A Molecular Dynamics-Based Model for Knudsen Number and Slip Velocity

Much research has been devoted to incestigating the relationship between Knudsen number and slip velocity using different lattice Boltzmann methods. However, these models are complex to implement for simulations in continuum regime, and have shown to diverge when compared with Direct Simulation Monte Carlo (DSMC) simulations at high Knudsen numbers. In this study, a molecular dynamics (MD)-based Knudsen number is presented, and the relationship between Knudsen number and slip velocity is presented. The proposed slip model directly correlates the Knudsen number with the slip velocity. The model is implemented on a shear-driven MD simulation of a Couette flow, and curve fitting is used to get an exponential solution for the slip velocity. The solution obtained from the proposed model as well as the solutions from the literature are compared with a DSMC simulation. The results show that the proposed exponential solution agrees well with DSMC simulations in comparison with the models from the literature. The exponential solution can serve as boundary conditions for simulating flows at different Knudsen numbers in continuum regime.