Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces

A lattice Boltzmann equation (LBE) method for incompressible binary fluids is proposed to model the contact line dynamics on partially wetting surfaces. Intermolecular interactions between a wall and fluids are represented by the inclusion of the cubic wall energy in the expression of the total free energy. The proposed boundary conditions eliminate the parasitic currents in the vicinity of the contact line. The LBE method is applied to micron-scale drop impact on dry surfaces, which is commonly encountered in drop-on-demand inkjet applications. For comparison with the existing experimental results [H. Dong, W.W. Carr, D.G. Bucknall, J.F. Morris, Temporally-resolved inkjet drop impaction on surfaces, AIChE J. 53 (2007) 2606–2617], computations are performed in the range of equilibrium contact angles from 31° to 107° for a fixed density ratio of 842, viscosity ratio of 51, Ohnesorge number (Oh) of 0.015, and two Weber numbers (We) of 13 and 103.     

梯度表面能材料表面上液滴形状的数值模拟

本文建立了固体表面上静止液滴的势能方程,根据能量最小化原理,当系统总势能取得最小值时,液滴将处于平衡状态.采用有限元方法,将初始自由液面离散化,通过曲面上节点的虚拟位移,改变自由液面的拓扑结构,使系统总势能取得最小值,从而得到静止液滴的形状.并应用该方法对均质表面和梯度表面能材料表面上的液滴界面进行了数值模拟,得到了均质材料表面和梯度表面能材料表面上静止液滴的界面形状及分布.     

Three-dimensional simulation of nonlinear dynamics of domain walls in films with perpendicular anisotropy

A three-dimensional computer simulation of static magnetization configurations and dynamic processes occurring in a domain wall moving in a uniaxial magnetic film with perpendicular anisotropy has been performed based on the numerical solution of Landau–Lifshitz–Gilbert equations. The calculated static states correspond to a domain wall containing Bloch lines with a surface magnetization distribution that depends on the thickness of the film. It has been shown that these structures can be characterized by particular values of the homotopy index. It has been found that the vortex and antivortex structures existing in the bulk of the film form vortex filaments. A method has been proposed for visualization of the joint motion of vortex filaments and Bloch points, which is based on the numerical calculation of the homotopy index and the winding number.     

Three-dimensional simulation of irregular dynamics of topological solitons in moving magnetic domain walls

A three-dimensional computer simulation of dynamic processes occurring in a domain wall moving in a soft-magnetic uniaxial film with in-plane anisotropy has been performed based on the micromagnetic approach. It has been shown that the domain wall motion is accompanied by topological transformations of the magnetization distribution, or, more specifically, by “fast” processes associated with the creation and annihilation of vortices, antivortices, and singular (Bloch) points. The method used for visualizing the topological structure of magnetization distributions is based on the numerical determination of topological charges of two types by means of the integration over the contours and surfaces with variable geometry. The obtained data indicate that the choice of the initial configuration predetermines the dynamic scenario of topological transformations.     

Lattice Boltzmann simulations of drops colliding with solid surfaces

Video images of drops colliding with solid surfaces shown by Rioboo et al. (2002) reveal that, for large drop velocities, the drops flatten and form a ring structure before receding and, in some cases, rebounding from the surface. They described the sequence of events in terms of four distinct regimes. During the initial kinematic phase, the dimensionless wetting radius of the drop follows a universal form if the drop Weber and Reynolds numbers are sufficiently large. In the second phase, the drop becomes highly flattened and the values of the Weber and Reynolds numbers influence the time evolution of the dimensionless wetting radius and its maximum value. This is followed by a third phase in which the wetting radius begins to decrease with time and the wettability of the surface influences the dynamics. This paper presents simulation results for the early stages of drop impact and spreading on a partially wetting solid surface. The simulations were performed with a modified version of the lattice Boltzmann method (LBM) developed by Inamuro et al. (2004) for a liquid-gas density ratio of 1000. The Inamuro et al. version of the LBM was modified by incorporating rigid, no-slip boundary conditions and incorporating a boundary condition on the normal derivative of the order parameter to impose the desired equilibrium contact angle.     

