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Copyright by SIAM. Unauthorized reproduction of this article is prohibited. SIAM J. APPL. MATH. c 2010 Society for Industrial and Applied Mathematics
 

Summary: Copyright by SIAM. Unauthorized reproduction of this article is prohibited.
SIAM J. APPL. MATH. c 2010 Society for Industrial and Applied Mathematics
Vol. 70, No. 7, pp. 27712795
THIN FILM EVOLUTION OVER A THIN POROUS LAYER:
MODELING A TEAR FILM ON A CONTACT LENS
KUMNIT NONG AND DANIEL M. ANDERSON
Abstract. We examine a mathematical model describing the behavior of the precontact lens tear
film of a human eye. Our work examines the effect of contact lens thickness and lens permeability on
the film dynamics. Also investigated are gravitational effects and the effects of different slip models
at the fluid-lens interface. A mathematical model for the evolution of the tear film is derived using a
lubrication approximation applied to the hydrodynamic equations of motion in the fluid film and the
porous layer. The model is a nonlinear fourth-order partial differential equation subject to boundary
conditions and an initial condition for post-blink film evolution. The evolution equation is solved
numerically, and the effects of various parameters on the rupture of the thin film are studied. We
find that increasing the lens thickness, permeability, and slip all contribute to an increase in the
film thinning rate, although for parameter values typical for contact lens wear, these modifications
are minor. Gravity plays a role similar to that for tear films in the absence of a contact lens. The
presence of the contact lens does, however, fundamentally change the nature of the rupture dynamics
as the inclusion of the porous lens leads to rupture in finite time rather than infinite time.
Key words. thin films, tear film, contact lens, porous layer, fluid porous slip, interface slip

  

Source: Anderson, Daniel M. - Department of Mathematical Sciences, George Mason University

 

Collections: Mathematics