Phase separation in a chaotic flow

The phase separation between two immiscible liquids advected by a bidimensional velocity field is investigated numerically by solving the corresponding Cahn-Hilliard equation. We study how the spinodal decomposition process depends on the presence-or absence-of Lagrangian chaos. A fully chaotic flow, in particular, limits the growth of domains, and for unequal volume fractions of the liquids, a characteristic exponential distribution of droplet sizes is obtained. The limiting domain size results from a balance between chaotic mixing and spinodal decomposition, measured in terms of Lyapunov exponent and diffusivity constant, respectively.     

An analysis of flow-induced miscibility of polymer blends

The phase behavior of blends of polystyrene and poly(vinyl methyl ether) undergoing shearing flow was examined. Experiments conducted at a constant level of flow-induced strain found that such flow elevates the phase boundary and pro-motes miscibility. In the framework of the Cahn-Hilliard model for spinodal decomposition, an expression was developed which predicts the effect of an external flow field on the spinodal. The basis for this expression is the minimization of strain energy in a two-component polymer system that is in a thermodynamic state near its phase-separation point. The zero shear viscosities of the blends were measured and demonstrated to be an indication of one- or two-phase flow.     

Evolution of the structure factor in a hyperbolic model of spinodal decomposition

We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. The memory effects are seen to affect the dynamics of phase transition at short times. The process of fast spinodal decomposition associated with a conserved order parameter - concentration is studied numerically. Details of a semi-implicit numerical scheme used to simulate the kinetics of spinodal decomposition and evolution of the structure factor are discussed. Analysis of the modeled structure factor predicted by a hyperbolic model of spinodal decomposition is presented in comparison with the parabolic model of Cahn and Hilliard. It is shown that during initial periods of decomposition the structure factor exhibits wave behavior. Analytical treatments explain such behavior by existence of damped oscillations in structure factor at earliest stages of phase separation and at large values of the wave-number. These oscillations disappear gradually in time and the hyperbolic evolution approaches the pure dissipative parabolic evolution of spinodal decomposition.     

Asymmetric landscapes of early spinodal decomposition

We address the effect of an asymmetric concentration-dependent mobility on the early stages of spinodal decomposition in polymer blends and solutions, and characterise it quantitatively. This is particularly important when one of the components has a slower dynamics than the other, e.g., because it is closer to its glass transition, or is weakly cross-linked. Composition mode coupling is proposed as the underlying physical mechanism, and then investigated by means of numerical simulations of the Cahn-Hilliard equation in one (1d) and two (2d) dimensions. In general, this coupling broadens the peak in the structure factor: in 1d an asymmetric concentration profile is obtained, with sharpened interfaces, whereas in 2d the formation is favoured of sharp peaks of the phase rich in the more mobile component. It is shown how the changing morphology of this phase-separating system can be described with the aid of Minkowski functionals. Received 28 August 2000 and Received in final form 18 July 2001     

On the theory of spinodal decomposition in solid and liquid binary mixtures

The kinetics of phase separation is discussed with emphasis on the transition between spinodal decomposition and nucleation. A reanalysis of the theory of Langer, Baron and Miller shows that it exhibits a spinodal line somewhat closer to the coexistence curve than the meanfield spinodal. There the same (as we think unphysical) critical singularities occur as in Cahn-Hilliard theory. The precise location of this spinodal line depends on the cell size of the coarse graining. For concentrations less than the spinodal one the structure factorS(k, t) converges then towards the structure factor of the metastable onephase state, implying an infinite lifetime of the latter.In order to include the effects of nucleation and growth we hence present an alternative treatment, extending our previous work on cluster dynamics. From a simple approximation for the radial concentration distribution function of clustersS(k, t) is computed numerically. Even at rather low concentrations the time evolution ofS(k, t) is then similar to what Langer et al. find at high concentrations, implying a very gradual transition from nucleation and growth to spinodal decomposition, at least for parameter values appropriate to the Ising model. This treatment, which is consistent with Lifshitz-Slyozov's coarsening law at late times, is extended to the early stages of phase separation in liquid mixtures.     

Computer simulation study of phase separation in a binary mixture with a glass-forming component

We present a computer simulation study of spinodal decomposition with one of the two phases freezing in a glassy state during phase separation. As a model we used the Cahn-Hilliard equation with a concentration-dependent mobility coefficient which decreases rapidly with increasing concentration of the glass-forming component. We solved the Cahn-Hilliard equation numerically for two dimensions. The domain growth depends crucially on the volume fraction of the glassy phase. For high volume fractions, when the glassy phase forms a percolating matrix, a novel coarsening mechanism is discovered, which arises from the migration and coalescence of liquid droplets within the glassy matrix. Various quantities characterizing the time-dependent domain pattern, like droplet size distribution, one- and two-point distribution function and structure factor of the concentration field, are computed. We checked the validity of the dynamic scaling hypothesis.     

