To effectively apply the superhydrophobic surface for flow control, it is necessary to understand the effect of air-water interface shape on the diffusion characteristics of trapped air pockets. In the present work, using the reflection interference contrast microscopy, we directly measure the temporal variation of the three-dimensional shape of the air-water interface formed on submerged hydrophobic surfaces in a channel flow. The grate and the circular hole are considered a roughness feature, its size is varied between 80 and $200\mu \mathrm{m}$, and the Reynolds numbers of 1850 and 5000 are considered based on channel half-height and bulk velocity. The temporal variation of the height, the curvature of the air-water interface, and the corresponding diffusion length is measured, and the diffusion process is classified into three phases. For each phase, the diffusion characteristics are analyzed in relation to the roughness structure type, size, and Reynolds number. Based on the analysis, we propose a scaling relation for the Sherwood number (dimensionless diffusion length). For the first two phases when the interface is pinned at the roughness edge, the Sherwood number is determined by the interface curvature (i.e., the contact angle between the interface and the roughness sidewall), but it is scaled with the Peclet number (the ratio between the shear rate and the diffusion rate) for the last phase when the interface is depinned and moves downward. These relations are also validated with the data available in the literature, and we think this is useful as a simple guideline to design a roughness geometry for the superhydrophobic surfaces.

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• Contact line dynamics
• Interfacial flows
• Multiphase flows
• Wetting