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Pneumatic micro-extrusion (PME) presents inherent challenges in achieving precise control over material deposition due to the small scale and high viscosity of the material flow. Traditional experimental methods often fall short in capturing the complex mechanisms, interactions, and dynamics governing material transport and deposition in PME, highlighting the necessity for advanced computational approaches to unveil these intricate physical phenomena. The primary objective of this study is to develop a robust computational framework for simulating material transport and deposition in PME, offering detailed insights into the fluid dynamics, flow complexities, and deposition characteristics intrinsic to the PME process. This involves systematically investigating the influence of key process parameters, such as material properties, print speed, and flow pressure, on deposition dynamics. Three-dimensional (3D) computational fluid dynamics (CFD) modeling was employed using ANSYS Fluent, with boundary conditions defined to replicate pneumatic extrusion on a moving substrate. The CFD simulations captured three distinct deposition regimes: (i) under-extrusion, (ii) normal extrusion, and (iii) over-extrusion. Results show that decreasing print speed at constant inlet velocity produced over-extrusion, with increased bead height and width due to material overflow. At normal extrusion, bead geometry remained stable, while under-extrusion reduced bead width and ultimately led to discontinuities when flow stresses exceeded cohesive strength. Notably, bead width decreased significantly between 10 mm/s and 15 mm/s, but showed little difference between 15 mm/s and 20 mm/s. Instead, the higher speed produced discontinuities consistent with experimental observations. Centerline velocity profiles revealed that the flow inside the cartridge was very slow at approximately 0.058 mm/s, whereas the velocity increased sharply within the nozzle throat, reaching nearly 12.88 mm/s. These predictions were further supported by validation experiments, where the measured nozzle velocity of 12.95 mm/s closely matched the CFD-simulated value of 12.88 mm/s, demonstrating strong agreement between simulation and experiment. Additionally, pressure decreased slightly with increasing print speed due to reduced backflow, while nozzle velocity and wall shear stress remained unchanged under fixed inlet velocity conditions. Overall, the outcomes of this study are expected to inform parameter optimization strategies and enhance PME process efficiency, providing critical insights into how variations in PME process dynamics influence print morphology and quality, advancing the path toward optimized fabrication of scaffolds for tissue engineering applications.