A theoretical analysis of the electromigration-induced void morphological evolution under high current density

In this work, analysis of electromigration-induced void morphological evolution in solder interconnects is performed based on mass diffusion theory. The analysis is conducted for three typical experimentally observed void shapes: circular, ellipse, and cardioid. Void morphological evolution is governed by the competition between the electric field and surface capillary force. In the developed model, both the electric field and capillary force on the void's surface are solved analytically. Based on the mass conversation principle, the normal velocity on the void surface during diffusion is obtained. The void morphological evolution behavior is investigated, and a physical model is developed to predict void collapse to a crack or to split into sub-voids under electric current. It is noted that when the electric current is being applied from the horizontal direction, a circular void may either move stably along the electric current direction or collapse to a finger shape, depending on the relative magnitude of the electric current and surface capillary force. However, the elliptical-shaped void will elongate along the electric current direction and finally collapse to the finger shape. On the other hand, the cardioid-shaped void could bifurcate into two sub-voids when the electric current reaches a critical value. The theoretical predictions agree well with the experimental observations.

Effect of perforation density distribution on production of perforated horizontal wellbore

To address the issue of horizontal well production affected by the distribution of perforation density in the wellbore,a numerical model for simulating two-phase flow in a horizontal well is established under two perforation density distribution conditions(i.e.increasing the perforation density at inlet and outlet sections respectively).The simulation results are compared with experimental results to verify the reliability of the numerical simulation method.The behaviors of the total pressure drop,superficial velocity of air-water two-phase flow,void fraction,liquid film thickness,air production and liquid production that occur with various flow patterns are investigated under two perforation density distribution conditions based on the numerical model.The total pressure drop,superficial velocity of the mixture and void fraction increase with the air flow rate when the water flow rate is constant.The liquid film thickness decreases when the air flow rate increases.The liquid and air productions increase when the perforation density increases at the inlet section compared with increasing the perforation density at the outlet section of the perforated horizontal wellbore.It is noted that the air production increases with the air flow rate.Liquid production increases with the bubble flow and begins to decrease at the transition point of the slug-stratified flow,then increases through the stratified wave flow.The normalized liquid flux is higher when the perforation density increases at the inlet section,and increases with the radial air flow rate.

On the interaction between bubbles and the free surface with high density ratio 3D lattice Boltzmann method

The bubbles rise up and burst at the free surface is a complex two-phase process.A free energy lattice Boltzmann method(LBM)model is adopted in this paper to study this phenomenon.The interface capturing technique[Zheng et al.,2006]is used to deal with the high density ratio problem.The Laplace law and the air-water interface capturing ability are validated for the multiphase model.The interaction between the single bubble or multiple bubbles and the free surface are studied by the multiphase model.The force acting on the bubble and the evolution of the free surface is studied.Meanwhile,effect of the initial distance between two adjacent bubbles on interaction effects of multiple bubbles is investigated as well.

A multicomponent multiphase lattice Boltzmann model with large liquid–gas density ratios for simulations of wetting phenomena

A multicomponent multiphase（MCMP） pseudopotential lattice Boltzmann（LB） model with large liquid–gas density ratios is proposed for simulating the wetting phenomena. In the proposed model, two layers of neighboring nodes are adopted to calculate the fluid–fluid cohesion force with higher isotropy order. In addition, the different-time-step method is employed to calculate the processes of particle propagation and collision for the two fluid components with a large pseudoparticle mass contrast. It is found that the spurious current is remarkably reduced by employing the higher isotropy order calculation of the fluid–fluid cohesion force. The maximum spurious current appearing at the phase interfaces is evidently influenced by the magnitudes of fluid–fluid and fluid–solid interaction strengths, but weakly affected by the time step ratio.The density ratio analyses show that the liquid–gas density ratio is dependent on both the fluid–fluid interaction strength and the time step ratio. For the liquid–gas flow simulations without solid phase, the maximum liquid–gas density ratio achieved by the present model is higher than 1000：1. However, the obtainable maximum liquid–gas density ratio in the solid–liquid–gas system is lower. Wetting phenomena of droplets contacting smooth/rough solid surfaces and the dynamic process of liquid movement in a capillary tube are simulated to validate the proposed model in different solid–liquid–gas coexisting systems. It is shown that the simulated intrinsic contact angles of droplets on smooth surfaces are in good agreement with those predicted by the constructed LB formula that is related to Young＇s equation. The apparent contact angles of droplets on rough surfaces compare reasonably well with the predictions of Cassie＇s law. For the simulation of liquid movement in a capillary tube, the linear relation between the liquid–gas interface position and simulation time is observed, which is identical to the analytical prediction. The simulation results regarding the wetting phenomena of droplets on smooth/rough surfaces and the dynamic process of liquid movement in the capillary tube demonstrate the quantitative capability of the proposed model.

