Exposure Time in Fluid Mechanics
The concept of exposure-time is a generalization of “age” – when one component of a flow is exposed to another, one can keep track of the associated exposure-time by literally moving the exposed component in a new dimension added to the governing equations of transport. Here are several examples in reactive transport from a ppt deck on this approach (56.2Mb, got movies, also links to papers).
Scalar Dissipation
The insert shows particles in a 2D shear flow including a dispersing solute cloud. We use the same clock approach but now with age in the vertical direction and advect particles at velocity proportional to the magnitude of the gradient of solute in the horizontal plane. The movie shows the evolution of the age as the cumulative exposure of solute particles to scalar dissipation which is a proxy for mixing and for reaction extent.
