Mathematical modeling of a contact lens and tear layer at equilibrium
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In this thesis, we study the capillary surface at a vertical wall, and a tear meniscus around a symmetric, spherical cap lens. We propose a mathematical model of a tear meniscus around a contact lens that is at static equilibrium using a calculus of variations approach. As the lens is in static equilibrium all the forces and moments sum to zero. The forces acting on the lens are its weight, force due to hydrostatic and atmospheric pressures and surface tension on the periphery of the lens due to the tear meniscus. We consider the two cases of presence or absence of a force due to the lower eyelid. The xed parameters in the model are weight of the lens, coe cient of surface tension, magnitude of gravitational acceleration, density of the tear liquid and physical parameters of the lens such as the diameter and base curve radius. The adjustable parameters in the model are contact angles of the tear meniscus with the cornea and contact lens respectively and the position of the lens on the cornea. Numerical experiments suggest that there exist range of values for the adjustable parameters that lead to physically reasonable solutions, for lens position; extent of overlap of the lower lid on the lens; pressure due to the lid on the lens; and contact angles between the tear meniscus and the cornea and contact lens respectively.