Numerical and theoretical investigations of the effect of the gangue-coal density ratio on the drawing mechanism in longwall top-coal caving

Discrete element calculations of the top-coal drawing process for diferent gangue-coal density ratios were conducted to investigate the efect of the gangue-coal density ratio on the drawing mechanism in longwall top-coal caving.The efects were analyzed for the drawing body,the top-coal boundary,and the recovery of top coal.The results show that for increasing density ratio,the initial drawing body on the goaf side is farther away from the drawing support and its width and volume gradually increase.The upper part of the sickle-shaped drawing body extends near the initial drawing body with increasing density ratio in the normal cycling stage,and the distance from the drawing body to the initial drawing body is its maximum width.The larger the density ratio,the smaller the height of the top coal above the goaf at the end of the initial drawing process.The height of the top-coal boundary decreases with increasing density ratio,until it reaches a limit.In a normal cycle,due to hysteretic development,the top-coal boundary moves toward the goaf until the density ratio is approximately 2.0,which is consistent with the physical experiment results.Finally,increasing the advance length of the working face is benefcial for increasing the overall recovery of top coal.

On the trajectory of nonturbulent liquid jets in subsonic crossflows at different density ratios

Numerical simulations using volume of fluid(VOF)method are performed to study the impact of liquid-to-gas density ratio on the trajectory of nonturbulent liquid jets in gaseous crossflows.In this paper,large eddy simulation(LES)turbulence model is coupled with the VOF method to describe the turbulence effects accurately.In addition,dynamic adaptive mesh refinement method with two refinement levels is applied to refine the size of the cells located at gas-liquid interface.Density ratio is changed from 10 to 5000 while other nondimensional numbers are kept constant.Large density ratios are considered in this paper since they are common in many practical applications such as solution precursor/suspension plasma sprays.Our simulations show that the penetration height,especially in the farfield,increases as the density ratio increases.A general correlation for the jet trajectory,which can be used for a wide range of density ratios,is developed based on our simulation results.

An improved lattice Boltzmann model for high gas and liquid density ratio in composite grids

Lattice Boltzmann method is one of the widely used in multiphase fluid flow.However,the two main disadvantages of this method are the instability of numerical calculations due to the large density ratio of two phases and impossibility of the temperature distribution to be fed back into the velocity distribution function when the temperature is simulated.Based on the combination prescribed by Inamuro,the large density ratio two-phase flow model and thermal model makes the density ratio of the model simulation to be increased to 2778:1 by optimizing the interface distribution function of two-phase which improves the accuracy of differential format.The phase transition term is added as source term into the distribution function controlling two phase order parameters to describe the temperature effect on the gas-liquid phase transition.The latent heat generated from the phase change is also added as a source term into the temperature distribution function which simulates the movement of the flow under the common coupling of density,velocity,pressure and temperature.The density and the temperature distribution of single bubble are simulated.Comparison of the simulation results with experimental results indicates a good agreement pointing out the effectiveness of the improved model.

Computation of compressible flows with high density ratio and pressure ratio

The WENO method, RKDG method, RKDG method with original ghost fluid method, and RKDG method with modified ghost fluid method are applied to singlemedium and two-medium air-air, air-liquid compressible flows with high density and pressure ratios： We also provide a numerical comparison and analysis for the above methods. Numerical results show that, compared with the other methods, the RKDG method with modified ghost fluid method can obtain high resolution results and the correct position of the shock, and the computed solutions are converged to the physical solutions as themesh is refined.

Floquet instability of a large density ratio liquid-gas coaxial jet with periodic fluctuation

By numerical simulation of basic flow, this paper extends Floquet stability analysis of interracial flow with periodic fluctuation into large density ratio range. Stability of a liquid aluminum jet in a coaxial nitrogen stream with velocity fluctuation is investigated by Chebyshev collocation method and the Floquet theory. Parametric resonance of the jet and the influences of different physical parameters on the instability are discussed. The results show qualitative agreement with the available experimental data.

