Bubble formation in water with addition of a hydrophobic solute

We show that phase separation can occur in a one-component liquid outside its coexistence curve (CX) with addition of a small amount of a solute. The solute concentration at the transition decreases with increasing the difference of the solvation chemical potential between liquid and gas. As a typical bubble-forming solute, we consider ${\rm O}_2$ in ambient liquid water, which exhibits mild hydrophobicity and its critical temperature is lower than that of water. Such a solute can be expelled from the liquid to form gaseous domains while the surrounding liquid pressure is higher than the saturated vapor pressure $p_{cx}$. This solute-induced bubble formation is a first-order transition in bulk and on a partially dried wall, while a gas film grows continuously on a completely dried wall. We set up a bubble free energy $\Delta G$ for bulk and surface bubbles with a small volume fraction $\phi$. It becomes a function of the bubble radius $R$ under the Laplace pressure balance. Then, for sufficiently large solute densities above a threshold, $\Delta G$ exhibits a local maximum at a critical radius and a minimum at an equilibrium radius. We also examine solute-induced nucleation taking place outside CX, where bubbles larger than the critical radius grow until attainment of equilibrium.