Abstract - The effect of air-borne nanoparticles (NPs) on human health is an active area of research, with clinical relevance evidenced by the current COVID-19 pandemic. As in vitro models for such studies, lung-on-a-chip (LOAC) devices can represent key physical and physiological aspects of alveolar tissues. However, wide-spread adoption of the LOAC device for NP testing has been hampered by low intra-laboratory and inter-laboratory reproducibility. To complement ongoing experimental work, we carried out finite-element simulations of the deposition of NPs on the epithelial layer of a well-established LOAC design. We solved the Navier-Stokes equations for the fluid flow in a three-dimensional domain, and studied the particle transport using Eulerian advection-diffusion for fine NPs and Lagrangian particle tracking for coarse NPs. Using Langmuir and Frumkin kinetics for surface adsorption and desorption, we investigated NP adsorption under different exercise and breath-holding patterns. Conditions mimicking physical exercise, through changes in air-flow volume and breathing frequency, enhance particle deposition. Puff profiles typical of smoking, with breath-holding between inhalation and exhalation, also increase particle deposition per breathing cycle. Lagrangian particle tracking shows Brownian motion and gravitational settling to be two key factors, which may cooperate or compete with each other for different particle sizes. Comparisons are made with experimental data where possible, and show qualitative and semi-quantitative agreement. These results suggest that computer simulations can potentially inform and accelerate the design and application of LOAC devices for analyzing particulate- and microbe-alveolar interactions.