An exact solution of the moving boundary problem for the expansion of a plasma cylinder in a magnetic field

An exact analytic solution has been obtained for a uniformly expanding, neutral, infinitely conducting plasma cylinder in an external uniform and constant magnetic field. The electrodynamical aspects related to the emission and transformation of energy have been considered as well. The results obtained can be used in analysing the recent experimental and simulation data.     

用转轮演示载流导线在磁场中的受力

介绍了用转轮方式演示载流导线在磁场中受力的原理和演示方法。     

流体黏性及表面张力对气泡运动特性的影响

基于气泡边界层理论,引入黏性修正,采用边界积分法,考虑黏性效应和表面张力在单气泡以及双气泡耦合作用过程中的影响.首先将建立的数值模型与Rayleigh-Plesset的解析解进行对比,发现二者符合良好,验证了数值模型的有效性;在此基础上,建立考虑流体弱黏性效应的双气泡耦合模型,研究流体黏性和表面张力作用下,气泡表面变形、射流速度、流场能量转换等物理量的变化规律;最后研究雷诺数和韦伯数对于气泡脉动特性的影响规律.结果表明,流体黏性会抑制气泡脉动和气泡射流发展,降低气泡半径和射流速度;表面张力不改变气泡脉动幅值,但缩短了脉动周期,提升气泡势能.     

On the stability of a free surface of a magnetic fluid under microgravity

We have investigated the behavior of a free surface of a suspension of ferrimagnetic particles in heptane under strongly reduced gravity. It was found that the free surface is destabilized when a homogeneous magnetic field parallel to the surface is applied. The strength of the critical magnetic field parallel to the surface varies with the volume concentration of magnetic particles in the suspension. We show that the destabilization of the fluid layer is forced by the influence of the suspension on the homogeneity of the magnetic field producing a magnetic field component normal to the fluid surface. The dependence of the critical magnetic field on the volume concentration of magnetic particles can be explained by applying the theory of the normal-field instability to this field component under conditions of strongly reduced gravity. The experiments were carried out at the drop tower ‘Bremen’ of the Center of Applied Space Technology and Microgravity (ZARM) in Bremen.     

Effects of surface tension on the dynamics of a single micro bubble near a rigid wall in an ultrasonic field

Acoustic cavitation is a very important hydrodynamic phenomenon, and is often implicated in a myriad of industrial, medical, and daily living applications. In these applications, the effect mechanism of liquid surface tension on improving the efficiency of acoustic cavitation is a crucial concern for researchers. In this study, the effects of liquid surface tension on the dynamics of an ultrasonic driven bubble near a rigid wall, which could be the main mechanism of efficiency improvement in the applications of acoustic cavitation, were investigated at the microscale level. A synchronous high-speed microscopic imaging method was used to clearly record the temporary evolution of single acoustic cavitation bubble in the liquids with different surface tension. Meanwhile, the bubble dynamic characteristics, such as the position and time of bubble collapse, the size and stability of the bubbles, the speed of bubble boundaries and the micro-jets, were analyzed and compared. In the case of the single bubbles near a rigid wall, it was found that low surface tension reduces the stability of the bubbles in the liquid medium. Meanwhile, the bubbles collapse earlier and farther from the rigid wall in the liquids with lower surface tension. In addition, the surface tension has no significant influence on the speed of the first micro-jet, but it can substantially increase the speed of second and the third micro-jets after the first collapse of the bubble. These effects of liquid surface tension on the bubble dynamics can explain the mechanism of surfactants in numerous fields of acoustic cavitation for facilitating its optimization and application.     

Experiments on breakups of a magnetic fluid drop through a micro-orifice

We experimentally study the breakups of a ferrofluid drop passing through a narrow passage under the attraction of an external field. After passing through the orifice, the fluid thread starts to neck down significantly and eventually breaks to form new droplets. The dynamics of the ferrofluid breakup are analyzed parametrically, including the diameter of the orifice and the local field strength. The patterns of fluid breakups can be characterized by two measurements of the breaking droplets, such as their sizes and stretching lengths. These two characteristic measurements mainly depend on the diameter of the orifice. Breaking droplets with less stretching and smaller sizes are resulted from a narrower orifice. On the other hand, the number of total breaking droplets that represents the transport effectiveness of ferrofluids significantly depends on both the diameter of the orifice and the local field strength. While a stronger field generates more breaking droplets, a maximum number of breaking droplets occurs at an intermediate orifice's diameter.     

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.     

