A conservative level set method for contact line dynamics

A new model for simulating contact line dynamics is proposed. We apply the idea of driving contact-line movement by enforcing the equilibrium contact angle at the boundary, to the conservative level set method for incompressible two-phase flow [E. Olsson, G. Kreiss, A conservative level set method for two phase flow, J. Comput. Phys. 210 (2005) 225–246]. A modified reinitialization procedure provides a diffusive mechanism for contact-line movement, and results in a smooth transition of the interface near the contact line without explicit reconstruction of the interface. We are able to capture contact-line movement without loosing the conservation. Numerical simulations of capillary dominated flows in two space dimensions demonstrate that the model is able to capture contact line dynamics qualitatively correct.     

Adaptive segmentation of magnetic resonance images with intensity inhomogeneity using level set method

It is a big challenge to segment magnetic resonance (MR) images with intensity inhomogeneity. The widely used segmentation algorithms are region based, which mostly rely on the intensity homogeneity, and could bring inaccurate results. In this paper, we propose a novel region-based active contour model in a variational level set formulation. Based on the fact that intensities in a relatively small local region are separable, a local intensity clustering criterion function is defined. Then, the local function is integrated around the neighborhood center to formulate a global intensity criterion function, which defines the energy term to drive the evolution of the active contour locally. Simultaneously, an intensity fitting term that drives the motion of the active contour globally is added to the energy. In order to segment the image fast and accurately, we utilize a coefficient to make the segmentation adaptive. Finally, the energy is incorporated into a level set formulation with a level set regularization term, and the energy minimization is conducted by a level set evolution process. Experiments on synthetic and real MR images show the effectiveness of our method.     

Variational piecewise constant level set methods for shape optimization of a two-density drum

We apply the piecewise constant level set method to a class of eigenvalue related two-phase shape optimization problems. Based on the augmented Lagrangian method and the Lagrange multiplier approach, we propose three effective variational methods for the constrained optimization problem. The corresponding gradient-type algorithms are detailed. The first Uzawa-type algorithm having applied to shape optimization in the literature is proven to be effective for our model, but it lacks stability and accuracy in satisfying the geometry constraint during the iteration. The two other novel algorithms we propose can overcome this limitation and satisfy the geometry constraint very accurately at each iteration. Moreover, they are both highly initial independent and more robust than the first algorithm. Without penalty parameters, the last projection Lagrangian algorithm has less severe restriction on the time step than the first two algorithms. Numerical results for various instances are presented and compared with those obtained by level set methods. The comparisons show effectiveness, efficiency and robustness of our methods. We expect our promising algorithms to be applied to other shape optimization and multiphase problems.     

Multi-bubble motion behavior of uniform magnetic field based on phase field model

Aiming at the interaction and coalescence of bubbles in gas–liquid two-phase flow, a multi-field coupling model was established to simulate deformation and dynamics of multi-bubble in gas–liquid two-phase flow by coupling magnetic field, phase field, continuity equation, and momentum equation. Using the phase field method to capture the interface of two phases, the geometric deformation and dynamics of a pair of coaxial vertical rising bubbles under the applied uniform magnetic field in the vertical direction were investigated. The correctness of results is verified by mass conservation method and the comparison of the existing results. The results show that the applied uniform magnetic field can effectively shorten the distance between the leading bubble and the trailing bubble, the time of bubbles coalescence, and increase the velocity of bubbles coalescence. Within a certain range, as the intensity of the applied uniform magnetic field increases, the velocity of bubbles coalescence is proportional to the intensity of the magnetic field, and the time of bubbles coalescence is inversely proportional to the intensity of the magnetic field.     

Distribution of micrometer-size particles in magnetic fluids in the presence of steady uniform magnetic field

In this paper, distribution of suspended micrometer-size particles in magnetic fluids is investigated. Microstructure formation of particles in magnetic fluids is simulated by using the discrete particle method based on the simplified Stokes dynamics. Not only magnetic particles but also nonmagnetic particles are rearranged in the field direction and form chain-like clusters due to the apparent magnetization in magnetic fluids in the presence of magnetic field. When the diameter of nonmagnetic particles is smaller than that of magnetic particles, nonmagnetic particles move into the empty space of microstructure of magnetic particles, and they are rearranged in the field direction. Uniformity of distribution of particles on the plane perpendicular to the field direction is maintained even after microstructure formation.     

Force and torque on a sphere with electric dipole moment moving in a dielectric fluid in the presence of a uniform magnetic field

The torque exerted by a magnetic field on a sphere with permanent electric dipole moment moving steadily in a dielectric fluid is calculated to lowest order in the dipole moment. Hence the force exerted on a steadily rotating sphere with electric dipole moment is found by Onsager symmetry. The modification from the vacuum values of torque and force depends only on the slip parameter and the static dielectric constant of the fluid. It is suggested that for a macroscopic ferro electric sphere the calculated effects could be measured experimentally without great difficulty.     