Ellipsoidal particles at fluid interfaces

For partially wetting, ellipsoidal colloids trapped at a fluid interface, their effective, interface-mediated interactions of capillary and fluctuation-induced type are analyzed. For contact angles different from 90( degrees ) , static interface deformations arise which lead to anisotropic capillary forces that are substantial already for micrometer-sized particles. The capillary problem is solved using an efficient perturbative treatment which allows a fast determination of the capillary interaction for all distances between and orientations of two particles. Besides static capillary forces, fluctuation-induced forces caused by thermally excited capillary waves arise at fluid interfaces. For the specific choice of a spatially fixed three-phase contact line, the asymptotic behavior of the fluctuation-induced force is determined analytically for both the close-distance and the long-distance regime and compared to numerical solutions.     

利用运动光束抑制高功率激光小尺度自聚焦

提出了近场“运动光束”的概念.指出光谱色散匀滑装置可以在近场产生运动光束,理论分析了运动光束的产生机理、条件、运动特性以及对小尺度自聚焦的抑制作用.通过数值模拟,得到计算结果与理论分析一致. 关键词： 运动光束 光谱色散匀滑 小尺度自聚焦 惯性约束聚变     

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。     

Evaporation-coupled wetting of ZrO2 by molten Mg in Ar atmosphere

The wetting behaviors of molten Mg drops on polycrystalline ZrO₂ substrate surfaces were studied in a controlled Ar atmosphere at 948–1173 K using an improved sessile drop method. The ZrO₂ substrate is virtually not wetted by molten Mg at temperatures below 1173 K. The wetting and evaporation stages according to different variation behaviors of contact angle, contact diameter and drop height were identified. Six representative modes were proposed to describe the evaporation-coupled wetting behaviors during different stages. The competitions between surface oxidation, chemical reaction and drop evaporation were discussed to account for the mechanisms for various wetting behaviors at different temperatures. The chemical reaction leads to the formation of more wettable MgO phase at the interface; however, it yields only an inconspicuous improvement in the wetting due to enhanced Mg evaporation.     

Theory of the interface between a classical plasma and a hard wall

The interfacial density profile of a classical one-component plasma confined by a hard wall is studied in planar and spherical geometries. The approach adapts to interfacial problems a modified hypernetted-chain approximation developed by Lado and by Rosenfeld and Ashcroft for the bulk structure of simple liquids. The specific new aim is to embody self-consistently into the theory a “contact theorem”, fixing the plasma density at the wall through an equilibrium condition which involves the electrical potential drop across the interface and the bulk pressure. The theory is brought into fully quantitative contact with computer simulation data for a plasma confined in a spherical cavity of large but finite radius. It is also shown that the interfacial potential at the point of zero charge is accurately reproduced by suitably combining the contact theorem with relevant bulk properties in a simple, approximate representation of the interfacial charge density profile.     

Der „Slant-line-Effekt“ in axialen Gasentladungen bei Gegenwart axialer Magnetfelder

In axial gasdischarges with superposed axial magnetic fields “inclined”- or “slant” — spectral lines can be observed, if at the same time radial electric fields are present. The inclination of the lines can be explained by the assumption of a completely or partially rotating plasma column. The velocity of rotation which is a function of the radius can only be measured by spectroscopic means. In this article a method is developped which permits the calculation of the velocity of rotation as well as the calculation of the distribution function of the particle velocity from spectroscopic measurements of the line profiles.     

