Abstarct: Over one billion individuals suffer from respiratory diseases worldwide, so that every year, four million lose their lives due to these illnesses. In recent years, the development of lung-on-a-chip system has provided a suitable platform for scientists and researchers to conduct more precise preclinical studies on respiratory diseases and drug development, representing a significant step towards improving health and increasing human lifespan. The lung-on-a-chip system, simulating the air-blood membrane in lung air sacs, consists of an air channel for cultivating lung cells and a blood channel for cultivating vascular cells, separated by a thin, permeable polymer membrane. It is worth mentioning that in most studies, the term "medium channel" is used instead of the "blood channel," as the culture medium serves as a suitable alternative to blood in biological studies, providing necessary substances for cells. Moreover, to model the contraction and expansion of the lungs during respiration, two side channels under sinusoidal stretching are employed to induce membrane stretching. Exposure to harmful environmental particles such as viruses, bacteria, pollutants, and toxic substances in industrial and urban environments is a significant factor in the onset or progression of chronic respiratory diseases, such as COVID-19 and asthma. Therefore, having sufficient knowledge regarding the dynamics of environmental pollutants and drug particles inside the lung-on-a-chip system to facilitate effective transport of these particles to the cultured cells can be a crucial step in precise medical and pharmaceutical studies. Key influencing factors on particle dynamics include the geometric properties of the lung-on-a-chip system, particle physical characteristics, membrane stretching intensity/frequency, and fluid flow properties. Given the challenges associated with constructing microsystems, specially creating thin, permeable membranes, and difficulties related to tracking and imaging the paths of nanoparticles inside these systems, experimental studies are often challenging, time-consuming, and sometimes impossible. In recent years, numerical studies have been recognized as a powerful, accurate, and cost-effective method to overcome the challenges associated with studying biological issues experimentally. The aim of this research is to provide a comprehensive understanding of particle dynamics in the lung-on-a-chip system by developing a complementary numerical study alongside experimental investigation. For this purpose, a numerical simulation model using the finite element method is applied to study particles with variable diameters in the order of nanometers. Initially, a 2D model of the lung-on-a-chip system, considering the air and medium channels separated by a thin permeable membrane, is studied. Developing such a model in the first step has been very useful in understanding the effects of particle diameter, fluid velocity, and membrane permeability on the distribution and dispersion of particles in two different fluid environments: air and medium. Subsequently, a comprehensive 3D numerical model, considering all components of the lung-on-a-chip system, is investigated. One of the main advantages of this model is its capability to examine particle dynamics in membrane stretching conditions, representing the respiratory state. Accordingly, incorporating permeable membrane stretching and channel wall deformation, as well as the movement of fluid and nanoparticle dynamics inside the air and medium channels, transforms the considered model into a multi-physics problem. It is worth mentioning that, to investigate the membrane stretching effect on fluid dynamics, a fluid-solid interaction model has been used. The results obtained from this research will contribute to optimizing effective quantities, the way particles are transported to the location of cultivated lung cells, the rate of particle transfer from the air channel to the medium channel, and the distribution of particles in the medium channel. This comprehensive study on the dynamics of particles in the lung-on-a-chip microsystem, overcoming challenges associated with experimental studies, can provide deep insights into the optimization of drug inhalation devices. Consequently, the conducted study in this research can be a significant step towards the development of inhaled medications, representing one of the most significant advancements in the field of pharmaceuticals today.