Domain Growth Kinetics in Active Binary Mixtures

We study motility-induced phase separation (MIPS) in symmetric and asymmetric active binary mixtures. We start with the coarse-grained run-and-tumble bacterial model that provides evolution equations for the density fields ${\rho }_i(\vec{r},t)$. Next, we study the phase separation dynamics by solving the evolution equations using the Euler discretization technique. We characterize the morphology of domains by calculating the equal-time correlation function $C(r,t)$ and the structure factor $S(k,t)$, both of which show dynamical scaling. The form of the scaling functions depends on the mixture composition and the relative activity of the species, $\mathrm{\Delta }$. For $k\to \mathrm{\infty }$, $S(k,t)$ follows Porod’s law: $S(k,t)\sim k^{-(d+1)}$ and the average domain size $L(t)$ shows a diffusive growth as $L(t)\sim t^{1\mathrm{/}3}$ for all mixtures.