The present invention relates to an aerosol-generating system comprising a liquid storage portion for storing liquid aerosol-forming substrate, wherein the liquid storage portion comprises a movable wall and an outlet, a vaporiser comprising a heating element having a structure defining an open-ended internal passage for heating deposited liquid aerosol-forming substrate, a pump configured for delivering liquid aerosol-forming substrate from the outlet of the liquid storage portion to the internal passage of the heating element, the pump comprising a micro stepper motor with a drive shaft that is configured to rotate for a predetermined amount upon performing one step of the micro stepper motor, a piston connected to the movable wall, and a lead screw connecting the drive shaft to the piston and configured to translate a rotation of the drive shaft into an axial movement of the piston and a corresponding axial movement of the movable wall, wherein the vaporiser is configured for heating the delivered liquid aerosol-forming substrate in the internal passage to a temperature sufficient to volatilize at least a part of the delivered liquid aerosol-forming substrate. The present invention further relates to a cartridge for an aerosol-generating system, wherein the cartridge comprises the liquid storage portion, the piston, and the lead screw. The present invention further relates to a method for generating aerosol.