Phase Separation in Active Binary Mixtures With Chemical Reaction

We study motility-induced phase separation~(MIPS) in active AB binary mixtures undergoing the chemical reaction $A\rightleftharpoons B$. Starting from the evolution equations for the density fields ${\rho }_i(\vec{r},t)$ describing MIPS, we phenomenologically incorporate the effects of the reaction through the reaction rate $\mathrm{\Gamma }$ into the equations. The steady-state domain morphologies depend on $\mathrm{\Gamma }$ and the relative activity of the species, $\mathrm{\Delta }$. For a sufficiently large $\mathrm{\Gamma }$ and $\mathrm{\Delta }\mathrm{\ne }1$, the more active component of the mixture forms a droplet morphology. We characterize the morphology of domains by calculating the equal-time correlation function $C(r,t)$ and the structure factor $S(k,t)$, exhibiting scaling violation. The average domain size, $L(t)$, follows a diffusive growth as $L(t)\sim t^{1\mathrm{/}3}$ before reaching the steady state domain size, $L_{\mathrm{s}\mathrm{s}}$. Additionally, $L_{\mathrm{s}\mathrm{s}}$ shows the scaling relation $L_{\mathrm{s}\mathrm{s}}\sim {\mathrm{\Gamma }}^{-1\mathrm{/}4}$, independent of $\mathrm{\Delta }$.