Mixing processes in the vitreous chamber induced by eye rotations

In this paper, we study a model of flow in the vitreous humour in the posterior chamber of the human eye, induced by saccadic eye rotations. We concentrate on the effect of the shape of the chamber upon the mixing properties of the induced flows. We make particle image velocimetry measurements of the fluid velocity in a transparent plastic (Perspex) model of the posterior chamber during sinusoidal torsional oscillations about a vertical axis. We use a Newtonian fluid to model the vitreous humour, which is most realistic when either the vitreous humour is liquefied or has been replaced by purely viscous tamponade fluids. The model of the posterior chamber is a sphere with an indentation, representing the effect of the lens. In spite of the purely periodic forcing, a steady streaming flow is generated, which plays a fundamental role in the mixing processes in the domain. The streaming flow differs markedly from that in a perfect sphere, and its topological characteristics change substantially as the frequency of oscillation varies. We discuss the flow characteristics in detail and show that, for physiological parameter values, the Péclet number (based on a suitable measure of the steady streaming velocity) is large, suggesting that advection strongly dominates over diffusion for mass transport phenomena. We also compute particle trajectories based on the streaming velocity and use these to investigate the stirring properties of the flow.