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Liquid microchannels on structured surfaces are built up using a wettability pattern consisting of hydrophilic stripes on a hydrophobic substrate. These channels undergo a shape instability at a certain amount of adsorbed volume, from a homogeneous state with a spatially constant cross section to a state with a single bulge. This instability is quite different from the classical Rayleigh Plateau instability and represents a bifurcation between two different morphologies of constant mean curvature. The bulge state can be used to construct channel networks that could be used as fluid microchips or microreactors.