We look at the drying process in a simple glass channel with dominant capillary effects as is the case in microfluidics. We find drying kinetics commonly observed for confined geometry, namely a constant period followed by a falling rate period. From visualization of the air/water interface with high resolution, we observe that the drying rate decreases without a drying front progression although this is the usually accepted mechanism for confined geometries. We show with FEM that in our specific geometry the falling rate period is due to changes in the shape of the air-water interface at the free surface where most evaporation occurs. Our simulations show that the sensitivity of the drying rate to the shape of the first air-water interface from the sample free surface implies that slight changes of the wetting or pinning conditions can significantly modify the drying rate.