In this paper, we consider numerical approximations for the viscous Cahn–Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system numerically is how to develop high order temporal discretization for the hyperbolic and nonlinear terms, allowing large time-marching step, while preserving the energy stability, i.e. the energy dissipative structure at the time-discrete level. We resolve this issue by developing two second-order time-marching schemes using the recently developed “Invariant Energy Quadratization” approach where all nonlinear terms are discretized semi-explicitly. In each time step, one only needs to solve a symmetric positive definite (SPD) linear system. All the proposed schemes are rigorously proven to be unconditionally energy stable, and the second-order convergence in time has been verified by time step refinement tests numerically. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy, and efficiency of the proposed schemes.

In this paper, the droplet formation process at a low capillary number in a flow focusing micro-channel is studied by performing a three-dimensional phase field benchmark based on the Cahn–Hilliard Navier–Stokes equations and the finite element method. Dynamic moving contact line and wetting condition are considered, and generalized Navier boundary condition (GNBC) is utilized to demonstrate the dynamic motion of the interface on wall surface. It is found that the mobility parameter plays a very critical role in the squeezing and breakup process to control the shape and size of droplets. We define the characteristic mobility Mc to represent the correct relaxation time of the interface. We also demonstrate that the characteristic mobility is associated with the physical process and should be kept as a constant as the product of the mobility tuning parameter χ and the square of interfacial thickness ε2. This criterion is applied for different interfacial thicknesses to correctly capture the physical process of droplet formation. Moreover, the size of the droplet, the velocity of the droplet along the downstream, and the period of droplet formation are compared between the numerical and experimental results which agree with each other both qualitatively and quantitatively. The presented model and criterion can be used to predict the dynamic behavior and movement of multiphase flows.

We present a particle-in-cell (PIC) method using a nonhomogeneous immersed-finite-element (IFE) field solver for modeling dielectric surface charging of complex-shaped objects in plasmas. The IFE solver allows PIC codes using a Cartesian mesh applied to simulations involving arbitrarily shaped objects with a similar accuracy as that using a body-fitting mesh. The object surface is treated as an interface. Surface charging is calculated directly from charge deposition at the interface, and the electrostatic fields on both sides of the interface are resolved self-consistently. The capability of the nonhomogeneous IFE-PIC method is demonstrated by a simulation study of the charging of an irregular-shaped asteroid in the solar wind.

This paper is to present a finite volume element (FVE) method based on the bilinear immersed finite element (IFE) for solving the boundary value problems of the diffusion equation with a discontinuous coefficient (interface problem). This method possesses the usual FVE method’s local conservation property and can use a structured mesh or even the Cartesian mesh to solve a boundary value problem whose coefficient has discontinuity along piecewise smooth nontrivial curves. Numerical examples are provided to demonstrate features of this method. In particular, this method can produce a numerical solution to an interface problem with the usual O(h2) (in L2 norm) and O(h) (in H1 norm) convergence rates. AMS subject classifications: 65N15, 65N30, 65N50, 35R05

ZnO, as a novel direct-wide-band-gap semiconductor material, is a potential candidate for short-wave opto-electronic devices. Due to its structural properties such as good c-axis orientation and excellent crystal lattice property, it has outstanding opto-electronic properties, especially its ultraviolet stimulated emission. By X-ray diffraction(XRD) and scanning electron microscope (SEM) , the influences of substrate temperature, the ratio of Ar to O_2 and thermal annealing temperature on ZnO crystal quality were studied. The results show that ZnO films desposited at 250℃ substrate temperature and Ar∶O_2=1∶4 have the best crystallization. Thermal annealing can improve the structural properties of ZnO. Highly c-axis oriented ZnO films on (100) silicon substrate were obtained by DC magnetron sputtering while the grain size was about 70nm.

The rate equations for particle produce, transport, and reaction with target surface, and sputtering peeling of ion and neutral particles with high energy are established. After these equations coupling up and taking account of other calculations, such as energy distribution functions, macroscopic flow velocity of gas, etc., the relation curves between sputtering rate and inlet flow of reaction gas for different discharge current are obtained, and the advantages of this analysis method are also discussed in the paper.

The compound fraction of target surface was gotten from the rate equations of sputtering and the transport equations of reactive particles. All of these equations are expressed by the constructional parameters of the chamber and macroscopic technology parameters. The calculating results from the TiN thin films deposited by reactive sputtering are well fit with the experimental data. The methodes provided in this paper will be benefit to the implementation of technology optimum as a new engineering methodes.

The purification model of macroscopic particles in descending process is established from the transport phenomena of particles and plasma chemicals. The concentration distribution, acceleration, velocity, and descending time of all kinds of particles and the removing amount of the impurities are calculated. Being identical with the experimental effects, the results show that about 97?% of impurities in silicon-germanium alloy powder can be removed.

The transport model of macroscopic particles in plasma is introduced, and the acceleration, the velocity and the time of the descent of the particles are calculated. The criterion of the gathering of the particles is obtained and a conclusion that the purity effects will be better in descending process. All these are very important for the industrial appliance of plasma.

研究了冷等离子体提纯硅粉薄层时硅粉的粒度与硅粉薄层的厚度对提纯效果的影响.实验表明,硅粉的颗粒大小在60-80μm之间,硅薄层的厚度为0.5mm时提纯效果较好.

Rising the temperature of silicon powder layer, the cold plasma can purify silicon up to more than 99.9%. The purifying mechanism is analyzed with the reaction kinetic method and the necessary equations have been set to discuss the effects on the purification of silicon powder layer. The removed rate of inclusion is improved with the increase of the temperature of silicon powder and reaction chamber.

The hydrometallurgical technology of purifying metallurgical grade silicon for solar grade silicon in medium scale was reported, with the emphasis on the low cost process and the high purity of silicon particle. The recovery rate of silicon powder, the silicon particle size and the acid concentration were described. The mechanism of ��passivation effect�� which occurs in high acid concentration abstraction was studied.

This paper presents particle simulation models for spacecraft charging and charged dust particle interactions on lunar surface. Full particle PIC simulations are carried out using real ion to electron mass ratio to obtain plasma sheath and wake, and the ∞oating potential of lunar lander in the lunar terminator region. Dust-in-plasma simulations are carried out to study electrostatic levitation of dusts and dust transport around lunar lander.