Displacement of a viscous liquid by a less-viscous liquid from the solid surfaces is relevant to many practical applications, including flow through porous chemical reactors, immiscible pollutant transport in soils, and hydrocarbon recovery. We study the spontaneous imbibition of water in capillary tubes partially filled with oil slugs of fixed length. High viscosity contrast of viscous-oil with water results in a tunable constant-rate capillary rise. The capability to control both the displacement rates and wettability makes this an attractive system to explore, and the results of the study bear a direct connection to the multiphase flow in porous media, where wettability plays a critical role.