Friction Factor Formulation for Rarefied Gas Flow in Rough Nanochannels Using Event-Driven Molecular Dynamics

Gas transport in rough nanochannels under rarefied conditions is of considerable interest in microscale and nanoscale flow applications. However, the influence of surface roughness on flow resistance in the transitional regime remains insufficiently understood. In this study, Event-Driven Molecular Dynamics (EDMD) simulations are used to investigate the effects of surface roughness height (k) and periodicity (Λ) on friction-factor behavior for Knudsen numbers between 0.25 and 0.35 and reported Reynolds numbers up to approximately 102. Here, Re is calculated from molecularly averaged density and mean velocity, the effective channel height, and the reduced MD-unit dynamic viscosity used in post-processing. Friction factors were evaluated from the equivalent pressure drop associated with the imposed periodic driving parameter after statistically steady conditions were reached. The results reveal variations in flow resistance with roughness geometry, enabling the development of empirical relations between the normalized friction factor and relative roughness. The resulting correlations describe the observed simulation trends within the parameter range investigated. In addition, velocity-profile and density-field analyses provide physical insight into the mechanisms governing the observed behavior. The findings suggest that classical continuum-based correlations may not fully capture roughness effects under the conditions investigated. The proposed formulation may serve as a practical tool for estimating friction-factor behavior within the investigated transitional rarefied-flow regime.