Two basic mechanisms are responsible for fluid mixing: diffusion and advection. In liquids, molecular diffusion alone is hardly efficient for mixing. Advection, that is the transport of matter by a flow, is required for better mixing.
The fluid flow obeys fundamental equations of fluid dynamics (such as the conservation of mass and the conservation of momentum) called Navier–Stokes equations. These equations are written for the Eulerian velocity field rather than for the Lagrangian position of fluid particles. Lagrangian trajectories are then obtained by integrating the flow. Studying the effect of advection on fluid mixing amounts to describing how different Lagrangian fluid particles explore the fluid domain and separate from each other.