Study on the Relationship of Seedling Density and Line Spacing to Leaf-stem Ratio, DW/FW Ratio and Grass Yield of Forage Sweet Sorghum

[ Objectives ] The aim was to optimize the configuration of seedling density and line spacing of forage sweet sorghum （ Sorghum blcolor （ L. ） Moench） and explore its high-yield cultivation techniques. [ Methods] Effects of such two influencing factors as line spacing and seedling density on the leaf-stem ratio, DW/FW ratio and grass yield of forage sweet sorghum were analyzed by using split-plot experiment design experiment method and LSD method of IBM. SPSS. Statis- tics. v22 stati, stics software. [ Results ~ Seedling density and line spacing had no obvious effect on the leaf-stem ratio and DW/FW ratio of forage sweet sorghum but had obvious influences on the grass yield. Moreover, the optimal combination of seedling density and line spacing for high yield of forage sweet sorghum was A2 B4, that is, seedling density was 225 000 plants/hm2, and line spacing was 40 cm. [ Conclusions] The results provided a theoretical basis and technical support for high-yield cultivation techniques of forage sweet sorghum.

Degradation of effective carrier-power-to-noise densityratio based on code trackingspectral sensitivitycoefficient for GNSS radio frequencycompatibilityin C band

The frequency band between 5 010 MHz and 5 030 MHz allocated as C band has been used as a candidate in the global navigation satellite systems （GNSS） along with more and more naviga- tion services in L band. The potential benefits and technical requirements of C band for satellite navi- gation have been analyzed before. However the degradation of effective carrier-power-to-noise densi- ty ratio（ A （C/No ）eu） based on code tracking spectral sensitivity coefficient（ CT_SSC ） as a compati- bility assessment methodology for potential GNSS radio frequency compatibility in C-Band has not been discussed clearly. So the compatibility of the signals in the C band between BeiDou （BD） B1 C and GPS L1C, L1C/A, Galileo E1Os as the interoperability or classical signals in L band is analyzed. Simulation results reveal the interference degree between BD III B1C and GPS L1C/A, L1C, Galileo E1OS. The results can also reveal that the multiplexed binary offset carrier （MBOC） and binary phase shift keying （BPSK） modulation is not appropriate for C band.

Numerical Simulation on Partially Liquid-Filled Sloshing with Baffle Under Different Density Ratios by the CLSVOF/IB Method

The density and viscosity ratios on partially liquid-filled sloshing with baffle have been investigated numerically in this study.As the key to success in the present simulation,the Coupled Level Set and the Volume of Fluid(CLSVOF)method and the Immersed Boundary(IB)method are used to capture gas/liquid and fluid/structure interfaces,respectively.Within the CLSVOF method,surface normal in weighting factors is calculated by the level set function,resulting in a more accurate solution.Furthermore,the Tangent of Hyperbola for INterface Capturing(THINC)coupled with the Weighted Linear Interface Calculation(WLIC)scheme is used for capturing moving interface.As a standard practice,we first validate the code by comparing it with experimental results of liquid sloshing,which involves large deformation of interface.In addition to the validation study of the present method,the problems of liquid sloshing with baffle are investigated to understand kinematics and dynamics behaviors under different density and viscosity ratios.

Experimental research on the mixed sand ratio and initial dry density of weathered sand improved expansive soil free load swelling rate

In this paper, through the indoor free load swelling rate test, expansive soil in a section of a first- class highway reconstruction project in Yichang City was studied. It emphatically analyzed the interrelations among free load swelling rate, non-load time, the proportion of mixed sand and initial dry density. Experimen- tal studies have shown that： Free load swelling deformation is mainly divided into three stages of rapid expan- sion, slow expansion and final stability; when the initial dry density is constant, free load swelling rate of the weathered sand modified soil will reduce rapidly before they slow down with the increase of sand proportion, and weathered sand modified soil free load swelling rate is not sensitive to the large amount of sand mixed; in the same mixed sand ratio, weathered sand modified soil free load swelling rate increases rapidly with the in- crease of initial dry density, there is a good linear correlation between them. To take appropriate control of the initial dry density during the expansive soil subgrade construction helps to reduce its swelling deformation and ensures the stability of the embankment.

