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Register a new userEffect of anisotropic diffusion on spinodal decomposition
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We study the phase transition dynamics of a fluid system in which the particles diffuse anisotropically in space. The motivation to study such a situation is provided by systems of interacting magnetic colloidal particles subject to the Lorentz force. The Smoluchowski equation for the many-particle probability distribution then aquires an anisotropic diffusion tensor. We show that anisotropic diffusion results in qualitatively different dynamics of spinodal decomposition compared to the isotropic case. Using the method of dynamical density functional theory, we predict that the intermediate-stage decomposition dynamics are slowed down significantly by anisotropy; the coupling between different Fourier modes is strongly reduced. Numerical calculations are performed for a model (Yukawa) fluid that exhibits gas-liquid phase separation.
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We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. We then study the process of spinodal decomposition in fast phase transitions associated with a conserved order parameter. The introduced memory effect plays an important role to obtain a finite group velocity. Then, we discuss the constraint for the parameters to satisfy causality. The memory effect is seen to affect the dynamics of phase transition at short times and has the effect of delaying, in a significant way, the process of rapid growth of the order parameter that follows a quench into the spinodal region.
We simulate late-stage coarsening of a 3-D symmetric binary fluid. With reduced units l,t (with scales set by viscosity, density and surface tension) our data extends two decades in t beyond earlier work. Across at least four decades, our own and others individual datasets (< 1 decade each) show viscous hydrodynamic scaling (l ~ a + b t), but b is not constant between runs as this scaling demands. This betrays either the unexpected intrusion of a discretization (or molecular) lengthscale, or an exceptionally slow crossover between viscous and inertial regimes.
In this letter we show that the late-time scaling state in spinodal decomposition is not unique. We performed lattice Boltzmann simulations of the phase-ordering of a 50%-50% binary mixture using as initial conditions for the phase-ordering both a symmetric morphology that was created by symmetric spinodal decomposition and a morphology of one phase dispersed in the other, created by viscoelastic spinodal decomposition. We found two different growth laws at late times, although both simulations differ only in the early time dynamics. The new scaling state consists of dispersed droplets. The growth law associated with this scaling state is consistent with a $Lsim t^{1/2}$ scaling law.
Spinodal decomposition is a ubiquitous phenomenon leading to phase separation from a uniform solution. We show that a spinodal decomposition occurs in a unique combination of two rutile compounds of TiO2 and VO2, which are chemically and physically distinguished from each other: TiO2 is a wide-gap insulator with photo catalytic activities and VO2 is assumed to be a strongly correlated electron system which exhibits a dramatic metal-insulator transition at 342 K. The spinodal decomposition takes place below 830 K at a critical composition of 34 mol% Ti, generates a unidirectional composition modulation along the c axis with a wavelength of approximately 6 nm, and finally results in the formation of self-assembled lamella structures made up of Ti-rich and V-rich layers stacked alternately with 30-50 nm wavelengths. A metal-insulator transition is not observed in quenched solid solutions with intermediate compositions but emerges in the thin V-rich layers as the result of phase separation. Interestingly, the metal-insulator transition remains as sharp as in pure VO2 even in such thin layers and takes place at significantly reduced temperatures of 310-340 K, which is probably due to a large misfit strain induced by lattice matching at the coherent interface.
Tracer particles immersed in suspensions of biological microswimmers such as E. coli or Chlamydomonas display phenomena unseen in conventional equilibrium systems, including strongly enhanced diffusivity relative to the Brownian value and non-Gaussian displacement statistics. In dilute, 3-dimensional suspensions, these phenomena have typically been explained by the hydrodynamic advection of point tracers by isolated microswimmers, while, at higher concentrations, correlations between pusher microswimmers such as E. coli can increase the effective diffusivity even further. Anisotropic tracers in active suspensions can be expected to exhibit even more complex behaviour than spherical ones, due to the presence of a nontrivial translation-rotation coupling. Using large-scale lattice Boltzmann simulations of model microswimmers described by extended force dipoles, we study the motion of ellipsoidal point tracers immersed in 3-dimensional microswimmer suspensions. We find that the rotational diffusivity of tracers is much less affected by swimmer-swimmer correlations than the translational diffusivity. We furthermore study the anisotropic translational diffusion in the particle frame and find that, in pusher suspensions, the diffusivity along the ellipsoid major axis is higher than in the direction perpendicular to it, albeit with a smaller ratio than for Brownian diffusion. Thus, we find that far field hydrodynamics cannot account for the anomalous coupling between translation and rotation observed in experiments, as was recently proposed. Finally, we study the probability distributions (PDFs) of translational and rotational displacements. In accordance with experimental observations, for short observation times we observe strongly non-Gaussian PDFs that collapse when rescaled with their variance, which we attribute to the ballistic nature of tracer motion at short times.
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