It is important to understand the movement of aerosols through ultrafine leak-paths with dimensions of similar order to the gas-borne particles when assessing the validity of leak-testing procedures for transport containers for radioactive materials. Experiments have been undertaken to investigate the penetration of micron-sized airborne particles using glass micro-capillaries as model leak-paths. Previous studies demonstrated a simple relationship between air leakage and total particle penetration rates at a constant driving pressure (100 kPa). The present work has demonstrated the importance of pressure in regulating the rate at which the leak-path is plugged by deposited particles. Much of this deposition appears to take place at the entrances of the capillaries where the air-flow converges.