A spontaneous, steady capillary flow is produced for a liquid index in a circular tube that is partially coated with a surface modifier to create a discontinuous wetting condition between upstream and downstream portions of the tube. As a means of demonstrating that the flow configuration may prove useful as a diagnostic tool in studies concerning capillarity and the physics associated with the moving contact line, average steady velocities are predicted and compared against a large experimental data set that includes the effects of tube dimensions and fluid properties. To access a wider range of tube diameters (0.516-9.88 mm), experiments are performed employing "U-tubes" tested in the low-gravity environment of a drop tower, in addition to straight capillary tubes tested horizontally in a laboratory. The sensitivity of the steady capillary flow to surface cleanliness is dramatic.