Dynamics and instability of current-carrying microbeams in a longitudinal magnetic field

The dynamics and instability of current-carrying slender microbeams immersed in a longitudinal magnetic field is investigated by considering the material length scale effect of the microbeam. On the basis of modified couple stress theory, a theoretical model considering the effect of Lorentz forces is developed to analyze the free vibration and possible instability of the microbeam. Using the differential quadrature method, the governing equations of motion are solved and the lowest three natural frequencies are determined. The obtained results reveal that the electric current and the longitudinal magnetic field tend to reduce the microbeam's flexural stiffness. It is therefore shown that the lowest natural frequencies would decrease with increasing magnetic field parameter. The mode shapes of the microbeam are found to be generally three-dimensional spatial in the presence of the longitudinal magnetic field. It is interesting that buckling instability would concurrently occur in the first mode or in the higher-order modes when the magnetic field parameter becomes sufficiently large.     

Effect of surface tension on a liquid-jet produced by the collapse of a laser-induced bubble against a rigid boundary

The effect of surface tension on the behavior of a liquid-jet is investigated experimentally by means of a fiber-coupled optical beam deflection (OBD) technique. It is found that a target under water is impacted in turn by a laser-plasma ablation force and by a high-speed liquid-jet impulse induced by bubble collapse in the vicinity of a rigid boundary. The liquid-jet impact is found to be the main damage mechanism in cavitation erosion. Furthermore, the liquid-jet increases monotonously with surface tension, so cavitation erosion rises sharply with increasing surface tension. Surface tension also reduces bubble collapse duration. From the experimental results and the modified Rayleigh theory, the maximum bubble radius is obtained and it is found to reduce with increasing surface tension.     

On the final configuration of a plane magnetic field dragged by a highly conducting fluid and anchored at the boundary

The final configuration of the magnetic field dragged by a plane conducting flow such that the feet of the field lines are fixed at the boundary is studied by asymptotic analysis on the small magnetic diffusivity. The first order approximation yields that the streamlines become also magnetic field lines and the magnetic potential satisfies an ordinary differential equation on the transversal variable whose boundary values are found by the addition of a boundary layer. It turns out that these values correspond to certain averages along the boundaries, except when there exist stagnation points, which dominate the magnetic potential diffusion. Corners of the boundary curves behave differently, because stagnation points there disappear after straightening the curve by a change of variables that also kills the zero of the velocity.     

The dynamic behavior of magnetic fluid adsorbed to small permanent magnet in alternating magnetic field

The dynamic behavior of a magnetic fluid adsorbed to a small NdFeB permanent magnet subjected to an alternating magnetic field was studied with a high speed video camera system. The directions of alternating magnetic field are parallel and opposite to that of the permanent magnet. It was found that the surface of magnetic fluid responds to the external alternating magnetic field in elongation and contraction with a lot of spikes. Generation of a capillary magnetic fluid jet was observed in the neighbourhood of a specific frequency of alternating field. The effect of gravitational force on surface phenomena of magnetic fluid adsorbed to the permanent magnet was revealed.     

Investigation of surface properties of liquid transition metals: Surface tension and surface entropy

In the present study, surface properties namely surface tension and surface entropy of liquid transition metals have been reported. The surface entropy of liquid Fe, Co and Ni metals has been investigated using the expression derived by Gosh et al. [R.C. Gosh, A.Z. Ziauddin Ahmed, G.M. Bhuiyan, Eur. Phys. J. B 56 (2007) 177]. To describe interionic interaction the pseudopotential approach has been used and radial distribution functions have been determined from the solution of Ornstein-Zernike integral equation. The calculated values of surface tension and surface entropy agree well with experiment. The present study shows that the expression derived by Gosh et al. leads to a good estimation for the surface entropy.     

The surface tension of liquid Cu-Fe-Sb alloys

The results of study on the influence of temperature and iron and antimony on the surface tension of liquid ternary Cu-Fe-Sb systems are presented. The measurements were carried out with the sessile drop method, in a broad range of the alloy additions concentration (Fe and Sb). It was demonstrated that the surface tension varies as a linear function of temperature and concentration of iron. It was also demonstrated that antimony, in examined alloys, shows the properties characteristic of a surface-active substance, significantly reducing the surface tension value. The changes of the surface tensions as a function of concentration of antimony were described with the Szyszkowski's equation. Composition of surface layer, enriched with an antimony, was determined basing on the model, which used data regarding properties of binary systems. The surface tension values of Cu-Fe-Sb systems was also computed from model and compared with experimental data. A good agreement was obtained.     

Model calculation of the surface tension of liquid Ga-Bi alloy

A convenient model, based on some assumptions, for calculating the composition and temperature dependence of the surface tension of binary liquid alloys is reported. The theoretical calculations of the surface tension of gallium-rich-bismuth alloys are presented. The calculated results are compared with the reported experimental data. A relatively good agreement with experimental behavior of the composition dependence of the surface tension was found, but a disagreement was observed with experimental temperature behavior of the surface tension of these alloys. The calculations were conducted in the temperature range from almost 320 K to about 800 K. The surface tension was calculated from eutectic composition (x_Bi = 0.0022) to x_Bi = 0.1, and worked out by linear equations. The model calculation and analysis indicate a first order surface phase transition in this system, which is in accord with experimental findings. For this system, γ decreases linearly with increasing temperature at fixed Bi mole fraction x_Bi, and thus, suggesting a positive surface excess entropy. It is also found that the surface tension isotherms show the linear dependence on the concentration, in the logarithm scale of x_Bi, in the very narrow concentration range.     

