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Title Mathematical modeling of a contact lens and tear layer at equilibrium
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Date Accessioned
University/Publisher Texas Tech University
Abstract 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.
Subjects/Keywords Contact lens, tear film
Contributors Iyer, Ram V. (Committee Chair); Toda, Magdalena D. (committee member); Aulisa, Eugenio (committee member)
Language en
Rights Unrestricted.
Country of Publication us
Record ID handle:2346/46968
Repository tdl
Date Indexed 2020-04-11

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Texas Tech University, Bhagya U.A. Athukorallage, July 2012 LIST OF FIGURES 1.1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Capillary surface at a vertical wall…

…vii 1 5 6 7 7 8 9 11 14 15 17 20 21 22 23 25 26 27 31 33 35 37 38 39 Texas Tech University, Bhagya U.A. Athukorallage, July 2012 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 Variation of θL1 , a, b and the reaction forces FL and FR with…

…Meniscus profiles z(x) and their slopes z (x) for the contact angles θE = 33◦ and θEC = 14.5◦ . . . . . . . . . . . . . . . . . . . . . . . . viii 41 42 44 47 49 50 52 56 57 59 60 Texas Tech University, Bhagya U.A. Athukorallage…

…of the potential 1 Texas Tech University, Bhagya U.A. Athukorallage, July 2012 energy is [3] δJ = γdA − δpdV. (1.2) In equation (1.2), γ is the surface energy per unit area and δp is the pressure difference between…

…neglect the force on the posterior side of the lens due to the viscous stress. We use the lens weight, coefficient of surface tension, density of the tear liquid, 1 τ =µ ∇u + ∇uT 2 2 Texas Tech University, Bhagya U.A. Athukorallage, July 2012…

…They use a version of Darcy’s law to model constitutive relation 3 Texas Tech University, Bhagya U.A. Athukorallage, July 2012 of tear, in which gravity is neglected. For the no blink or quasi-static blink case, this constitutive relation yields a…

…reasonable solutions. 4 Texas Tech University, Bhagya U.A. Athukorallage, July 2012 CHAPTER 2 CAPILLARY SURFACES In this chapter, the basic definitions and theorems that we used to analyze meniscus profiles at a flat vertical wall and around a disk are…

…1 ) 20 73 100 58 Tear 45 Mercury 20 485 Acetone 20 24 Water/oil 20 ≈ 50 Liquid Water 5 Texas Tech University, Bhagya U.A. Athukorallage, July 2012 2.1.2 Young’s equation Consider a static equilibrium of a liquid drop that is deposited on an…

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