We establish a rigorous proof of the energy stability for the proposed time-marching scheme. A finite difference method based on staggered grids is then used to spatially discretize the constructed time-marching scheme. We also prove that the fully discrete scheme satisfies the discrete energy dissipation law. Our numerical results demonstrate the accuracy and energy stability of the proposed scheme. Using our numerical scheme, we analyze the contact line dynamics based on a shear flow-driven droplet sliding case. Three-dimensional droplet spreading is also investigated based on a chemically patterned surface. Our numerical simulation accurately predicts the expected energy evolution and it successfully reproduces the expected phenomena where an oil droplet contracts inward on a hydrophobic zone and then spreads outward rapidly on a hydrophilic zone.     

Computational Modeling of Liquid Droplets Moving on Rough Surfaces

We present a de-coupled approach for computational modeling of liquid droplets moving on rough substrate surfaces. The computational model comprises solving the membrane deformation problem and the fluid flow problem in a segregated manner. The droplet shape is first computed by solving the Young-Laplace equation where contact constraints, due to the droplet-substrate contact, are applied through the penalty method [1]. The resulting configuration constitutes the domain for the fluid flow problem, where the bulk fluid behavior is modeled by the unsteady Stokes' flow model expressed in Arbitrary Lagrangian-Eulerian (ALE) framework. The entire analysis is performed in the framework of Finite Element Method (FEM). Application of the approach to the case of a droplet moving on a rough surface is presented as an example. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Droplet spreading: Intermediate scaling law by PDE methods

We consider the spreading of a thin droplet of viscous liquid on a plane surface driven by capillarity. The standard lubrication approximation leads to an evolution equation for the film height h that is ill‐posed when the spreading is limited by the no‐slip boundary condition at the liquid‐solid interface due to a singularity at the moving contact line. The most common relaxation of the no‐slip boundary condition removes this singularity but introduces a new physical length scale: the slippage length b. It is believed that this microscopic‐length scale only enters logarithmically in the effective (that is, macroscopic) spreading behavior. In this paper, we rigorously show that the naively expected spreading rate is indeed only altered by a logarithmic term involving b. More precisely, we prove a scaling law for the diameter of the apparent (that is, macroscopic) support of the droplet in time. This is an intermediate scaling law: It takes an initial layer to “forget” the initial droplet shape, whereas after a long time, the droplet is so thin that its spreading is governed by the physics on the scale b. Our proof works by deriving suitable estimates for physically relevant integral quantities: the free energy, the length of the apparent support, and their respective rates of change. As opposed to matched asymptotic methods, this PDE approach closely mimics a simple heuristic argument based on the gradient flow structure. © 2002 John Wiley & Sons, Inc.     

Single Droplet Pattern in the Cylindrical Phase of Diblock Copolymer Morphology

The Ohta–Kawasaki density functional theory of diblock copolymers gives rise to a nonlocal free boundary problem. Under a proper condition between the block composition fraction and the nonlocal interaction parameter, a pattern of a single droplet is proved to exist in a general planar domain. A smaller parameter range is identified where the droplet solution is stable. The droplet is a set that is close to a round disc. The boundary of the droplet satisfies an equation that involves the curvature of the boundary and a quantity that depends nonlocally on the whole pattern. The location of the droplet is determined by the regular part of a Green’s function of the domain. This droplet pattern describes one cylinder in space in the cylindrical phase of diblock copolymer morphology.     

A fuel droplet vaporization model in a hot air stream

The gasification behavior of a fuel droplet has been studied. The convective heat transfer is focused on in most literature on droplet evaporation. In this paper, a mathematic model of droplet evaporation is improved. Considering the presence of simultaneous mass and heat transfer at the interface between phases, a proper heat transfer equation for droplet evaporation model is established. Based on the model, a computer simulation program was developed, and the predictions of the model are compared with the experimental data. Sample calculations show the capabilities of the model for droplet evaporation.     

Well‐posedness for the Navier Slip Thin‐Film equation in the case of partial wetting

Consider a viscous liquid droplet spreading on a surface. The classical slip condition at the liquid‐solid interface is the no‐slip condition. However, this condition yields infinite dissipation rate when the contact line moves (“no‐slip paradox”). For this reason other slip conditions such as the Navier slip condition have been proposed. We prove well‐posedness for a reduced 1‐D fluid model related to Navier slip. It turns out that the profile of the droplet cannot be described by a smooth function (not even for an initially smooth profile). However, existence and uniqueness can be proved in larger classes of spaces that allow for certain classes of singular expansions at the moving contact point. © 2011 Wiley Periodicals, Inc.     

Predictions of the gas–liquid flow in wet electrostatic precipitators

Based on Computational Fluid Dynamics (CFD), the present paper aims to simulate several important phenomena in a wet type ESP from the liquid spray generation to gas-droplet flow in electric field. A single passage between the adjacent plates is considered for the simulation domain. Firstly, the electric field intensity and ion charge density are solved locally around a corona emitter of a barbed wire electrode, which are applied to the entire ESP using periodic conditions. Next, the Euler–Lagrange method is used to simulate the gas-droplet flow. Water droplets are tracked statistically along their trajectories, together with evaporation and particle charging. Finally, the deposition density on the plate is taken as the input for the liquid film model. The liquid film is simulated separately using the homogenous Eulerian approach in ANSYS-CFX. In the current case, since the free surface of the thin water film is difficult to resolve, a special method is devised to determine the film thickness.As parametric study, the variables considered include the nozzle pressure, initial spray spreading patterns (solid versus hollow spray) and plate wettability. The droplet emission rate and film thickness distribution are the results of interest. Main findings: electric field has strong effect on the droplet trajectories. Hollow spray is preferred to solid spray for its lower droplet emission. The liquid film uniformity is sensitive to the plate wettability.     

A proof of the invariance of the contact angle in electrowetting

We prove the invariance of the contact angle in liquid–solid electrowetting phenomena: an electrified droplet is spreading on a solid surface. The drop minimizes its energy. We express the differential of this energy with respect to the shape of the drop and deduce necessary conditions for optimality. By variational methods, using well-chosen test functions, we obtain the main result about the contact angle between the drop and the solid.     

曲率的形状梯度和经典梯度:微纳米曲面上的驱动力

近期的实验和分子动力学模拟均表明:圆锥面上粘附液滴能自发地定向运动,且自发定向运动的方向与粘附面的亲水、疏水性质无关．针对这一重要现象,拟从曲面微纳米力学几何化的角度,提供一般性的理论解释．借助于粒子对势,研究了孤立粒子与微纳米硬曲面之间的相互作用,分析了粒子/硬曲面相互作用的几何学基础．可以证实:（a） 粒子/硬曲面的作用势均具有统一的曲率化形式,均可以统一地表达成曲面平均曲率和Gauss曲率的函数;（b） 基于曲率化的作用势,能够实现曲面微纳米力学的几何化;（c） 曲率与曲率的内蕴梯度构成卷曲空间上的驱动力;（d） 驱动力方向与曲面的亲水、疏水性质无关,解释了自发定向运动实验．