二维液桥计算模型及湿颗粒材料离散元模拟

本文研究了二维情况两直接相邻颗粒间液体以液桥形式存在时的液桥临界断裂距离及液桥力的计算过程。导出了用颗粒半径、三相接触角和液桥体积表示的二维液桥临界断裂距离拟合公式及两个接触或非接触颗粒间液桥毛细力随液桥体积的变化关系。引入Voronoi胞元计算定义基于参考颗粒介观结构的物质点的平均饱和度。提出了考虑液桥效应的二维湿颗粒离散元模型,并用以模拟不同初始均匀饱和度下湿颗粒集合体中的吸力效应,验证其有效捕捉以应变局部化为特征的破坏模式的能力。     

Capillary bridges and capillary forces between two axisymmetric power–law particles

Capillary interactions are fundamentally important in many scientific and industrial fields. However, most existing models of the capillary bridges and capillary forces between two solids with a mediated liquid, are based on extremely simple geometrical configurations, such as sphere–plate, sphere–sphere, and plate–plate. The capillary bridge and capillary force between two axisymmetric power–law profile particles with a mediated constant-volume liquid are investigated in this study. A dimensionless method is adopted to calculate the capillary bridge shape between two power–law profile particles based on the Young–Laplace equation. The critical rupture criterion of the liquid bridge is shown in four forms that produce consistent results. It was found that the dimensionless rupture distance changes little when the shape index is larger than 2. The results show that the power–law index has a significant influence on the capillary force between two power–law particles. This is directly attributed to the different shape profiles of power–law particles with different indices. Effects of various other parameters such as ratio of the particle equivalent radii, liquid contact angle, liquid volume, and interparticle distance on the capillary force between two power–law particles are also examined.     

两异径湿球颗粒间静态液桥力的近似解析公式及数值评测

针对异径球形湿颗粒间液桥力,以Young-Laplace公式为基础,结合环形近似法并引入等效半径,在宽松设定的条件下推导出了简化的近似解析公式。此公式形式简洁,且当两球半径相等时,可回归到Pitois等提出的径球液桥力公式。本文对此近似解析公式进行参数敏感度分析,发现随着颗粒间距的增大,液桥力对颗粒半径的敏感度降低。此外,本文近似解析公式与其他实验和理论结果进行对比发现,该近似解析公式与上述实验和数值结果相当吻合,表明该近似解析公式可以较准确地计算接触角较小时的异径球颗粒间的液桥力,因而适于湿颗粒系统的数值模拟。     

片状颗粒间液桥力变化规律的计算研究

研究颗粒间液桥力有助于揭示非饱和土持水特性的内在机理. 为探究片状颗粒间液桥力演化规律, 从细观尺度研究非饱和土的水力特性机理, 使用Surface Evolver软件在两平行的片状颗粒间构建出三维液桥模型, 分析了液桥拉伸过程中接触角、液桥体积、分离距离以及固液接触线钉扎效应等对液桥力变化规律的影响. 基于圆弧假定, 计算相应条件下液桥力以及接触半径的大小, 并与上述模拟结果进行对比分析. 结果表明: 片状颗粒间液桥力随液桥体积增大而递增, 随分离距离的增大而递减, 随固液接触角的增大先增后减或一直递减; 液桥体积一定时, 在钉扎状态下, 其液桥力随着分离距离的增大迅速递增达到峰值, 而后逐渐降低; Surface Evolver模拟与液桥界面环形近似的计算结果相对比, 当固液接触角较大时(θ = 60°和θ = 80°), 二者相对误差在6%以内, 而当固液接触角减小到30°及以下时, 相对误差随之增大, 且颗粒间分离距离越大, 相对误差越大.      

