Evaporation-Induced Liquid Expansion and Bubble Formation in Binary Mixtures

We observe an anomalous liquid expansion after quenching a binary mixture at coexistence to low pressures in the vapor phase by numerical calculations. This evaporation-induced expansion can be attributed to the pressure imbalance near the liquid-vapor interface, which originates from the interplay between the complex thermodynamics of binary mixtures both in the vapor and liquid phases, as well as their dynamical asymmetries. In addition, careful modulation of the pressure quench in the vapor phase can result in spinodal bubble formation inside liquid phase. The results indicate that the thermodynamics-kinetics interplay could foster our fundamental understanding of the evaporation process and promote its practical applications.

Figure 1

(a) Equilibrium phase diagram of negative azeotrope mixture. The blue arrow illustrates the pressure quench from the dimensionless initial pressure $p_{\mathrm{init}}=0.084$ (orange) to $p_{\text{final}}=0.078$ (violet). (b) Liquid-vapor phase coexistence at $p_{\mathrm{init}}=0.084$. The phase coexistence is marked in panel (a), providing the density fraction of $A$ in the coexisting liquid and vapor phases.

Figure 2

(a)–(b) Time evolution of $A$ density after a pressure quench, $p=0.084\to 0.078$, at the boundary for (a) $\alpha =1.0$ and (b) $\alpha =0.1$. (c)–(d) The time evolution of B density. (e)–(f) The variation of pressure along the $z$ axis.

Figure 3

(a) Contour plot of bulk pressure as a function of $A$ and $B$ densities, ${\varphi }_A$ and ${\varphi }_B$. The red and green lines show the coexistence densities, whereas the dashed white line represents the spinodal line. The black circle shows the critical point, the orange and cyan squares depict the initial and final points in the vapor and liquid phases, respectively. The black and yellow lines show the trajectories during pressure quench for dynamical asymmetries, $\alpha =0.1$ and 1.0. (b)–(c) Evolution of ${\varphi }_A(z)$ and ${\varphi }_B(z)$ in the (b) vapor ($z=54w$) and (c) liquid ($z=162w$) phases during the pressure quench. (d) The initial flux of $A$ (with $\alpha =1.0$ and 0.1, see Supplemental Material [67]) and $B$ species at the boundary $z=0$ after the pressure quench $\delta p$. Dashed green line shows the zero flux.

Figure 4

(a) Equilibrium phase diagram of the binary mixtures with the same labels as Fig. 1. The blue line shows the evolution of liquid from $p=0.084$ to 0.078 as in Fig. 2 ($z=162w$). The orange and cyan curves show the trajectories inside a bubble ($5.4w$, $124.3w$) and the liquid ($5.4w$, $108.1w$) within the 2D film; see panel (b). (b) Time evolution of two-dimensional $A$ density, ${\varphi }_A(x,z)$, from $p=0.088$ to 0.078 at $\alpha =1.0$ with $t=0$, 150, and $500\tau$. (c) Trajectories of the densities inside a bubble and the liquid on the ${\varphi }_A-{\varphi }_B$ plane after a rapid one-step quench. (d) Same as (c) (for the liquid) after a slow, continuous quench (multiple small-step quench).