Finite-size effect on self-diffusion

The finite-size effect on self-diffusion is critical for fluid transport across scales, from nanoscale microfluidic devices to macroscale engineering systems, significantly influencing performance. In this paper, we systematically investigate this effect by introducing two dimensionless parameters that scale the system size relative to the mean free path (λ). The results reveal a three-phase evolution of self-diffusion: (1) a linear reduction phase dominated by molecular ballistic motion, (2) a nonlinear transition phase governed by the competition between ballistic and thermal motion, and (3) a stable linear phase dominated by thermal motion. By mapping these phases and their underlying physical mechanisms, our research provides a trans-scale understanding of the evolution of physical properties in finite-size domains and offers valuable insights for optimizing the transport performance of engineering systems.