重力影响下板间液桥断裂距离研究

运用实验测量和数值模拟两种方法对两平板间特征尺度为毫米量级的液桥断裂距离进行了研究,定量地给出了在有重力和无重力两种条件下,液桥断裂距离随着液桥体积和固体表面润湿性质变化的规律。结果显示,重力对液桥断裂距离的影响随着液桥特征尺寸的增大而增大,当特征尺寸达到毛细长度时,重力对亲水表面间液桥断裂距离的影响可达11%以上,对于疏水表面间的断裂距离影响更增加到20%以上。通过Surface Evolver软件可以很好地模拟准静态液桥拉伸-断裂过程,得到准确的液桥断裂距离。结果表明,即使在液桥特征尺寸小于毛细长度的条件下,液桥断裂距离也不能完全忽略重力的影响。     

考虑毛细作用微梁剥离的实验和力学模型

毛细力诱发的粘附现象在自然界和工农业生产中广泛存在,例如微机电系统、微纳米自组装、油气驱替等．本文系统研究了两根微梁的毛细粘附行为,包括梁剥离过程中液桥的形貌以及剥离力-位移变化规律．试验发现,微梁在毛细力作用下的剥离部分经历了液膜粘附和液滴粘附两个阶段．考虑两个阶段的液桥形状特征,分别建立系统的能量泛函,采用变分原理推导了考虑毛细力的微梁剥离的非线性微分方程和边界条件．基于Matlab 编程求解方程,得到了剥离力-位移曲线,理论计算与试验结果具有很好的一致性．另外,参数研究表明,接触角和表面张力系数对液膜粘附的微梁剥离影响显著,而对液滴粘附的剥离影响较小;微梁刚度对两个阶段的剥离都有明显影响．本文的试验结果和理论分析对于实际工程中微结构的定量设计具有一定参考价值．     

The capillary force in micro- and nano-indentation with different indenter shapes

The influence of the indenter shapes and various parameters on the magnitude of the capillary force is studied on the basis of models describing the wet adhesion of indenters and substrates joined by liquid bridges. In the former, we consider several shapes, such as conical, spherical and truncated conical one with a spherical end. In the latter, the effects of the contact angle, the radius of the wetting circle, the volume of the liquid bridge, the environmental humidity, the gap between the indenter and the substrate, the conical angle, the radius of the spherical indenter, the opening angle of the spherical end in the truncated conical indenter are included. The meniscus of the bridge is described using a circular approximation, which is reasonable under some conditions. Different dependences of the capillary force on the indenter shapes and the geometric parameters are observed. The results can be applicable to the micro- and nano-indentation experiments. It shows that the measured hardness is underestimated due to the effect of the capillary force.     

Liquid bridge force between two unequal-sized spheres or a sphere and a plane

Liquid bridge force acting between wet particles is an important property in particle characterization. This paper deals with liquid bridge force between either two unequal-sized spherical particles or a sphere and a flat plate under conditions where gravitational effect arising from bridge distortion is negligible. In order to calculate the force of the liquid bridge efficiently and accurately, expressions of liquid configuration and liquid bridge force were derived by building a mechanical model, which assumes the liquid bridge to be circular in shape between either two unequal-sized spheres or a sphere and a plane. To assess the accuracy of the numerical results of the calculated liquid bridge forces, they were compared to the published experimental data.     

Analysis of liquid bridge between spherical particles

A pair of central moving spherical particles connected by a pendular liquid bridge with interstitial Newtonlan fluid is otten encountered in particulate coalescence process. In this paper, by assuming perfect-wet condition, the effects of liquid volume and separation distance on static liquid bridge are analyzed, and the relation between rupture energy and liquid bridge volume is also studied. These points would be of significance in industrial processes related to adhesive particles.     

