Phase Separation in Active Binary Mixtures With Chemical Reaction

Abstract

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 $\ddot{I}{}_i(\vec{r},t)$ describing MIPS, we phenomenologically incorporate the effects of the reaction through the reaction rate $\hat{I}“$ into the equations. The steady-state domain morphologies depend on $\hat{I}“$ and the relative activity of the species, $\hat{I}”$. For a sufficiently large $\hat{I}“$ and $\hat{I}”\ne 1$, 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 $L(t)\sim t^{1/3}$ before reaching the steady state domain size, $L_{\mathrm{ss}}$. Additionally, $L_{\mathrm{ss}}$ shows the scaling relation $L_{\mathrm{ss}}\sim \hat{I}{“}^{-1/4}$, independent of $\hat{I}”$.

16 Pages, 7 Figures, Accepted to Soft Matter