Fig. 3: Interactions between bubbles and gas layer on MA surfaces.

a The streamlines colored in the velocity magnitude around a bubble (dimensionless equivalent bubble diameter D₀/L = 3.0) approaching the MA surface with b/a increasing from 0.3 to 3.5 obtained by particle image velocimetry tests. b Maximum velocities V_m before bubbles decelerate as a function of the conical geometric parameter b/a. Error bars represent standard deviation calculated from three independent experiments. c The elongation parameter \(\eta\) versus time t during the approaching process on MA surfaces with varying b/a ratios. The inset shows the change in bubble radius after deformation. d Correlation of the dimensionless terminal deformation η_terminal/D₀ as a function of We^* = C_mρD₀V²_m/σ. η_terminal is the terminal deformation of the bubble upon surface contact, and C_m is the added mass coefficient. e Force analysis of the TPLs pinning on the microstructures. f The schematic diagram of the gas layer stability. A stable gas layer under film pressure ensures the formation of thin film that facilitate the fast bubble capture. g The relationship of the conical distance L and the ∆P_cr under b/a = 1.7, predicted by the augmented Young-Laplace equation (Supplementary Note 5). h Phase diagram summarizing the dimensionless bubble size D₀/L and the b/a required for the efficient capture. Each case is repeated twenty times and the fast-capture is considered successful if the bubble is captured on the first contact with the surfaces for all cases. The black line separating the cases of \({\bar{P}}_{{{{\rm{m}}}}}\le \Delta {P}_{{{{\rm{cr}}}}}\) and \({\bar{P}}_{{{{\rm{m}}}}} > \Delta {P}_{{{{\rm{cr}}}}}\) is obtained by theoretical evaluation.