Metastability and ripening of multi-component liquid mixtures

Abstract

Understanding how multi-component liquid mixtures undergo phase separation is central to elucidating biophysical organization in the cell. Here, combining analytical and numerical results, we characterise the dynamics of mixtures with disordered interactions among the components. We first study how two coexisting phases become unstable, leading to multiphase coexistence. We then show that the scaling of droplet radius as $t^{1/3}$ and droplet number as $n^{-2/3}$, characteristic of Ostwald ripening in two dimensions, can be severely delayed. This delay arises from glass-like relaxation and the emergence of long-lived metastable states characterized by different wetting angles.

Figures (5)

• Figure 1: Schematic for the dynamics of multi-component phase-separating mixtures. (a) Two coexisting phases characterised by different solute compositions (inset) (b) pairwise solute interactions are encoded in a matrix $\chi$ composed of Gaussian random variables with mean $b$. (c) Two phases can be locally stable, while three phases emerge at later times. (d) Ripening dynamics in the presence of multiple coexisting phases. (e) Different initial conditions can lead to different long-lived metastable states charcaterized by different wetting angles.
• Figure 2: Top: schematic of the dilute (phase II) and dense phase (phase I). (a-b) Numerical distribution of solute volume fraction in the dilute (II) and dense (I) phases. (c-d) Eigenvalues of the Hessian matrix evaluated at the dilute (II) and dense (I) phases, respectively. The peak corresponding to isolated eigenvalues lies to the left of the continuum spectrum in phase II, and to the left of it in phase I. The continuum part can deviate from the Wigner semicircle developing an exponential tail (inset).
• Figure 3: (a) Snapshots of the total solute volume fraction, $\phi_\text{tot}$ showing ripening of a mixture of $M=15$ solutes. (b) average radius and (c) number of $\phi_\text{tot}$-rich droplets as a function of time, for $M=1$, $M=5$, $M=10$, and $M=15$ number of solutes. Ostwald ripening scaling is highlighted with a dashed line.
• Figure 4: (a) Snapshots two solute volume fractions, $\phi_5$ and $\phi_{11}$ showing ripening of a mixture of $M=15$ solutes. (b) average area $A^\alpha$ and (c) number of droplets $n^\alpha$ as a function of time, for two distinct phases $\alpha = \text{I},\text{II}$. Dashed black lines show power laws with exponents significantly different from Ostwald ripening.
• Figure 5: (a) Dynamical evolution of a multi-component ($M=15$) mixture with the same parameter values as in previous figure, but initialized with $N(0) = 500$ (left) and $N(0) = 200$ (right) initial droplets. On the left, droplets ripen while remaining separated in space as shown in Fig. \ref{['fig:ripe_comps']}. On the right, droplets grow until different phases nucleate at their interface, leading to distinct phases wetting on each other. (b) volume fraction $\phi_8$ snapshots