The smaller bubble whose diameter is below 1 micrometer is called nanobubble or ultra-fine bubble. The size of nano bubble is so small and invisible that the diameter distribution is generally evaluated as a mean square distance(MSD) of brownian motion that is measured by Dynamic Light Scattering(DLS) method based on the Einstein-Stokes equation. The equation, however, is not clarified for the application to the bubble sizing. In our previous study, the different behavior between solid particle and bubble with the same diameter at sub-micro scale was confirmed. In this study, the Brownian motion of nano bubble as well as the solid Pt particle whose diameter are around a few nano meters were simulated with the Molecular Dynamics(MD) method. The simulation employed Lennard Jones(LJ) potential to estimate the MSD of the bubbles and particles by tracing the trajectories of the center of gravity of them and resulted that the displacement of solid particles in liquid argon was less than the predicted amount by the Einstein-Stokes equation. In order to confirm apparent viscosity caused by periodic boundary conditions, the drop velocity of the particle due to the gravity force is measured and apparent viscosity is obtained using Stokes’ low with this velocity. Considering this apparent viscosity, the diameter of the solid particle is approximated using the Einstein-Stokes equation under its diameter of 4 nm. The bubble diameter obtained by the Brownian motion is lower than the Einstein-Stokes equatio
