各向异性表面张力对定向凝固中共晶生长形态稳定性的影响

研究各向异性表面张力对定向凝固中共晶生长形态稳定性的影响.应用多重变量展开法导出了共晶界面表达式和扰动振幅的变化率满足的色散关系.结果表明,共晶生长系统有两种整体不稳定性机理:由非震荡导致的"交换稳定性"机理和由震荡导致的"整体波动不稳定性"机理.震荡有四种典型模式,即:反对称-反对称(AA-),对称-反对称(SA-)、反对称-对称(AS-)和对称-对称(SS-)模式.稳定性分析表明:共晶界面形态稳定性取决于Peclet数ε的某一个临界值ε_*,当ε大于临界值ε_*时,共晶界面形态不稳定;当ε小于临界值ε_*时,共晶界面形态稳定.随着各向异性表面张力增大,对应于AA-,SA-和SS-模式的临界值ε_(aa*),ε_(sa*)和ε_(ss*)随之减小,表明各向异性表面张力减小这三种模式的稳定性区域;然而,随着各向异性表面张力增大,对应于AS-模式的临界值ε_(as*)随之增大,表明各向异性表面张力增大AS-模式的稳定性区域.     

Phase field investigation on the initial planarinstability with surface tension anisotropy during directional solidification of binary alloys

Phase field investigation reveals that the stability of the planar interface is related to the anisotropic intensity of surface tension and the misorientation of preferred crystallographic orientation with respect to the heat flow direction. The large anisotropic intensity may compete to determine the stability of the planar interface. The destabilizing effect or the stabilizing effect depends on the misorientation. Moreover, the interface morphology of initial instability is also affected by the surface tension anisotropy.     

各向异性表面张力对深胞晶界面形态稳定性的影响

应用匹配渐近展开法和多变量展开法研究各向异性表面张力对定向凝固中深胞晶界面形态稳定性的影响, 通过寻找定向凝固系统的模式解获得了深胞晶界面形态满足的量子化条件. 结果表明, 与各向同性的定向凝固系统中深胞晶界面形态稳定性比较, 考虑各向异性表面张力的定向凝固中深胞晶生长界面形态也有两种整体不稳定性机制: 整体波动不稳定性和低频不稳定性. 随着各向异性表面张力的增加, 中性模式产生强振荡的枝晶结构的整体波动不稳定性的不稳定区域减小, 中性模式产生弱振荡的胞晶结构的低频不稳定性的不稳定区域增加.     

Anisotropic surface tension and the liquid drop model

The liquid drop model assumes that the surface tension of all nuclei is isotropic. The consequences of relaxing this assumption are studied. First a macroscopic theory of anisotropic surface tension is presented. Then with a particular choice for the functional form of the surface tension tensor, this theory is applied to a charged liquid drop. A small anisotropy in the surface tension can significantly distort a highly charged drop and lower its fission barrier.     

Viscoelastic theory for nematic interfaces

A complete macroscopic theory for compressible nematic-viscous fluid interfaces is developed and used to characterize the interfacial elastic, viscous, and viscoelastic material properties. The derived expression for the interfacial stress tensor includes elastic and viscous components. Surface gradients of the interfacial elastic stress tensor generates tangential Marangoni forces as well as normal forces. The latter may be present even in planar surfaces, implying that in principle static planar interfaces may accommodate pressure jumps. The asymmetric interfacial viscous stress tensor takes into account the surface nematic ordering and is given in terms of the interfacial rate of deformation and interfacial Jaumann derivative. The material function that describes the anisotropic viscoelasticity is the dynamic interfacial tension, which includes the interfacial tension and dilational viscosities. Viscous dissipation due to interfacial compressibility is described by the anisotropic dilational viscosity, and it is shown to describe the Boussinesq surface fluid appropriate for Newtonian interfaces when the director is homeotropic. Three characteristic interfacial shear viscosities are defined according to whether the surface orientation is along the velocity direction, the velocity gradient, or the unit normal. In the last case the expression reduces to the interfacial shear viscosity of the Boussinesq surface fluid. The theory provides a theoretical framework to study interfacial stability, thin liquid film stability and hydrodynamics, and any other interfacial rheology phenomena.     