A new two-part test based on density ratio model for zero-inflated continuous distributions

In this paper,we consider testing the hypothesis concerning the means of two independent semicontinuous distributions whose observations are zero-inflated,characterized by a sizable number of zeros and positive observations from a continuous distribution.The continuous parts of the two semicontinuous distributions are assumed to follow a density ratio model.A new two-part test is developed for this kind of data.The proposed test takes the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution.The test is proved to follow a 2 distribution with two degrees of freedom.Simulation studies show that the proposed test controls the type I error rates at the desired level,and is competitive to,and most of the time more powerful than two popular tests.A real data example from a dietary intervention study is used to illustrate the usefulness of the proposed test.

Effect of injection angle,density ratio,and viscosity on droplet formation in a microfluidic T-junction

The T-junction microchannel device makes available a sharp edge to form micro-droplets from biomaterial solutions. This article investigates the effects of injection angle, flow rate ratio, density ratio,viscosity ratio, contact angle, and slip length in the process of formation of uniform droplets in microfluidic T-junctions. The governing equations were solved by the commercial software. The results show that contact angle, slip length, and injection angles near the perpendicular and parallel conditions have an increasing effect on the diameter of generated droplets, while flow rate, density and viscosity ratios, and other injection angles had a decreasing effect on the diameter.

Research progress of monocyte/high density lipoprotein ratio in cardiovascular diseases

In recent years,monocyte to high density lipoprotein cholesterol ratio(MHR)has attracted wide attention as a new marker of inflammatory response.This indicator includes two aspects:inflammatory response and lipid accumulation,which are the two most basic characteristics of Atherosclerosis(AS).AS is closely related to the occurrence of Cardiovascular diseases(CVD).A large number of existing studies have confirmed that MHR is an inflammatory marker that can dynamically reflect the trend of inflammation,can reflect the chronic inflammatory response in blood vessels,and can evaluate the occurrence,development and prognosis of cardiovascular disease in a non-invasive manner.This article reviews recent studies on the role of monocytes and high-density lipoproteins in chronic inflammation of blood vessels,as well as the current status of research on MHR and cardiovascular disease in the light of recent literature.

Persistence in Non-Autonomous Lotka-Volterra System with Predator-Prey Ratio-Dependence and Density Dependence

The main purpose of this article is considering the persistence non-autonomous Lotka-Volterra system with predator-prey ratio-dependence and density dependence. We get the sufficient conditions of persistence of system, further have the necessary conditions, also the uniform persistence condition, which can be easily checked for the model is obtained.

Local Empirical Likelihood Diagnosis of Varying Coefficient Density-Ratio Models Based on Case-Control Data

In this paper, a varying-coefficient density-ratio model for case-control studies is developed. We investigate the local empirical likelihood diagnosis of varying coefficient density-ratio model for case-control data. The local empirical log-likelihood ratios for the nonparametric coefficient functions are introduced. First, the estimation equations based on empirical likelihood method are established. Then, a few of diagnostic statistics are proposed. At last, we also examine the performance of proposed method for finite sample sizes through simulation studies.

Effects of binder strength and aggregate size on the compressive strength and void ratio of porous concrete

To test the influence of binder strength, porous concretes with 4 binder strengths between 30.0-135.0 MPa and 5 void ratios between 15%-35% were tested. The results indicated that for the same aggregate, the rates of strength reduction due to the increases in void ratio were the same for binders with different strengths. To study the influence of aggregate size, 3 single size aggregates with nominal sizes of 5.0, 13.0 and 20.0 mm （Nos. 7, 6 and 5 according to JIS A 5001） were used to make porous concrete. The strengths of porous concrete are found to be dependent on aggregate size. The rate of strength reduction of porous concrete with small aggregate size is found to be higher than that with larger aggregate size. At the same void ratio, the strength of porous concrete with large aggregate is larger than that with small aggregate. The general equations for porous concrete are related to compressive strength and void ratio for different binder strengths and aggregate sizes.

Study on the packed volume and the void ratio of idealized human red blood cells using a ?nite-discrete element method

Numerical simulations are performed to examine the packing behavior of human red blood cells(RBCs). A combined ?nite-discrete element method(FDEM) is utilized, in which the RBCs are modeled as no-friction and no-adhesion solid bodies. The packed volume and the void ratio of a large number of randomly packed RBCs are clari?ed,and the effects of the RBC shape, the mesh size, the cell number, and the container size are investigated. The results show that the packed human RBCs with normal shape have a void ratio of 28.45%, which is slightly higher than that of the ?at or thick cells used in this study. Such information is bene?cial to the further understanding on the geometric features of human RBCs and the research on RBC simulations.