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Mathematical modelling of the motion of hard contact lenses

Published online by Cambridge University Press:  26 September 2008

J. A. Moriarty  and
E. L. Terrill
J. A. Moriarty
Affiliation:
OCIAM, Mathematical Institute, 24–29 St. Giles', Oxford OX1 3LB, UK
E. L. Terrill
Affiliation:
OCIAM, Mathematical Institute, 24–29 St. Giles', Oxford OX1 3LB, UK
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Abstract

In this paper we examine the movement of hard contact lenses on the eye. In so doing, we take into account hydrodynamic forces underneath the lens, as well as surface tension forces at the lens periphery. This involves solving for the free surface of the tear film away from the lens in order to determine the magnitudes of the pressure and surface tension forces on the lens. The analysis, which assumes quasi-steady motion, is carried out in both two and three dimensions.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 6 , December 1996 , pp. 575 - 594
Copyright
Copyright © Cambridge University Press 1996

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References

[1] Miller, D. (1963) An analysis of the physical forces applied to a corneal contact lens. Arch. Opthalmol. 70 (6), 823–829.CrossRefGoogle ScholarPubMed
[2] Greber, I. & Dybbs, A. (1972) Fluid dynamic analysis of contact lens motion. Case Western Research Univ. Rpt. FTAS/TR-72–81.Google Scholar
[3] Hayashi, T. T. & Fatt, I. (1980) Forces retaining a contact lens on the eye between blinks. Am. J. Optom. & Physiol. Optics 57 (8), 485–507.CrossRefGoogle ScholarPubMed
[4] Kikkawa, Y. (1969) The mechanism of contact lens adherence and centralization. Am. J. Optom. Arch. Am. Acad. Optom. 47 (4), 275–281.CrossRefGoogle Scholar
[5] Mackie, I. A., Mason, D. & Perry, B. J. (1970) Factors influencing corneal contact lens centration. Br. J. Physiol. Opt. 25 (2), 87–103.Google ScholarPubMed
[6] Allaire, P. E., Allison, S. W. & Gooray, A. M. (1982) Tear-film dynamics and oxygen tension under a circular contact lens. Am. J. Optom. & Physiol. Optics 59 (1), 13–20.Google Scholar
[7] Conway, H. D. (1982) Effects of base curvature on squeeze pressures in contact lenses. Am. J. Optom. & Physiol. Optics 59 (2), 152–154.CrossRefGoogle ScholarPubMed
[8] Conway, H. D. (1982) The motion of a contact lens over the eye during blinking. Am. J. Optom. & Physiol. Optics 59 (10), 770–773.CrossRefGoogle ScholarPubMed
[9] Conway, H. D. & Richman, M. (1982) Effects of contact lens deformation on tear film pressures induced during blinking. Am. J. Optom. & Physiol. Optics 59 (1), 13–20.CrossRefGoogle ScholarPubMed
[10] Conway, H. D. & Knoll, H. A. (1986) Further studies of contact lens motion during blinking. Am. J. Optom. & Physiol. Optics 63 (10), 824–829.CrossRefGoogle ScholarPubMed
[11] Landau, L. & Levich, V. G. (1942) Dragging of a liquid by a moving plate. Acta Physicochim. U.R.S.S. 17, 42–54.Google Scholar
[12] McLeod, J. B. (1995) Solution of a contact lens problem. Euro. J. Applied Math., (to appear).Google Scholar
[13] Martin, D. K. & Holden, B. A. (1986) Forces developed beneath hydrogel contact lenses due to squeeze pressure. Phys. Med. Biol. 30 (6), 635–649.CrossRefGoogle Scholar
[14] Tuck, E. O. & Schwartz, L. W. (1990) A numerical and asymptotic study of some third-order ordinary differential equations relevant to draining flows. SIAM Review 32, 453–469.CrossRefGoogle Scholar
[15] Carrier, G. F., Krook, M. & Pearson, C. E. (1966) Functions of a Complex Variable: Theory and Technique. McGraw Hill.Google Scholar