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Register a new userMorphology Formation in Binary Mixtures upon Gradual Destabilisation
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Spontaneous liquid-liquid phase separation is commonly understood in terms of phenomenological mean-field theories. These theories correctly predict the structural features of the fluid at sufficiently long time scales and wavelengths. However, these conditions are not met in various examples in biology and materials science where the mixture is slowly destabilised, and phase separation takes place close to the critical point. Using kinetic Monte Carlo and molecular dynamics simulations of a binary surface fluid under these conditions, we show that the characteristic length scale of the emerging structure decreases, in 2D, with the 4/15 dynamic critical exponent of the quench rate rather than the mean-field 1/6th power. Hence, the dynamics of cluster formation governed by thermodynamically undriven Brownian motion is much more sensitive on the rate of destabilisation than expected from mean-field theory. We discuss the expected implications of this finding to 3D systems with ordering liquid crystals, as well as phase-separating passive or active particles.
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Multicomponent systems are ubiquitous in nature and industry. While the physics of few-component liquid mixtures (i.e., binary and ternary ones) is well-understood and routinely taught in undergraduate courses, the thermodynamic and kinetic properties of $N$-component mixtures with $N>3$ have remained relatively unexplored. An example of such a mixture is provided by the intracellular fluid, in which protein-rich droplets phase separate into distinct membraneless organelles. In this work, we investigate equilibrium phase behavior and morphology of $N$-component liquid mixtures within the Flory-Huggins theory of regular solutions. In order to determine the number of coexisting phases and their compositions, we developed a new algorithm for constructing complete phase diagrams, based on numerical convexification of the discretized free energy landscape. Together with a Cahn-Hilliard approach for kinetics, we employ this method to study mixtures with $N=4$ and $5$ components. We report on both the coarsening behavior of such systems, as well as the resulting morphologies in three spatial dimensions. We discuss how the number of coexisting phases and their compositions can be extracted with Principal Component Analysis (PCA) and K-Means clustering algorithms. Finally, we discuss how one can reverse engineer the interaction parameters and volume fractions of components in order to achieve a range of desired packing structures, such as nested `Russian dolls and encapsulated Janus droplets.
If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy (TIRM), with femto-Newton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere-planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.
We evaluate in this work the hydrodynamic transport coefficients of a granular binary mixture in $d$ dimensions. In order to eliminate the observed disagreement (for strong dissipation) between computer simulations and previously calculated theoretical transport coefficients for a monocomponent gas, we obtain explicit expressions of the seven Navier-Stokes transport coefficients with the use of a new Sonine approach in the Chapman-Enskog theory. Our new approach consists in replacing, where appropriate in the Chapman-Enskog procedure, the Maxwell-Boltzmann distribution weight function (used in the standard first Sonine approximation) by the homogeneous cooling state distribution for each species. The rationale for doing this lies in the fact that, as it is well known, the non-Maxwellian contributions to the distribution function of the granular mixture become more important in the range of strong dissipation we are interested in. The form of the transport coefficients is quite common in both standard and modified Sonine approximations, the distinction appearing in the explicit form of the different collision frequencies associated with the transport coefficients. Additionally, we numerically solve by means of the direct simulation Monte Carlo method the inelastic Boltzmann equation to get the diffusion and the shear viscosity coefficients for two and three dimensions. As in the case of a monocomponent gas, the modified Sonine approximation improves the estimates of the standard one, showing again the reliability of this method at strong values of dissipation.
An approach to obtain the structural properties of additive binary hard-sphere mixtures is presented. Such an approach, which is a nontrivial generalization of the one recently used for monocomponent hard-sphere fluids [S. Pieprzyk, A. C. Branka, and D. M. Heyes, Phys. Rev. E 95, 062104 (2017)], combines accurate molecular-dynamics simulation data, the pole structure representation of the total correlation functions, and the Ornstein-Zernike equation. A comparison of the direct correlation functions obtained with the present scheme with those derived from theoretical results stemming from the Percus-Yevick (PY) closure and the so-called rational-function approximation (RFA) is performed. The density dependence of the leading poles of the Fourier transforms of the total correlation functions and the decay of the pair correlation functions of the mixtures are also addressed and compared to the predictions of the two theoretical approximations. A very good overall agreement between the results of the present scheme and those of the RFA is found, thus suggesting that the latter (which is an improvement over the PY approximation) can safely be used to predict reasonably well the long-range behavior, including the structural crossover, of the correlation functions of additive binary hard-sphere mixtures.
A theoretical study of the structure formation observed very recently [Phys. Rev. Lett. 90, 128303 (2003)] in binary colloids is presented. In our model solely the dipole-dipole interaction of the particles is considered, electrohidrodynamic effects are excluded. Based on molecular dynamics simulations and analytic calculations we show that the total concentration of the particles, the relative concentration and the relative dipole moment of the components determine the structure of the colloid. At low concentrations the kinetic aggregation of particles results in fractal structures which show a crossover behavior when increasing the concentration. At high concentration various lattice structures are obtained in a good agreement with experiments.
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