When an immiscible fluid is flowing over a fluid-infused surface with transverse grooves in a microchannel, the infused fluid is either left in or cleaned away from the grooves by the flowing fluid. The cleaning status depends on the geometric parameters of the groove and the contact angle of the flowing fluids. The critical width of the grooves for the infused fluid enclosed in or driven out of the grooves is derived. This study helps to understand the stability of the Cassie status in a low-shear flow where the surface tension plays the key role.