Effect of the induced magnetic field on peristaltic flow of a couple stress fluid

We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number Rm and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.     

旋转磁场对凝固组织形成的影响

研究了旋转磁场作用下Pb-45%Sn亚共晶合金的凝固组织.实验发现,旋转磁场的频率恒定时,凝固组织的晶粒尺寸随着磁场强度的增强而线性减小,同时,初生相的生长形态从枝晶转变为椭球状.X射线测试结果表明,初生相Pb发生了点阵膨胀,并且晶格常数随着磁场强度的增强先变大后减小,磁场强度在此存在一个临界值.能谱分析显示,随着磁场强度的增强,初生相Pb内Sn的含量逐渐降低.根据电磁场理论和扩散定律,对上述现象进行了理论分析,揭示出旋转磁场引起了液相强烈流动,加快了溶质原子的扩散以及对熔体的加热效应,导致了形核率的提高和长大速度的降低. 关键词： 旋转磁场 液相流动 晶格常数 溶质分配     

导电流体中气泡径向振动行为的磁场控制

液态金属中气泡行为是磁流体力学的重要方面。为对磁场条件下导电流体中气泡动力学行为作全面理解,基于磁流体动力学方法建立了磁场条件下导电流体中气泡径向振动的无量纲化动力学方程,数值研究了磁场对导电流体中气泡径向非线性振动稳定性、泡内温度、泡内气压及液体空化阈值的影响。结果显示:磁场增强了气泡非线性振动的稳定性,随着磁场增强且当作用在泡上的电磁力与惯性力数量级可比时,气泡运动为稳定的周期性振动;同时,磁场引起泡内温度、泡内压力及液体空化阈值变化。研究表明,可用磁场调节和控制液态金属中气泡的运动使其满足工程应用需求。     

临界电流磁矢量分析法在YBCO线圈上的验证

高温超导磁体临界电流磁矢量分析法准确地预测了BSCCO高温超导磁体的临界电流,为了进一步验证该方法预测YBCO高温超导磁体临界电流的准确性,文中作者用9.3m二代高温超导YBCO带材绕制了一个内径为70mm,外径为100mm,共35匝的单饼,测试了单饼5-15匝,15-25匝,25-35匝和5-35匝在77K下的临界电流,并用磁矢量分析法进行了仿真分析。通过对比发现,仿真分析和实验结果的误差在5%左右,最大误差是6.75%,最小误差是4.77%,验证了磁矢量分析法在预测YBCO高温超导磁体临界电流时的准确性。     

Ultrasound velocimetry of ferrofluid spin-up flow measurements using a spherical coil assembly to impose a uniform rotating magnetic field

Ferrofluid spin-up flow is studied within a sphere subjected to a uniform rotating magnetic field from two surrounding spherical coils carrying sinusoidally varying currents at right angles and 90° phase difference. Ultrasound velocimetry measurements in a full sphere of ferrofluid shows no measureable flow. There is significant bulk flow in a partially filled sphere (1-14 mm/s) of ferrofluid or a finite height cylinder of ferrofluid with no cover (1-4 mm/s) placed in the spherical coil apparatus. The flow is due to free surface effects and the non-uniform magnetic field associated with the shape demagnetizing effects. Flow is also observed in the fully filled ferrofluid sphere (1-20 mm/s) when the field is made non-uniform by adding a permanent magnet or a DC or AC excited small solenoidal coil. This confirms that a non-uniform magnetic field or a non-uniform distribution of magnetization due to a non-uniform magnetic field are causes of spin-up flow in ferrofluids with no free surface, while tangential magnetic surface stress contributes to flow in the presence of a free surface.Recent work has fitted velocity flow measurements of ferrofluid filled finite height cylinders with no free surface, subjected to uniform rotating magnetic fields, neglecting the container shape effects which cause non-uniform demagnetizing fields, and resulting in much larger non-physical effective values of spin viscosity η′∼10⁻⁸−10⁻¹² N s than those obtained from theoretical spin diffusion analysis where η′≤10⁻¹⁸ N s. COMSOL Multiphysics finite element computer simulations of spherical geometry in a uniform rotating magnetic field using non-physically large experimental fit values of spin viscosity η′∼10⁻⁸−10⁻¹² N s with a zero spin-velocity boundary condition at the outer wall predicts measureable flow, while simulations setting spin viscosity to zero (η′=0) results in negligible flow, in agreement with the ultrasound velocimetry measurements. COMSOL simulations also confirm that a non-uniform rotating magnetic field or a uniform rotating magnetic field with a non-uniform distribution of magnetization due to an external magnet or a current carrying coil can drive a measureable flow in an infinitely long ferrofluid cylinder with zero spin viscosity (η′=0).     

