This paper describes a novel pumping device without mechanical moving parts based on the periodic generation and collapse of a single vapour bubble in a channel. The channel shape is such that it creates an asymmetry in the surface tension forces, which results in a pumping effect. The principle can be implemented over a broad range of channel sizes and repetition frequencies. For illustration purposes, a particular implementation is described here where the working fluid is a salt solution in water, the channel diameters are of the order of 1 mm and the repetition frequency is between 1-10 Hz. In these conditions, the device develops a head of a few centimetres of water with typical flow rates in the range of 100 µl per minute. It appears possible to increase both head and flow rate by adjusting geometrical parameters and operating conditions. A simple modification of the design would render the same principle also applicable to the pumping of non-conducting liquids.