Lattice Boltzmann study of the interaction between a single solid particle and a thin liquid film

The isothermal single-component multi-phase lattice Boltzmann method(LBM) combined with the particle motion model is used to simulate the detailed process of liquid film rupture induced by a single spherical particle.The entire process of the liquid film rupture can be divided into two stages.In Stage 1,the particle contacts with the liquid film and moves into it due to the interfacial force and finally penetrates the liquid film.Then in Stage 2,the upper and lower liquid surfaces of the thin film are driven by the capillary force and approach to each other along the surface of the particle,resulting in a complete rupture.It is found that a hydrophobic particle with a contact angle of 106.7° shows the shortest rupture duration when the liquid film thickness is less than the particle radius.When the thickness of the liquid film is greater than the immersed depth of the particle at equilibrium,the time of liquid film rupture caused by a hydrophobic particle will be increased.On the other hand,a moderately hydrophilic particle can form a bridge in the middle of the liquid film to enhance the stability of the thin liquid film.     

Surface tension and buoyancy-driven flow in a non-isothermal liquid bridge

The Navier–Stokes–Boussinesq equations governing the transport of momentum, mass and heat in a non-isothermal liquid bridge with a temperature-dependent surface tension are solved using a vorticity-stream-function formulation together with a non-orthogonal co-ordinate transformation. The equations are discretized using a pseudo-unsteady semi-implicit finite difference scheme and are solved by the ADI method. A Picard-type iteration is adopted which consists of inner and outer iterative processes. The outer iteration is used to update the shape of the free surface. Two schemes have been used for the outer iteration; both use the force balance normal to the free surface as the distinguished boundary condition. The first scheme involves successive approximation by the direct solution of the distinguished boundary condition. The second scheme uses the artificial force imbalance between the fluid pressure, viscous and capillary forces at the free surface which arises when the boundary condition for force balance normal to the surface is not satisfied. This artificial imbalance is then used to change the surface shape until the distinguished boundary condition is satisfied. These schemes have been used to examine a variety of model liquid bridge situations including purely thermocapillary-driven flow situations and mixed thermocapillary- and bouyancy-driven flow.     

Removal of Particle Bridges From a Porous Material by Ultrasonic Irradiation

Particle bridge formation during the flow of a liquid with particles through a porous material is a fouling mechanism that can block the pores and, hence, decrease the permeability of the material. Ultrasonic irradiation of the material is a cleaning method that can restore the permeability. We make a numerical study of this cleaning method using the lattice-Boltzmann method. We start from a pore blocked by two spherical particles attached to the pore wall by colloidal adhesion forces, thus forming a particle bridge. Next we calculate the hydrodynamic force exerted by a high-frequency acoustic wave on the two particles. By comparing the hydrodynamic force and the adhesion force we investigate, whether the particle bridge will be removed by the ultrasonic irradiation. A sensitivity study is carried out to investigate the influence of some relevant parameters, such as the acoustic wave amplitude, the acoustic frequency, the fluid flow velocity and the ratio of particle diameter and pore diameter. An upscaling procedure is applied to translate the microscopic results for the removal of the particles at the pore level to the permeability improvement of the material at the macroscopic level. A comparison is made between numerical results and experimental data. The agreement is reasonable.     

Separation efficiency of liquid–solid undergoing vibration based on breakage of liquid bridge

Vibrating separation is a significant method for liquid–solid separation. A typical example is the vibrating screen to dewater wet granular matter. The properties of granular matter and the vibrating parameters significantly affect the separation efficiency. This study investigates the effect of vibration parameters in separation based on the breakage of large-scale liquid bridge numerically by using a calibrated simulation model. Through analysing the simulation results, the liquid bridge shape and the volume between two sphere particles for various particle sizes and particle distances were studied in the static condition under the effect of gravity. The results show a general reducing trend of liquid bridge volume when the radius ratio of two particles increases, particularly when the ratio increases to 5. Additionally, a set of vibrating motion was applied to the liquid bridge in the simulation model. A group of experiments were also performed to validate the simulation model with vibration. Then, the effect of vibrating peak acceleration, distance between spheres and radius on the separation efficiency which was reflected by the residual water were investigated. It is found that separation efficiency increased obviously with the peak acceleration and the increase slowed down after the peak acceleration over 1 m/s².     