耦合界面力的两相流相场格子Boltzmann模型

提出了一种改进的基于相场理论的两相流格子Boltzmann模型.通过引入一种新的更加简化的外力项分布函数,使得此模型克服了前人工作中界面力尺度与理论分析不一致的问题,并且通过Chapman-Enskog多尺度分析表明,所提出的模型能够准确恢复到追踪界面的Cahn-Hilliard方程和不可压的Navier-Stokes方程,并且宏观速度的计算更为简化.利用所提模型对几个经典两相流问题,包括静态液滴测试、液滴合并问题、亚稳态分解以及瑞利-泰勒不稳定性进行了数值模拟,发现本模型可以获得量级为10^-9极小的虚假速度,并且这些算例获取的数值解与解析解或已有的文献结果相吻合,从而验证了模型的准确性和可行性.最后,利用所发展的两相流格子Boltzmann模型研究了随机扰动的瑞利-泰勒不稳定性问题,并着重分析了雷诺数对流体相界面的影响.发现对于高雷诺数情形,在演化前期,流体界面出现一排“蘑菇”形状,而在演化后期,流体界面呈现十分复杂的混沌拓扑结构.不同于高雷诺数情形,低雷诺数时流体界面变得相对光滑,在演化后期未观察到混沌拓扑结构.     

Mesoscale simulations of curvature-inducing protein partitioning on lipid bilayer membranes in the presence of mean curvature fields

The membrane-surface migration of curvature-inducing proteins in response to membrane curvature gradients has been investigated using Monte Carlo simulations of a curvilinear membrane model based on the Helfrich Hamiltonian. Consistent with theoretical and experimental data, we find the proteins that generate curvature can also sense the background membrane curvature, wherein they preferentially partition to the high curvature regions. The partitioning strength depends linearly on local membrane curvature and the slope (or the coupling constant) of the partitioning probability versus mean curvature depends on the membrane bending rigidity and instantaneous curvature field caused by different proteins. Our simulation study allows us to quantitatively characterize and identify the important factors affecting the coupling constant (slope), which may be difficult to determine in experiments. Furthermore, the membrane model is used to study budding of vesicles where it is found that in order to stabilize a mature vesicle with a stable ‘neck-region’ (or stable membrane overhangs), the area (extent) of the intrinsic curvature region needs to exceed a threshold-critical value. The migration and partitioning of curvature-inducing proteins in a budding vesicle with a stable neck (with a characteristic negative value of the Gaussian curvature) is investigated.     

Phase field simulation of spinodal decomposition under external magnetic field

A computational model was developed to simulate the spinodal decomposition process of ferromagnetic alloys under an external magnetic field. In this model, the temporal evolution of the modulated structure was described by a phase field method, and the magnetic configuration was solved by using a micromagnetic method. The spinodal decomposition and coarsening processes of a single magnetic particle and an A-B hypothetical system under an external magnetic field were simulated using the proposed model. The simulation results show that the precipitated particles were elongated along the direction of the external magnetic field. The dependence of the modulated structure of an A-B hypothetic system on external magnetic field is much more sensitive than that of the single particle structure. The simulation results also demonstrate that the modulation of the external magnetic field is effective even if the spinodal decomposition has been completed and a stable modulated structure was formed.     

Effect of Convection on Domain Growth During Demixing Transitions in Fluids

Current analytical work on the effect of convection on the late stages of spinodal decomposition in liquids is briefly described. The morphology formed during the spinodal decomposition process depends on the relative composition of the two species. Droplet spinodal decomposition occurs when the concentration of one of the species is small. Convective transport has a significant effect on the scaling laws in the late-stage coarsening of droplets in translational or shear flows. In addition, convective transport could result in an attractive interaction between non-Brownian droplets which could lead to coalescence. The effect of convective transport for the growth of random interfaces in a near-symmetric quench was analysed using an area distribution function, which gives the distribution of surface area of the interface in curvature space. It was found that the curvature of the interface decreases proportional to time t in the late stages of spinodal decomposition, and the surface area also decreases proportional to t .     

Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation

In this paper we prove the existence of doubly periodic solutions of certain nonlinear elliptic problems on ² and study the geometry of their nodal domains. In particular, we will show that if we perturb a nonlinear elliptic equation exhibiting a small amplitude doubly periodic solution whose nodal domains form a checkerboard pattern, then the perturbed equation will have a unique nearby solution which is still doubly periodic, but for which the nodal line structure breaks up. Moreover, we indicate what can happen if we start with a large amplitude doubly periodic solution whose nodal domains form a checkerboard pattern, and we relate these solutions to the Cahn-Hilliard equation and spinodal decomposition.     

Experimental test for the hyperbolic model of spinodal decomposition in the binary system

A model has been presented for the physical decay with the relaxation of the diffusion flux described by the hyperbolic diffusion equation. The analysis of such a hyperbolic model provides the predictions for the critical parameters of the decay, which are compared with the conclusions of the Cahn-Hilliard theory. It has been shown that the hyperbolic model predicts the nonlinearity of the dispersion curve for the spinodal decay, which is controlled by the ratio of the diffusion and correlation lengths. The predicted behavior of the dispersion curve is compared with the experimental data on phase separation in binary glasses.     