Sonoprocessing of wetting of SiC by liquid Al: A thermodynamic and kinetic study

The sonoprocessing of droplet spreading during the wetting process of molten aluminum droplets on SiC ceramic substrates at 700 °C is investigated in this paper. When wetting is assisted by a 20 kHz frequency ultrasonic field, the wettability of liquid metal gets enhanced, which has been determined by the variations in thermodynamic energy and wetting kinetics. Wetting kinetic characteristics are divided into two stages according to pinning and depinning states of substrate/droplet contact lines. The droplet is static when the contact line is pinning, while it is forced to move when the contact line is depinning. When analyzing the pinning stage, high-speed photography reveals the evidence of oxide films being rapidly crushed outside the aluminum droplet. In this work, atomic models of spherical Al core being wrapped by alumina shell are tentatively built, whose dioxide microstructures are being transformed from face-centered cubic into liquid at the atomic scale. At the same time, the wetting experiment reveals that the oxide films show changes in the period of sonoprocessing from 3rd to 5th second.During the ultrasonic spreading behavior in the late stage, there is a trend of evident expansion of the base contact area. The entire ultrasonic process lasts for no longer than 10 s. With the aid of ultrasonic sinusoidal waves, the wettability of metal Al gets a rapid improvement. Both molecular dynamic (MD) investigations and the experiments results reveal that the precursor film phenomenon is never found unless wetting is assisted by ultrasonic treatments. However, the precursor film appears near the triple line after using ultrasonics in the droplet wetting process, whose formation is driven by ultrasonic oscillations. Due to the precursor film, the ultrasonic wetting contact angle is lower than the non-ultrasonic contact angle. In addition, the time-variant effective ultrasonic energy has been quantitatively evaluated. The numerical expressions of thermodynamic variables are well verified by former ultrasonic spreading test results, which altogether provide an intrinsic explanation of the fast-decreasing contact angle of Al/SiC.     

Resonant field amplification near the RWM stability boundary in a tokamak

Evolution of a resistive wall mode (RWM)—a magnetic field perturbation produced by a plasma and partially stabilized by a conducting wall—is considered. It is assumed that there is a small resonant harmonic in the spectrum of the static error field. It is shown that the effect of this harmonic on the dynamics of stable RWMs increases as the plasma approaches the RWM stability boundary. The error field is “amplified” during the transition through this boundary. The smaller the rotation velocity of the perturbation and the longer the time during which the plasma stays near the stability boundary, the stronger this amplification is.     

亲水性微观粗糙表面润湿状态转变性能研究

以亲水性微观粗糙表面上不同几何形貌及分布的微柱阵列为对象, 讨论了液滴在亲水性粗糙表面上的润湿过程以及润湿状态的转变阶段. 从能量角度分别考察了微观粗糙结构几何形貌及分布、微柱几何参数、固体表面亲水性、接触角滞后作用等因素对液滴润湿状态转变的影响规律. 研究发现: 在亲水粗糙表面, 正方形微柱呈正六边形阵列分布时, 液滴更容易形成稳定的Cassie状态, 或者液滴仅发生Cassie状态向中间浸润状态的转变; 与此同时, 减小微柱间距、增大方柱宽度或圆柱直径、增大微柱高度、增强固体表面的亲水性将有利于液滴处于稳定的Cassie状态, 或阻止润湿状态向伪-Wenzel或Wenzel状态转变; 然而, 当液滴处于Cassie状态时, 较小的固-液界面面积分数或减弱固体表面亲水性能均有利于增大液滴的表观接触角, 因此在亲水表面设计粗糙结构时应综合考虑润湿状态稳定性和较大表观接触角两方面因素; 此外, 接触角滞后作用对于液滴状态的稳定性以及疏水性能的实现具有相反作用的影响. 研究结果为液滴在亲水表面获得稳定Cassie状态的粗糙结构设计方法提供了理论依据. 关键词： 亲水表面 微观粗糙结构 表面自由能 润湿状态转变     

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.     

