Date of Award


Document Type


Degree Name

Master of Science (MS)


College of Science and Mathematics


Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Ashwin Vaidya

Committee Member

David Trubatch

Committee Member

Philip Yecko


The human eye is a complicated and delicate organ. The structure of the eye is such that it provides for clear vision of the world. The cornea and conjunctiva at the front of the eye are avascular structures that require nutrients and moisture to be provided by the tear film. The tear film also provides for the removal of debris from the surface of the eye. The tear film has several layers: a lipid layer, an aqueous solution, and mucus. The optical clarity and structural uniformity of the tear film is maintained by the blinking motion of the eyelid. During a blink, tears are removed from the eye, thus removing debris from the system. I attempt to show how this blinking action causes fluid motion that helps to remove debris from behind the eyelid.

The eye system can be compared to a slider bearing with fluid between the plates. This fluid is modeled as a thin film lubricant using second-order fluid equations. The resulting fluid will be modeled as shear-thinning, shear steady and shear-thickening, which makes the viscosity of the fluid dependent on the relative motion of the container boundaries. The amount of elasticity found in the fluid, and its effect on fluid flow are also examined. Once the nature of the fluids is modeled, a particle is added to the system and its movement through the bearing is analyzed. This type of analysis is usually restricted to geophysical situations.

The motion of the fluid is found to have a strong dependence on the geometry of the bearing. The particle is found to move smoothly through the bearing in a relationship highly dependent on the motion of the fluid. It can be deduced from the displayed movements that a particle that enters the fluid within the tear film will be carried by the tear film into one of the menisci from which it will be removed by the tear drainage apparatus.

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Mathematics Commons