各向异性表面张力对定向凝固中深胞晶生长的影响

利用匹配渐近展开法和多变量展开法求出定向凝固深胞晶生长的浓度场和界面形态的全局渐近解,研究各向异性表面张力对定向凝固深胞晶生长的影响.结果表明,各向异性表面张力对定向凝固过程深胞晶生长有显著的影响.随着各向异性表面张力增大,胞晶前端部分浓度减小而胞晶界面收缩;胞晶根部的浓度增大而界面曲率增大或根部的曲率半径减小,各向异性表面张力使得深胞晶界面振幅增加.本文结果能够计算定向凝固过程中深胞晶生长的浓度、界面形态.     

Anisotropy of exchange stiffness and its effect on the properties of magnets

Using the spin-spiral formulation of the tight-binding linear muffin-tin orbital method, the principal components of the exchange stiffness tensor are calculated for typical hard magnets including tetragonal CoPt-type and hexagonal YCo₅ alloys. The exchange stiffness is strongly anisotropic in all studied alloys. This anisotropy makes the domain wall surface tension anisotropic. Competition between this anisotropic surface tension and magnetostatic energy controls the formation and dynamics of nanoscale domain structures in hard magnets. Anisotropic domain wall bending is described in detail from the general point of view and with application to cellular Sm–Co magnets. It is shown that the repulsive cell-boundary pinning mechanism in these magnets is feasible only due to the anisotropic exchange stiffness if suitably oriented initial pinning centers are available. In polytwinned CoPt-type magnets the exchange stiffness anisotropy controls the orientation of macrodomain wall segments. These segments may reorient both statically during microstructural coarsening and dynamically during the macrodomain wall splitting in external field. Reorientation of segments may facilitate their pinning at antiphase boundaries.     

The interaction between a disclination in a nematic liquid crystal and a rubbed surface

For the case of a rubbed surface with a finite anisotropic surface tension, a model is developed for the structure and energy of a surface disclination and of an edge disclination near the surface. It is found that there is an energy barrier against detaching a disclination from the surface, and also that there is a critical distance within which a disclination is attracted, and beyond which it is repelled, by the surface. These properties may provide a measurement of the anisotropy of the surface tension.     

Stability of an encapsulated bubble shell

The stability of an encapsulated bubble filled with gas is studied where gas is allowed to diffuse out of the bubble. A mechanistic model that takes into account shell stiffness and surface tension is considered. A critical shell radius for loss of mechanical stability is derived based on a technique adapted for small radius, where surface tension effects become substantial. A new parameter is defined that determines the relative importance of surface tension forces and shell stiffness for shell stability. The developed technique allows to predict, for a given bubble population and gas saturation level of the surrounding liquid, a range of bubble sizes which may collapse in time. Surface tension effects are dominant in determining the critical radius but have a negligible effect on the minimal radius for collapse. The influence of the surface tension on the stability of the shell is illustrated for Optison, a typical ultrasound contrast agent.     

Nanopore wall effect on surface tension of methane

Local pressure is known to be anisotropic across the interfaces separating fluids in equilibrium. Tangential pressure profiles show characteristic negative peaks as a result of surface tension forces parallel to the interface. Nearby attractive forces parallel to the interface are larger than the repulsive forces and, hence, constitute the surface tension. In this work, using molecular dynamics simulations of methane inside nano-scale pores, we show this surface tension behaviour could be significantly influenced by confinement effects. The layering structure, characterised by damped oscillations in local liquid density and tangential pressures, extends deep into the pore and can be a few nanometers thick. The surface tension is measured numerically using local pressures across the interface. Results show that the tension is smaller under confinement and becomes a variable in small pores, mainly controlled by the thickness of the liquid density layering (or liquid saturation) and the pore width. If the liquid saturation inside the pore is high enough, the vapour–liquid interface is not interfered by the pore wall and the surface tension remains the same as the bulk values. The results are important for understanding phase change and multi-phase transport phenomena in nanoporous materials.     

Dynamics of interface in three-dimensional anisotropic bistable reaction-diffusion system

This paper presents a theoretical investigation of dynamics of interface (wave front) in three-dimensional (3D) reaction-diffusion (RD) system for bistable media with anisotropy constructed by means of anisotropic surface tension. An equation of motion for the wave front is derived to carry out stability analysis of transverse perturbations, which discloses mechanism of pattern formation such as labyrinthine in 3D bistable media. Particularly, the effects of anisotropy on wave propagation are studied. It was found that, sufficiently strong anisotropy can induce dynamical instabilities and lead to breakup of the wave front. With the fast-inhibitor limit, the bistable system can further be described by a variational dynamics so that the boundary integral method is adopted to study the dynamics of wave fronts.     