A capillary force model for interactions between two spheres

Based on the method of energy principle, an analytical approach for computing the capillary force for sphere/sphere geometry is presented in this paper. In modeling the capillary force, we consider spheres with both equal and non-equal radii, for both symmetric and asymmetric configurations at liquid/solid interfaces. We use numerical analysis to investigate the validity and efficiency of the derived model. The effect of various parameters including humidity, distance between two spheres, radii of spheres and contact angles on the meniscus force are investigated. Finally the results obtained from the model are compared with experimental measurements, and the accuracy and precision of the presented approach is verified.     

ENERGY DISSIPATION IN TAPPING MODE ATOMIC FORCE MICROSCOPY

原子力显微镜有多种成像模式,其中轻敲模式是最为常用的扫描方式.轻敲模式能获取样品表面形貌的高度信息和相位信息,其中相位信息具有更多的价值,如能反映样品的表面能、弹性、亲疏水性等.依据振动力学理论,相位与振动系统的能量耗散有关.探针样品间的能量耗散对于理解轻敲模式下原子力显微镜的成像机理至关重要,样品特性和测量环境会影响能量耗散.本文在不考虑毛细力影响下,基于JKR接触模型,给出了探针样品相互作用下的加卸载曲线,结合原子力显微镜力曲线实验,给出了探针-样品分离失稳点的位置,从而计算一个完整接触分离过程的能量耗散,进而讨论考虑表面粗糙度对能量耗散的影响.在轻敲模式下考虑毛细力影响,通过特征时间对比,证明挤出效应是液桥生成的主导因素,在等容条件下,用数值方法计算了不同相对湿度对能量耗散的影响.通过一维振子模型,简要说明原子力显微镜相位像与样品表面能、杨氏模量、表面粗糙度、相对湿度之间的关系.分析表明,表面粗糙度和环境湿度均会引起相位的变化,进而认为它们是引起赝像的因素.     

钟摆状态下湿颗粒坍塌流动行为及其动力相似性

基于建立的湿颗粒离散动力学模型,本文系统研究了钟摆状态下湿颗粒柱在重力驱动下的坍塌流动过程,主要考虑了颗粒粒径、液体表面张力系数和液体含量等参数对系统坍塌流动模式和动力学行为的影响。研究发现,在湿颗粒系统中,颗粒粒径和液体表面张力系数会改变颗粒间的毛细力大小,引起系统发生不同的坍塌流动模式,而液体含量仅定量影响颗粒坍塌后的堆积形态。在此基础上,进一步探讨了不同模式下系统坍塌流动行为与模型参数的相关性,发现无量纲Bond数是决定钟摆状态下湿颗粒物质坍塌流动动力学行为的本质因素。     

A generalized equation for rheology of emulsions and suspensions of deformable particles subjected to simple shear at low Reynolds number

We present analyses to provide a generalized rheological equation for suspensions and emulsions of non-Brownian particles. These multiparticle systems are subjected to a steady straining flow at low Reynolds number. We first consider the effect of a single deformable fluid particle on the ambient velocity and stress fields to constrain the rheological behavior of dilute mixtures. In the homogenization process, we introduce a first volume correction by considering a finite domain for the incompressible matrix. We then extend the solution for the rheology of concentrated system using an incremental differential method operating in a fixed and finite volume, where we account for the effective volume of particles through a crowding factor. This approach provides a self-consistent method to approximate hydrodynamic interactions between bubbles, droplets, or solid particles in concentrated systems. The resultant non-linear model predicts the relative viscosity over particle volume fractions ranging from dilute to the the random close packing in the limit of small deformation (capillary or Weissenberg numbers) for any viscosity ratio between the dispersed and continuous phases. The predictions from our model are tested against published datasets and other constitutive equations over different ranges of viscosity ratio, volume fraction, and shear rate. These comparisons show that our model, is in excellent agreement with published datasets. Moreover, comparisons with experimental data show that the model performs very well when extrapolated to high capillary numbers (C a?1). We also predict the existence of two dimensionless numbers; a critical viscosity ratio and critical capillary numbers that characterize transitions in the macroscopic rheological behavior of emulsions. Finally, we present a regime diagram in terms of the viscosity ratio and capillary number that constrains conditions where emulsions behave like Newtonian or Non-Newtonian fluids.     

