Non-expert summaryExperimental exploration of the exchange of two immiscible fluids in a wedge. Due to antagonist principal curvature, the more wetting fluid exchange with the less wetting fluid in the wedge, through a capillary instability. The instability develops in the form of fingers pinching into droplets. The less wetting fluid is thus displaced out of the wedge. Measurements are performed for varying geometry and viscosity. Discussion but no conclusion of the physical mechanisms are proposed in light of the more well known viscous fingering instability.