Lagrangian chaos and mixing of fluids

After describing the significance of the mixing of fluids by laminar flows, we give a personal survey of Lagrangian chaos, the chaotic motion of fluid particles, in two-dimensional timeperiodic flows and in three-dimensional steady flows. Next, a few studies of the chaotic mixing, mixing of fluids using Lagrangian chaos, are introduced. Finally, some results of the study of the mixing in a two-dimensional time-periodic flow based on a transport matrix are shown.