Numerical simulation of non-viscous liquid pinch-off using a coupled level set-boundary integral method

Simulations of the pinch-off of an inviscid fluid column are carried out based upon a potential flow model with capillary forces. The interface location and the time evolution of the free surface boundary condition are both approximated by means of level set techniques on a fixed domain. The interface velocity is obtained via a Galerkin boundary integral solution of the 3D axisymmetric Laplace equation. A short-time analytical solution of the Raleigh–Taylor instability in a liquid column is available, and this result is compared with our numerical experiments to validate the algorithm. The method is capable of handling pinch-off and after pinch-off events, and simulations showing the time evolution of the fluid tube are presented.     

Effect of tensile stress on the variation of magnetic field of low-alloy steel

The surface magnetic field intensity H_p(y) of low-carbon steel plate specimen was measured after tensile test and unloading; variation of H_p(y) was studied. It was found that H_p(y) signals first decreased with increase in stress, and then reversed to the initial field when the stress was greater than 160 MPa. Under yield stress, H_p(y) reached its maximum, and then decreased slightly with further increase in stress. The initial magnetic signals have great impact on the variation of magnetic field.     

Stability of hydromagnetic Dean flow between two arbitrarily spaced concentric circular cylinders in the presence of a uniform axial magnetic field

The effect of a uniform axial magnetic field on the stability of the flow of an incompressible viscous electrically conducting fluid between two arbitrarily spaced concentric circular cylinders driven by a constant azimuthal pressure gradient is studied. The linearized stability equations for steady axisymmetric disturbances form an eigenvalue problem, which are solved by using a classical Runge–Kutta scheme combined with a shooting method, termed unit disturbance method. It is observed that for fixed gap width, the magnetic field has a stabilizing influence on the flow for both perfectly conducting and nonconducting walls. It is also found that for a given value of magnetic parameter, stabilization is more as the gap width increases. Further the electrically nonconducting walls are found to be more destabilizing than the perfectly conducting walls. The critical value of the radii ratio (0<η<1) beyond which the first unstable mode becomes nonaxisymmetric is determined for various values of the magnetic parameter.     

Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium

In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.     

Deformation and motion by gravity and magnetic field of a droplet of water-based magnetic fluid on a hydrophobic surface

Motion and deformation of a water-based magnetic fluid on a hydrophobic surface were investigated under gravity and a magnetic field. Surface energy and the resultant contact angle of the magnetic fluid depend on the surfactant concentration. The fluid viscosity is governed mainly by magnetite concentration. The front edge of the droplet moved under a weak external field. The rear edge required a higher external field for movement. The forces of gravity and the magnetic field for moving of the front edge are almost equal. However, those of the rear edge are different. The motion of magnetic fluids by an external field depends on concentrations of surfactants and magnetic particles, the external field, and experimental assembly.     

外磁场对介质表面次级电子倍增效应的影响

本文采用Particle-in-cell数值方法模拟研究了不同强度外磁场条件下的次级电子倍增效应过程,分析了外磁场对次级电子倍增效应的影响.结果表明,当外磁场达到一定强度时,次级电子倍增效应在微波传输的一半时间内被抑制.通过外磁场抑制,在理想条件下可以使介质窗的微波传输功率容量提高4倍以上.     

Effect of variation of dielectric constant on the magnetic field modulation of exciplex luminescence

The effect of variation of dielectric constant on the relative magnetic field effect in singlet luminescence has been studied using a typical exciplex system at a saturating field. The study indicates strong specificity in the perturbation of the magnetic field effect by alcoholic solvents. In contrast to alcohols where relative singlet magnetic field effect is of the order of 2% only, the magnetic field effect in non-alcoholic medium reaches as high as 9%. Moreover, dielectric constant variation in alcohols yields curves which are distinctly different from those in non-alcoholic media. It turns out that this dependence of magnetic field effect on dielectric constant is similar in all non-alcoholic solvent mixtures. An analytical study based on Hong and Noolandi’s solution of Smoluchowski equation has been made. Derived expressions can interpret experimental curves reasonably well.     

基于水平集方法二维模型的软性磨粒两相流流场特性分析方法

两相流场特性分析是软性磨粒流精密加工方法的技术关键. 针对此问题, 利用水平集方法(LSM)结构拓扑变换原理, 建立了描述磨粒流在另一流体中运动变化的二维模型. 该模型中, 用LSM捕捉两相流之间的界面, 从而对两相流的运动情况和相关参数进行模拟仿真, 深入讨论了磨粒流加工机理. 研究表明: 以LSM原理建立的二维模型, 成功地仿真模拟了两相流相变过程; 利用k-ε湍流模型与Preston方程相结合的数值分析方法, 对流道内各区域的速度等流场特性进行讨论, 为软性磨粒流加工提供了前期基础性研究. 关键词： 水平集方法 结构化表面 软性磨粒流 k-ε湍流模型')" href="#">k-ε湍流模型     

Spin precession of a charged particle in a uniform magnetic field on a static space-time

We investigate the ratio of spin precession frequency to orbital frequency for a spinning charged particle confined to circular orbit in the equatorial plane of a compact object, with a uniform magnetic field, as described by the Wald and the Ernst potentials. In order to see the difference in behaviours for particles with differentg values we consider the cases of electron and proton separately.