Surface wetting by kinetic control of liquid-liquid phase separation

Motivated by the observations of intracellular phase separations and the wetting of cell membranes by protein droplets, we study the nonequilibrium surface wetting by Monte Carlo simulations of a lattice gas model involving particle creation. We find that, even when complete wetting should occur in equilibrium, the fast creation of particles can hinder the surface wetting for a long time due to the bulk droplet formation. Performing molecular dynamics simulations, we show that this situation also holds in colloidal particle systems when the disorder density is sufficiently high. The results suggest an intracellular control mechanism of surface wetting by changing the speed of component synthesis.

Figure 1

(a) Phase diagram of equilibrium state with representative snapshots of configurations. The red solid line is the onset of phase separation, and the blue dashed line is the theoretical boundary between partial wetting and complete wetting. We used $L=50$, $\rho =0.1$, and $t_{\mathrm{tot}}/{\tau }_{\mathrm{diff}}=10000$ in the Monte Carlo simulation. Schematic figures of (b) a nonwetting circular droplet with radius $R$ and (c) a partially wetting droplet with a wetting angle $\theta$ are also shown.

Figure 2

(a) Time evolution ($0\le t\le t_{\mathrm{tot}}=1800{\tau }_{\mathrm{diff}}$) of the mean density $\rho$ for ${\tau }_{\mathrm{cre}}/{\tau }_{\mathrm{diff}}=0.1$ (blue solid), 1 (red dashed), 5 (purple dotted), and 10 (green dashed-dotted) with ${\rho }_{\mathrm{sat}}=0.1$. (b) The heat map of the wetting fraction ${\varphi }_{\mathrm{w}}$ at $t=t_{\mathrm{tot}}$ ($=1800{\tau }_{\mathrm{diff}}$) (yellow for ${\varphi }_{\mathrm{w}}\le 0.7$, orange for $0.7<{\varphi }_{\mathrm{w}}\le 0.9$, and purple for ${\varphi }_{\mathrm{w}}>0.9$) as a function of the creation time ${\tau }_{\mathrm{cre}}$ and the interaction strength $J$, with typical final configurations. The value of ${\varphi }_{\mathrm{w}}$ at each point is statistically averaged over 30 independent numerical simulations. We used $L=30$ and ${\rho }_{\mathrm{sat}}=0.1$. (c) The heat map similar to (b) at ${\tau }_{\mathrm{cre}}/{\tau }_{\mathrm{diff}}=0.01$ as a function of the total time $t_{\mathrm{tot}}$ and the interaction strength $J$. The value of ${\varphi }_{\mathrm{w}}$ at each point is averaged over 100 independent numerical simulations. The other parameters are the same as (b).

Figure 3

(a) The heat map of the wetting fraction ${\varphi }_{\mathrm{w}}$ as a function of the creation-annihilation time ${\tau }_{\mathrm{cre}}$ and the interaction strength $J$ in the model including creation-annihilation processes [with colors used in the same way as Fig. 2]. We used $L=30$, ${\rho }_{\mathrm{sat}}=0.1$, and $t_{\mathrm{tot}}/{\tau }_{\mathrm{diff}}=1800$. (b) ${\varphi }_{\mathrm{w}}$ as a function of the total time $t_{\mathrm{tot}}$ ($45\le t_{\mathrm{tot}}/{\tau }_{\mathrm{diff}}\le 1800$) and the interaction strength $J$ for a fixed value of ${\tau }_{\mathrm{cre}}/{\tau }_{\mathrm{diff}}$ ($=0.1$). The other parameters are the same as in (a). Each value of ${\varphi }_{\mathrm{w}}$ in (a) and (b) is statistically averaged over 10 and 30 independent simulations, respectively.

Figure 4

(a) The heat map of the mean wetting fraction ${\varphi }_{\mathrm{w}}$ at $t=t_{\mathrm{tot}}$ ($=6.5{\tau }_{\mathrm{diff}}$) (yellow for ${\varphi }_{\mathrm{w}}\le 0.85$, orange for $0.85<{\varphi }_{\mathrm{w}}\le 0.95$, and purple for ${\varphi }_{\mathrm{w}}>0.95$) as a function of the density of disorder particles ${\rho }_{\mathrm{imp}}$ and the interaction strength of the Lennard-Jones potential $J_{\mathrm{LJ}}$. (b) The same heat map as a function of the creation time ${\tau }_{\mathrm{cre}}$ and the interaction strength of the Lennard-Jones potential $J_{\mathrm{LJ}}$ at $t=t_{\mathrm{tot}}\simeq 6.5{\tau }_{\mathrm{diff}}$ for ${\rho }_{\mathrm{imp}}\simeq 0.0123\mu {\mathrm{m}}^{-3}$, with typical final configurations. The value of ${\varphi }_{\mathrm{w}}$ at each point is statistically averaged over more than 50 independent numerical simulations.