Phase separation kinetics of 2-TIPS at low density: Cluster growth by ballistic agglomeration

Abstract

We study the kinetics of two-temperature induced phase separation (2-TIPS) in dilute binary mixtures of active ("hot") and passive ("cold") particles using molecular dynamics simulations and a coarse-grained hydrodynamic model. Following a temperature quench, cold particles nucleate into mobile clusters that move ballistically and merge through successive coalescence events. The resulting domain growth exhibits dynamic scaling with a growth exponent of approximately 0.7, markedly faster than diffusive coarsening. We identify this regime as ballistic agglomeration of cold clusters, demonstrating a distinct nonequilibrium growth mechanism in low-density scalar active systems.

Figures (4)

• Figure 1: Figures (a), (b) and (c) illustrate the instantaneous snapshots of phase separating hot (red) and cold (blue) particles for density $\rho^*=0.1$ and quench temperature $T_h^*=25$ at different instances of time. Initially ($t=5 \times 10^5$), small circular cold nuclei form, which later coalesce into larger, elongated clusters ($t=10^6,5 \times10^6$). (b) Magnified view of a cold cluster showing hexagonal ordering of cold particles and trapping of hot particles within the cluster.
• Figure 2: (a) Plot of the correlation function $C_{\phi}(r,t)$ as function of rescaled distance $r/l(t)$, where $l(t)$ is the characteristic length at density $\rho^*=0.1$ for $T_h^*=25$ at different instants of time. Inset illustrates plot of two-point spatial correlation function of $\phi$, $C_{\phi}(r,t)$ as function of distance between the points $r$ at density $\rho^*=0.1$ for $T_h^*=25$ at different instants of time. The correlation function $C_{\phi}(r,t)$ exhibits dynamic scaling. (b) Log-log plot of characteristic length $l(t)$ versus time $t$ shows algebraic growth of $l(t)$. We see that the growth exponent $1/z$ has a value close to 0.71 at late times.
• Figure 3: (a) The MSD $\Delta(t)$ of cold clusters is plotted against time $t$ on a log-log scale. The black curve represents the power law dependence of MSD on time with exponent $\gamma \approx 2$, implying ballistic nature of cluster motion. (b) Log-log plot of average mass $m$ of clusters versus average radius of gyration $R_g$. The power law exponent associated ($m \sim R_g^{d_f}$) with it is $d_f \approx 1.7$. (c) Log-log plot of average rms velocity of clusters $v$ versus average mass $m$. The associated power law decay exponent ($v \sim m^{-z'}$) is $z' \approx 0.45$.
• Figure 4: Panel (a) shows the emergence of phase separation in the mixture through series of snapshots at different times where the color shows the value of phase separation order parameter $\phi$ according to the colorbar. Panel (b) shows the plot of scaled correlation, $C(r/l)$vs.$r/l$, at different times for $\rho_0 \approx 0.40$ and $\chi_{cg}=2.20$. (Inset) Plot of the unscaled correlation function, $C(r)$vs$r$. Panel (c) shows the plot of time dependent characteristics length $l(t)$vs.$t$ in log-log scale for $\chi_{cg}=2.20$ for $\rho_0 \approx 0.40$ and $0.30$, respectively. Panel (d) shows the plot of MSD of center of droplets in the scaling regime. Time $t=0$ in the plot is the reference time after which a droplet is tracked.