An aerosol-generating system is provided, including: a liquid storage portion including a container configured to hold a liquid aerosol-forming substrate and defining an opening at an end thereof; a heater assembly extending across the opening along a plane transverse to a longitudinal axis of the portion and including an arrangement of one or more electrically conductive flat filaments; a capillary material disposed between the portion and the heater assembly and being configured to convey the substrate to the one or more filaments; and conductive contacts, disposed in electrical contact with corresponding contacts of the heater assembly, the portion being disposed at a first side of the heater assembly and a first airflow channel being disposed at a second side of the heater assembly, and the first airflow channel defining an airflow pathway that extends in a direction orthogonal to the plane and to a surface of the capillary material.