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 ${\rho }_i(\vec{r},t)$ describing MIPS, we phenomenologically incorporate the effects of the reaction through the reaction rate $\Gamma$ into the equations. The steady-state domain morphologies depend on $\Gamma$ and the relative activity of the species, $\Delta$. For a sufficiently large $\Gamma$ and $\Delta \ne 1$, 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 $L_{\mathrm{ss}}\sim {\Gamma }^{-1/4}$, independent of $\Delta$.

16 Pages, 7 Figures, Accepted to Soft Matter

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