Phase separation in binary systems with internal multiplicative noise

A study of a phase separation process in stochastic systems with a field dependent kinetic coefficient and an internal multiplicative noise is presented. Dynamics of spinodal decomposition at early and late stages is investigated by computer simulations where the domain growth law is generalized. A mean field approach was carried out in order to obtain the stationary probability, bifurcation and phase diagrams displaying reentrant phase transitions. We relate our approach to entropy driven phase transitions theory.     

Surface spinodal decomposition in coherent metal-hydrogen and other alloys

Spinodal decomposition in metal hydrides and alloys near a surface under the influence of elastic interactions is investigated. As long as the crystals remain coherent this process sets in prior to spinodal decomposition in the bulk. A statistical theory containing thermal fluctuations and nonlinear effects is developed and solutions are found in a mean field approximation. The theory is applied to niobium-hydride and a possible explanation for the appearance of quasiperiodic-phase precipitates in quenched probes is given.     

Analysis of long crack lines in paper webs

A differential cluster variation method (DCVM) is proposed for analysis of spinoidal decomposition in alloys. In this method, lattice symmetry operations in the presence of an infinitesimal composition gradient are utilized to deduce the connection equations for the correlation functions and to reduce the number of independent variables in the cluster variation analysis. Application of the method is made to calculate the gradient energy coefficient in the Cahn-Hilliard free energy function and the fastest growing wavelength for spinodal decomposition in Al-Li alloys. It is shown that the gradient coefficient of congruently ordered Al-Li alloys is much larger than that of the disordered system. In such an alloy system, the calculated fastest growing wavelength is approximately 10 nm, which is an order of magnitude larger than the experimentally observed domain size. This may provide a theoretical explanation why spinodal decomposition after a congruent ordering is dominated by the antiphase boundaries.Received: 17 November 2003, Published online: 2 April 2004PACS: 64.75. + g Solubility, segregation, and mixing; phase separation - 81.30.-t Phase diagrams and microstructures developed by solidification and solid-solid phase transformations - 05.70.Ln Nonequilibrium and irreversible thermodynamics     

Volume effects in the theory of equilibrium and quasiequilibrium states of multicomponent solid solutions

A phenomenological theory of equilibrium and quasiequilibrium states of multicomponent solid solutions is constructed taking account of volume effects. Quasiequilibrium states are characterized by the fact that only some of the conditions for thermal dynamic equilibrium of the system are satisfied. The short-range parts of the interatomic interactions are taken into account by introducing the proper volumes of the atoms based on a generalized lattice model. The long-range parts of the potentials are taken into account in the effective-field approximation. The equations for the quasiequilibrium components in the solutions are introduced taking account of the nonuniformity in the distributions of the less mobile nonequilibrium components. The conditions for spinodal decomposition of a solid solution with an arbitrary number of components in the equilibrium and quasiequilibrium cases are obtained. An equation for equilibrium spinodal decomposition of a three-component microheterogeneous solid solution is found. Fiz. Tverd. Tela (St. Petersburg) 41, 1609–1613 (September 1999)     

Model for a Universe described by a non-minimally coupled scalar field and interacting dark matter

In this work the evolution of a Universe model is investigated where a scalar field, non-minimally coupled to space-time curvature, plays the role of quintessence and drives the Universe to a present accelerated expansion. A non-relativistic dark matter constituent that interacts directly with dark energy is also considered, where the dark matter particle mass is assumed to be proportional to the value of the scalar field. Two models for dark matter pressure are considered: the usual one, pressureless, and another that comes from a thermodynamic theory and relates the pressure with the coupling between the scalar field and the curvature scalar. Although the model has a strong dependence on the initial conditions, it is shown that the mixture consisted of dark components plus baryonic matter and radiation can reproduce the expected red-shift behavior of the deceleration parameter, density parameters and luminosity distance.     

Experimental small-angle X-ray scattering investigation of initial stages of the spinodal decomposition in model sodium silicate glasses

The kinetics of the initial stages of the spinodal decomposition in model glasses of the Na₂O-SiO₂ system has been investigated in situ. It has been demonstrated that there is a quantitative agreement of the experimental results obtained in the framework of the Stephenson theory with the basic principles of modern theories and the data on direct determination of the viscosity, mobility, and diffusion. It has been found that the spatial-temporal evolution of the heterogeneous structure has a multistage character during spinodal decomposition. The characteristic size of the phase regions at each stage varies with time according to the power law. The sequence of stages and the values of exponents for the spinodal decomposition are as follows: 1/20, 1/4, 1/2, and 1/3.     

Density functional theory of vapor to liquid heterogeneous nucleation: Lennard–Jones fluid on solid substrate

Density functional theory has been applied to investigate the vapor to liquid heterogeneous nucleation on a flat solid surface, by invoking a model free energy density functional along with an exponential density model. The effects of supersaturation of the vapor and the strength of the solid-fluid interaction on the nucleation barrier have been investigated for Lennard–Jones fluid with 12–6 fluid–fluid and 9–3 solid–fluid interaction model. The spinodal decomposition of vapor has been observed at higher supersaturation or at higher strength of the solid–fluid interaction. The shape, density profile and the free energy of formation of droplets of any arbitrary size have been obtained in this work.