A lattice Boltzmann method for incompressible two-phase flows on partial wetting surface with large density ratio

This paper reports a new numerical scheme of the lattice Boltzmann method for calculating liquid droplet behaviour on particle wetting surfaces typically for the system of liquid–gas of a large density ratio. The method combines the existing models of Inamuro et al. [T. Inamuro, T. Ogata, S. Tajima, N. Konishi, A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys. 198 (2004) 628–644] and Briant et al. [A.J. Briant, P. Papatzacos, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion in a liquid–gas system, Philos. Trans. Roy. Soc. London A 360 (2002) 485–495; A.J. Briant, A.J. Wagner, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion: I. Liquid–gas systems. Phys. Rev. E 69 (2004) 031602; A.J. Briant, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion: II. Binary fluids, Phys. Rev. E 69 (2004) 031603] and has developed novel treatment for partial wetting boundaries which involve droplets spreading on a hydrophobic surface combined with the surface of relative low contact angles and strips of relative high contact angles. The interaction between the fluid–fluid interface and the partial wetting wall has been typically considered. Applying the current method, the dynamics of liquid drops on uniform and heterogeneous wetting walls are simulated numerically. The results of the simulation agree well with those of theoretical prediction and show that the present LBM can be used as a reliable way to study fluidic control on heterogeneous surfaces and other wetting related subjects.     

润湿梯度作用下液滴在倾斜表面向上运动的格子Boltzmann模拟

采用基于Shan-Chen伪势模型的格子Boltzmann方法,对液滴在存在润湿梯度的倾斜表面上克服重力、自下而上运动的过程进行模拟。探究润湿梯度、液滴尺寸、Bond数以及表面倾斜角度对液滴运动的影响。计算结果表明：液滴在运动过程中,内部会出现沿斜面向上的速度矢量,润湿梯度越大,液滴运动速度越快,润湿长度也越长,且动态接触角减小速率越快。液滴尺寸和Bond数对液滴运动的影响较小,但存在临界Bond数,超过该临界Bond数时,液滴将沿梯度润湿表面向下运动。表面倾角对液滴运动有显著影响,倾角增大,液滴运动速度和润湿长度都明显减小。     

Vibration-induced climbing of drops

We report an experimental study of liquid drops moving against gravity, when placed on a vertically vibrating inclined plate, which is partially wetted by the drop. The frequency of vibrations ranges from 30 to 200 Hz, and, above a threshold in vibration acceleration, drops experience an upward motion. We attribute this surprising motion to the deformations of the drop, as a consequence of an up or down symmetry breaking induced by the presence of the substrate. We relate the direction of motion to contact angle measurements. This phenomenon can be used to move a drop along an arbitrary path in a plane, without special surface treatments or localized forcing.     

3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids

This work presents a three-dimensional finite-element algorithm, based on the phase-field model, for computing interfacial flows of Newtonian and complex fluids. A 3D adaptive meshing scheme produces fine grid covering the interface and coarse mesh in the bulk. It is key to accurate resolution of the interface at manageable computational costs. The coupled Navier–Stokes and Cahn–Hilliard equations, plus the constitutive equation for non-Newtonian fluids, are solved using second-order implicit time stepping. Within each time step, Newton iteration is used to handle the nonlinearity, and the linear algebraic system is solved by preconditioned Krylov methods. The phase-field model, with a physically diffuse interface, affords the method several advantages in computing interfacial dynamics. One is the ease in simulating topological changes such as interfacial rupture and coalescence. Another is the capability of computing contact line motion without invoking ad hoc slip conditions. As validation of the 3D numerical scheme, we have computed drop deformation in an elongational flow, relaxation of a deformed drop to the spherical shape, and drop spreading on a partially wetting substrate. The results are compared with numerical and experimental results in the literature as well as our own axisymmetric computations where appropriate. Excellent agreement is achieved provided that the 3D interface is adequately resolved by using a sufficiently thin diffuse interface and refined grid. Since our model involves several coupled partial differential equations and we use a fully implicit scheme, the matrix inversion requires a large memory. This puts a limit on the scale of problems that can be simulated in 3D, especially for viscoelastic fluids.