Important dimensionless groups were investigated to find basic experimental correlations in vibrating systems. When mass transfer occurred in the system, it was deduced that eddy diffusion took place locally near the vibrating bodies without having turbulent flow in the whole system. The eddy diffusivity in the system turned out to be proportional to the factor, α²f. For a system in a single vibrational mode, α²f/vD was a very important dimensionless group. For a combined vibrational mode system, ραfD/μ, and for a crowded bubble system ρ（αf）²l/σ became important. These conclusions were confirmed both by dimensional analysis and by experimental results.