We present a unified theoretical and numerical study of dual bubble ripening on flat substrates under constant contact angle conditions. A theoretical framework is established by deriving the bubble growth rate $k_{\theta }$ and the kinetic equation for the curvature radius $R_B$, showing that $k_{\theta }$ decreases with contact angle yet remains positive, in agreement with simulations by lattice Boltzmann method (LBM). For dual bubbles on both homogeneous and heterogeneous substrates, the evolution of $R_B$ modeled by LBM follows the classical Ostwald ripening, independent of contact angles, and matches our theoretical predictions across a wide range of surface wettabilities. The normalized interfacial area change also follows a Gibbs free energy minimization mechanism. Furthermore, for heterogeneous substrates with different bubble contact angles, we find that the “reversed volume ripening” occurs when $\frac{R_1}{R_2}\in (1,\sqrt{\frac{{\theta }_2-sin{\theta }_{2}cos{\theta }_2}{{\theta }_1-sin{\theta }_{1}cos{\theta }_1}})$, i.e., the bubble with smaller volume grows at the expense of that with larger volume. For both ripening cases, they strictly follow the governing rule that ripening is driven by the chemical potential difference induced by curvature difference, regardless of different volume evolution mechanisms. Our work provides new insights into the interplay between interfacial kinetics and substrate wettability of constrained bubble ripening.

Close

PrevNext

View figure in article

• Drops & bubbles
• Multiphase flows
• Gas-liquid interfaces