Detection of transport barriers in fluid-dynamical systems
Understanding mixing processes that occur in the human vitreous chamber is of fundamental importance owing to the relevant clinical implications in drug delivery treatments of several eye conditions.
In this research we rely on experimental observations on a physical model of the human eye to perform an analysis based on Lagrangian trajectories. In particular, we study barriers to transport (i.e. material surfaces which cannot be crossed by the fluid) by using nonlinear dynamical systems theoretical and numerical tools.
Bifurcations in the system dynamics are investigated by varying the main physical parameters of the problem.
Upper half of the eyeball. Three trajectories are shown, whose time evolution is coded by colors,
from cyan (initial point) to magenta (end point).
2d transport barriers (green and red lines) are also plotted in the equatorial plane.
The trajectories show the motion of the drug particles owing to sinusoidal eye movements around the vertical axis.