Exact equilibrium shapes of Ising crystals on triangular/honeycomb lattices

The anisotropic surface tension for an Ising system below the critical point on a triangular or a honeycomb lattice can be computed through duality. Using the Wulff construction, the equilibrium shape of a crystal (droplet of one phase inside a sea of the other) is found. An exact and simple equation for this shape is derived.     

Experimental investigation of Marangoni convection in nanofluids

Onset of regular convection in nanoparticle doped isotropic and anisotropic fluids with one free surface under absorption of light with Gaussian distribution of intensity due to temperature dependence of surface tension coefficient is experimentally studied. It is shown that nanoparticles essentially increase the thermal conductivity of the mixture, which leads to decrease of the velocity of convective motion. Dependence of velocity of hydrodynamic motions on intensity of laser beam and concentration of nanoparticles is also studied.     

Elliptical multielectron dimples on liquid and solid helium surfaces

The structure of multielectron dimples on helium substrates is investigated for conditions deviating from axial symmetry. Main sources for an ellipticity of dimples are an anisotropy of the surface tension, as for the liquid-solid He interface, or anisotropic boundary conditions, as for liquid He between vertical parallel plates.     

Eight-vertex model: Anisotropic interfacial tension and equilibrium crystal shape

The anisotropic interfacial tension of the eight-vertex model is found by a new method, which introduces two inhomogeneous systems. As the width of the system becomes large, a doublet of the largest eigenvalues of the row-row transfer matrix is asymptotically degenerate. The anisotropic interfacial tension is calculated from their finite-size correction terms in this limit. By the use of the anisotropic interfacial tension, the equilibrium crystal shape of the eight-vertex model is derived via Wulff's construction. The equilibrium crystal shape is represented as a simple algebraic curve. We discuss the close relation between the algebraic curve and the form of an elliptic function appearing in the expression of the interfacial tension.     

液体表面张力系数测试仪的研制

介绍一种测定液体表面张力的自制简易装置,可以测量不同物质、不同浓度液体的表面张力系数。仪器制作取材方便,安装调试简单,尤其是改进了常规液膜"拉脱"方法(焦利秤、扭秤和螺旋升降台),使得自组表面张力系数测试仪精度高,稳定性好。     

HYDRODYNAMIC STABILITY OF TWO-COMPONENT FLUID HEATED FROM BELOW AND WITH SURFACE ADSORPTION

The stability of a two-component Benard fluid with surface adsorption in reduced- gratuity condition is examined by using linear stability analysis. Results show that the surface tension effect of the active solute plays a dual role on the stability of the fluid, A few dimensionless combinations are introduced to delimit the regions where the stabilizing or destabilizing role, or both, of the solute tension come into plan.     

Electrostatic origin of the Frank elastic energy and anisotropic line tension of the domains in monolayers at the air-water interface

The free energy of condensed phase domains in monolayers at the air-water interface has been analyzed by taking into account the surface pressure, line tension, and electrostatic energy due to the normal and in-plane spontaneous polarization. We found that this free energy was reduced to the sum of the Frank elastic energy and anisotropic line tension, which were used to reproduce the shapes of domains in fatty acid monolayers, in the limit of small orientational deformation. Domains in monolayers are interesting systems as a meeting point between the physics of liquid crystals and electrostatics.     

Steady needle growth with 3-D anisotropic surface tension

The effect of the anisotropic interfacial energy on dendritic growth has been an important subject, and has preoccupied many researchers in the field of materials science and condensed matter physics. The present paper is dedicated to the study of the effect of full 3-D anisotropic surface tension on the steady state solution of dendritic growth. We obtain the analytical form of the first order approximation solution in the regular asymptotic expansion around the Ivantsov’s needle growth solution, which extends the steady needle growth solution of the system with isotropic surface tension obtained by Xu and Yu (J. J. Xu and D. S. Yu, J. Cryst. Growth, 1998, 187: 314; J. J. Xu, Interfacial Wave Theory of Pattern Formation: Selection of Dendrite Growth and Viscous Fingering in a Hele-Shaw Flow, Berlin: Springer-Verlag, 1997).The solution is expanded in the general Laguerre series in any finite region around the needle-tip, and it is also expanded in a power series in the far field behind the tip. Both solutions are then numerically matched in the intermediate region. Based on this global valid solution, the dependence of Peclet number Pe and the interface’s morphology on the anisotropy parameter of surface tension as well as other physical parameters involved are determined. On the basis of this global valid solution, we explore the effect of the anisotropy parameter on the Peclet number of growth, as well as the morphology of the interface.     

Microscopic selection of fluid fingering patterns

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accordance with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.