Dynamics of a single peak of the Rosensweig instability in a magnetic fluid

To describe the dynamics of a single peak of the Rosensweig instability a model is proposed which approximates the peak by a half-ellipsoid atop a layer of magnetic fluid. The resulting nonlinear equation for the height of the peak leads to the correct subcritical character of the bifurcation for static induction. For a time-dependent induction the effects of inertia and damping are incorporated. The results of the model show qualitative agreement with the experimental findings, as in the appearance of period doubling, trebling, and higher multiples of the driving period. Furthermore, a quantitative agreement is also found for the parameter ranges of frequency and induction in which these phenomena occur.     

The surface tension and density of the Cu-Ag-In alloys

The surface tension and the densities of the Cu-Ag-In alloys have been measured by means of the sessile drop method. The density of these alloys depends linearly on temperature in the case of all the investigated compositions. The surface tension shows a linear dependence on temperature except for the lowest temperatures. For most of the alloys, the surface tension at the lowest temperature is lower than that predicted by the straight line. The experimental values of the surface tension of the Cu-Ag-In alloys are compared with those computed from the model, and quite good agreement is observed.     

A molecular dynamics study of effective parameters on nano-droplet surface tension

The main purpose of this paper is to numerically study the effect of droplet radius, temperature, and surface wettability on droplet surface tension. Moreover, the validity of Young-Laplace equation (Y-L) for nano-droplet is examined. Simulations of droplet surrounded by its vapor and droplet on solid surface are carried out and the results are compared to each other in order to comprehend the role of surface wettability on droplet surface tension. The pair potential for the liquid-liquid and liquid-solid interaction is considered using Lennard-Jones model. Different numbers of atoms and surface wettabilities are employed to generate droplet of different radiuses. In addition, contact angle of droplet on solid surface is computed. Pressure tensor and density profile is locally calculated. Furthermore, liquid pressure is evaluated far from the interface using the virial theorem and gas pressure is obtained using an equation of state. In order to calculate the surface tension, two different approaches are employed; Young-Laplace equation and direct molecular dynamics (MD) simulation. The surface tension increases with increase in droplet radius and it is seen that the surface wettability does not directly influence the surface tension.     

Structure-mechanical approach to surface tension of solids

Some problems of applying the Lippmann equation to adsorption studies on solid electrodes are shortly reviewed. A novel nonthermodynamic approach to consider the role of elastic and plastic deformation of electrode surfaces during adsorption is proposed. The extremely thin electrode surface layers affected electrically and mechanically by adsorbate are supposed to be free of dislocations because of volume discrepancy. The nearest structure-mechanical analogs of such layers are the whisker crystals whose side surface could have one- and two-dimensional defects, but have no active dislocations. Like whiskers, surface metal layers should possess a high ultimate strength close to the theoretical one and a purely elastic deformation. Affected only by adsorbate, the surface electrode layer should be considered as absolutely elastic body, whose plastic deformation is impossible, i.e. the Lippmann equation and other equations containing terms of plastic deformation cannot be used in thermodynamics of the solid metal surface.     

A surface tension study of liquid threads

According to symmetry of liquid threads, definitions of surface tension in axial direction and angular direction are given. The formulas of surface tension in axial direction γ_z and surface tension in angular direction γ_θ are derived. A scheme to calculate Δγ = γ_z − γ_θ is designed. We investigate seven different systems (the numbers of molecules N are 1600, 2240, 2880,3360,4000,4800 and 5280) by molecular dynamics simulations. For liquid threads, Δγ increases with the decreasing radius of dividing surface. It shows that there exists surface tension anisotropy for liquid threads. The results obtained by molecular dynamics simulations support that surface tension is dependent on the dividing surface curvature.     

黏性、表面张力和磁场对Rayleigh-Taylor不稳定性气泡演化影响的理论分析

采用理论分析的方法考察了磁场中非理想流体中Rayleigh-Taylor(RT)不稳定性气泡的演化过程,在与磁场垂直的平面中,综合考虑流体黏性和表面张力的影响,推导了二维非理想磁流体RT不稳定性气泡运动的控制方程组,给出了不同情况下气泡速度的渐近解和数值解,分析了流体黏性、表面张力和磁场对气泡发展的影响,分析结果表明:流体黏性和表面张力能够降低气泡速度和振幅,即能够抑制RT不稳定性;而磁场对RT不稳定性的影响是由非线性部分引起的,并且磁场非线性部分的方向决定了磁场是促进还是抑制RT不稳定性的发展,