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This paper presents an elastohydrodynamic model of the human eyelid wiper. Standard lubrication theory is applied to the fluid layer between the eyelid wiper and ocular surface. The role of the lubrication film is to reduce the shear stresses by preventing solid to solid contact between the eyelid wiper and ocular surface. For the lubrication film to be effective, it is required that the orientation of the eyelid wiper changes between the opening and closing phases of a blink. In order to model this, the hydrodynamic model is coupled with an elastic mattress model for the soft tissue of the eyelid wiper and ocular surface. This leads to a one-dimensional non-linear partial differential equation governing the fluid pressure in the lubrication film. In order to solve the differential equation, a loading condition or constraint equation must be specified. The resulting system is then solved numerically. The model allows predictions of the tear film flux from under the upper eyelid, as well as normal and shear stresses acting on the ocular surface. These factors are important in relation to dry eye syndrome, deformation of the cornea and contact lens design. It is found that the pressure and shear stress under the eyelid act across a length of approximately 0.1 mm which is consistent with clinical observations. It order to achieve a flow of tears from under the upper eyelid during a blink, the model requires that the normal force the eyelid applies to the ocular surface during the closing phase of the blink is significantly higher than during the opening phase of the blink.

This paper investigates the effect of surfactants during tear film deposition and subsequent thinning. The surfactants occur naturally on the surface of the tear film in the form of a lipid layer. A lubrication model is developed that describes lipid spreading and film height evolution. It is shown that lipids may play an important role in drawing the tear film up the cornea during the opening phase of the blink. Further, nonuniform distributions of lipids may lead to a rapid thinning of the tear film behind the advancing lipid front (shock). Experiments using a fluorescein dye technique and using a tearscope were undertaken in order to visualise the motion of the lipid layer and any associated shocks immediately after a blink. It is found that the lipid layer continues to spread upwards on the cornea after the opening phase of the blink, in agreement with the model. Using the experimental data, lipid particles were tracked in order to determine the surface velocity and these results are compared to the model predictions.

This paper investigates the deposition of the tear film on the cornea of the human eye. The tear film is laid down by the motion of the upper eyelid and then subsequently flows and thins. Of particular interest is the stability of the tear layer and the development of dry patches on the cornea. While there has been significant research on the behaviour of tear films between blinks, this paper focuses on understanding the mechanisms which control the shape and thickness of the deposited film and how this affects the subsequent film behaviour. Numerical and analytical methods are applied to a lubrication model which includes the effects of surface tension, viscosity, gravity and evaporation. The model reveals the importance of the eyelid velocity, motion of the surface lipid layer and the storage of tear film between blinks.

An SEI metapopulation model is developed for the spread of an infectious agent by migration. The model portrays two age classes on a number of patches connected by migration routes which are used as host animals mature. A feature of this model is that the basic reproduction ratio may be computed directly, using a scheme that separates topography, demography, and epidemiology. We also provide formulas for individual patch basic reproduction numbers and discuss their connection with the basic reproduction ratio for the system. The model is applied to the problem of spatial spread of bovine tuberculosis in a possum population. The temporal dynamics of infection are investigated for some generic networks of migration links, and the basic reproduction ratio is computed-its value is not greatly different from that for a homogeneous model. Three scenarios are considered for the control of bovine tuberculosis in possums where the spatial aspect is shown to be crucial for the design of disease management operations.

A fluid mechanical model is developed for the filtering mechanism in mussels that enables estimates to be made of the pressure drop through the gill filaments due to (i) the latero-frontal filtering cilia, (ii) the lateral (pumping) cilia and through the non-ciliated zone at the ventral end of the filament. Calculations indicate that the lateral cilia can generate a sufficient pressure change to 'pump' water through the gill filaments. The velocity profile across the filaments indicates that a backflow can occur in the centre of the channel. Normally the latero-frontal cilia would damp out this backflow but in the case when all the cilia are upright, two 'standing' eddies may form at the mouth of the channel, forcing the incoming water to the side.

A two-layer Newtonian fluid model for muco-ciliary transport in the lung is developed where the viscosity of the upper mucous layer is very much greater than the viscosity of the lower periciliary layer. Theory is presented for both cases when the cilia penetrate, and do not penetrate, the very viscous mucous layer. Calculations suggest that, in normal circumstances, it is not essential for the cilia to penetrate the mucus to provide positive transport. However, it does suggest that there is a weak optimal penetration depth of the cilia of between 10-20% of the cilium length. In the case of high ciliary inactivity (e.g. 90% inactive), penetration of cilia into the mucus is essential for normal transport rates suggesting the mucociliary system may be deliberately overdesigned to cater for a whole range of pathological circumstances.