Bubble dynamics and rupture in carbonated water droplet on hydrophobic surface

Carbonated water droplets have significant potential for self-cleaning of hydrophobic surfaces since the dissolution of CO₂ gas can generate bubbles reducing interfacial shear and propelling droplets. The effective droplet control depends on the dynamics of bubble formation, coalescence, and rupture during self-cleaning. CO₂ bubbles generated and released from droplet interface at the hydrophobic surface accumulate at droplet apex region and form a foam-like structure. As bubble film reaches a critical thickness, it ruptures as a result of force imbalance between interfacial tension and gas pressure. A film retraction and formation of vertical jet (Worthington jet) occur following the rupture, which creates a complicated droplet behavior on hydrophobic surface. Consequently, the present study investigates bubble formation, coalescence, and rupture within the carbonated water droplets. Bubble velocity in droplet interior is formulated using Epstein-Plesset relation and it is also measured by using high-speed recording facility. Film thickness and jet velocity are formulated incorporating the force balance. We have shown that bubble buoyancy force (∼ 0.41 × 10^-7 N) is greater than the drag force (∼ 2.23 × 10^-8 N) and the force of gravity (∼ 0.43 × 10^-10 N). Since discrepancies are observed between predictions and measured data, equation developed for jet velocity is further modified to include the effect of recoil pressure. After the modifications, jet velocity takes the form V j = γ (1 + C n π − O h) ρ g R b − b , C_n being the correction factor and it varies within 0.1 to 0.05 based on the experimental data, i.e. C_n = 0.1 for R b − b R d ≤ 0.15) and C_n = 0.05 (for 0.15 < R b − b R d ≤ 0.19). The proposed amendments notably improve the agreement between predicted and experimentally observed jet velocities.