不等径颗粒间液桥力学参数及形态的试验研究

作为一种自然界中广泛存在的力, 液桥力的研究对制药、重金属回收、颗粒分离等领域具有十分重要的意义. 利用纳米多功能拉伸试验机测量不等径颗粒间液桥拉伸过程中的液桥力?位移曲线, 同时配合CCD工业相机记录拉伸全过程液桥形态的变化. 首先分析了液桥力?位移曲线形态、最大液桥力、断裂距离随粒径比及液桥体积的变化规律, 其次基于圆环假设及Y-L方程对本文试验结果的合理性进行验算, 最后针对圆环假设在液桥力计算中存在的不足分析了其原因, 并结合重力对液桥形态的影响对液桥拉伸全过程的形态变化进行了具体分析. 结果表明: 最大液桥力受粒径比的影响较大而受液桥体积的影响较小, 与最大液桥力相反, 断裂距离受液桥体积的影响较大而受粒径比的影响较小; 圆环假设可以较好地预测最大液桥力大小但对拉伸过程中的液桥力预测不准, 这是由于当液桥力达到最大值后液桥的外轮廓已不能用圆环表示; 根据重力对液桥形态的影响, 将拉伸过程液桥外轮廓的变化简化为重力影响可以忽略时的圆环形?抛物线形, 重力影响处于过渡阶段或影响较小时的长轴与短轴之比不断增大的椭圆形, 以及重力影响不可忽略时的“冷却塔形”?双曲线形.      

Experimental investigation on capillary force of composite wick structure by IR thermal imaging camera

A novel sintered–grooved composite wick structures has been developed for two-phase heat transfer devices. With ethanol as the working fluid, risen meniscus test is conducted to study the capillary force of wick structures. Infrared (IR) thermal imaging is used to identify and locate the liquid meniscus. The effects of sintered layer, V-grooves and powder size on capillary force are explored. The results show that the capillary force of composite wick structures is larger than that of grooved and sintered ones. Interaction wetting between groove and sintered powder happens during the liquid rise in composite wick, which provides an additional source of capillary force. It exhibits a variation of capillary force of composite wicks with different powder size due to the difference of open pore size and quantity in sintered porous matrix.     

滴状模式下液桥形成及断裂的电流体动力学特性研究

对电场作用下微通道荷电液滴脱落过程中液桥形成及断裂的显微演变特征进行了可视化实验研究.借助时空分辨率较高的高速摄像技术精确捕捉了电场作用下液桥形成及断裂的界面演化过程,研究了液桥的界面结构变化及其断裂的动力学显微演变行为,获得了时间特征数、电邦德数及半月面形成角对液桥长度及断裂顺序的作用规律.实验结果显示,液桥断裂长度取决于黏度与表面张力之比,而受荷电弛豫时间的影响甚微,低电压工况下各实验介质液桥相对长度的变化并不明显,而在较高电压工况下相对液桥长度的增长速度加快.随着电邦德数的不断增加,液桥长度的变化在较高邦德数下更为明显且存在突变区,此时伴随着雾化模式的转变,表明液桥的突变恰恰是雾化模式过渡的信号.不同物性介质的射流过渡行为由于液桥上下游形成角的变化而存在较大差异.对于无水乙醇介质,电邦德数的增加使滴状模式首先过渡到纺锤模式,而对于生物柴油,滴状模式后会首先出现脉动模式而非纺锤模式.