A cartridge for an aerosol-generating system is provided, including a storage portion to hold a liquid aerosol-forming substrate; and a heater assembly including an electrical heating element to heat the substrate to form aerosol, and a capillary body to convey the substrate to the element disposed at a porous outer surface of the body, the storage portion being at a first portion of the cartridge, a first airflow channel being at another portion of the cartridge adjacent to the element and defining a first airflow path extending from an air inlet toward the element in a first direction, a second airflow channel defining a second airflow path extending toward the element in a second direction, and a third airflow channel defining a third airflow path extending from the element toward an air outlet in a third direction and to convey aerosol, and the first, second, and third directions are different.