In this theoretical study, the cross-sectional areas of small, sessile drops were calculated for solid surfaces with a wide range of wettability. These areas were then used to estimate obstruction of rectangular gas flow channels by sessile liquid drops. Our findings suggest that even a small improvement in wettability (i.e., a lower contact angle) will lead to a substantial decrease in blockage. This work has implications for small channels that contain two-phase flow, such as those found in fuel cells.