A liquid chromatographic method and apparatus is disclosed which employs an improved pump not requiring driven pistons or sliding seals. The pump comprises at least one length of tubing forming a chamber disposed between first and second check valves, controllable heating means to periodically heat liquid in said chamber effective to pump relatively low volumes of liquid from the chamber at relatively high pressures, means for measuring the pressure developed by the pump, and control means to increase and decrease the amount of heat imparted to the liquid to maintain the pump operation at a controlled pressure setpoint.