A novel method is presented to monitor carbon nanotube (CNT) growth by formation of CNT stacks. By this process, CNT growth kinetics are investigated for densely packed CNT films in the gas-diffusion-controlled regime. CNT stacks are fabricated by water-assisted selective etching and the cyclic introduction of ethylene into the chemical vapor deposition (CVD) reactor. Formation of the CNT stacks allows monitoring of the CNT growth evolution, thereby providing insight into the growth kinetics. A parabolic increase of CNT length versus time is observed, indicating a gas-diffusion-controlled growth mode. The densely packed, well-aligned CNT films act as porous barrier layers to the diffusion of ethylene precursor to the catalyst nanoparticles, since these films form via a base-growth mode under the conditions invoked in our system. By adjustment of CNT growth time and temperature, a quantitative time-evolution analysis is performed to investigate the CNT growth model and extract the gas precursor mass transfer coefficient in the CNT films. The self-diffusion of gases in the densely packed CNT films is found to be Knudsen diffusion with a diffusion coefficient on the order of 10(-4) cm(2)/s.