Settling and Deformation of a Thin Elastic Shell on a Thin Fluid Layer Lying on a Solid Surface

Chauhan, Anuj; Radke, Clayton J.

doi:10.1006/jcis.2001.8008

Cited by 30 publications

(23 citation statements)

References 8 publications

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“…During blinking, the eyelid applies normal and shear forces on the contact lens causing it to move, rotate and distort. For example, using elastohydrodynamic theory, Chauhan and Radke (2002) investigated the behaviour of a soft contact lens both during the blink and the inter-blink period. In that model, the pressure distribution under the eyelid was not calculated and they assumed an axisymmetric parabolic pressure profile.…”

Section: Electronic Supplementary Materialsmentioning

confidence: 99%

Elastohydrodynamics of the Eyelid Wiper

et al. 2007

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This paper presents an elastohydrodynamic model of the human eyelid wiper. Standard lubrication theory is applied to the fluid layer between the eyelid wiper and ocular surface. The role of the lubrication film is to reduce the shear stresses by preventing solid to solid contact between the eyelid wiper and ocular surface. For the lubrication film to be effective, it is required that the orientation of the eyelid wiper changes between the opening and closing phases of a blink. In order to model this, the hydrodynamic model is coupled with an elastic mattress model for the soft tissue of the eyelid wiper and ocular surface. This leads to a one-dimensional non-linear partial differential equation governing the fluid pressure in the lubrication film. In order to solve the differential equation, a loading condition or constraint equation must be specified. The resulting system is then solved numerically. The model allows predictions of the tear film flux from under the upper eyelid, as well as normal and shear stresses acting on the ocular surface. These factors are important in relation to dry eye syndrome, deformation of the cornea and contact lens design. It is found that the pressure and shear stress under the eyelid act across a length of approximately 0.1 mm which is consistent with clinical observations. It order to achieve a flow of tears from under the upper eyelid during a blink, the model requires that the normal force the eyelid applies to the ocular surface during the closing phase of the blink is significantly higher than during the opening phase of the blink.

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Section: Electronic Supplementary Materialsmentioning

confidence: 99%

Elastohydrodynamics of the Eyelid Wiper

et al. 2007

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“…Recoil is driven primarily by the release of lens elastic energy stored during the inward motion of the lens. 1,2 In this case, lens elasticity is im- portant, and the pressure differences between the anterior and posterior surfaces are complicated. 2 The rigid, porous-disk model is no longer appropriate.…”

Section: Discussionmentioning

confidence: 98%

“…1,2 In this case, lens elasticity is im- portant, and the pressure differences between the anterior and posterior surfaces are complicated. 2 The rigid, porous-disk model is no longer appropriate. Nevertheless, the extremely small hydrodynamic permeabilities of SCLs dictate little or no tear flow through the lens during recoil.…”

Section: Discussionmentioning

confidence: 98%

“…Lens settling is a complicated elastohydrodynamic process with the only available model predicting eventual lens adherence. 2 For conventional hydroxyethylmethacrylate (HEMA)-based hydrogel lenses, severe adherence is not a commonly reported clinical event, although available data for the transient thickness of the post-lens tear film (PoLTF) during settling are sparse. 1 Conversely, silicone-rubber lenses, which are highly permeable to oxygen diffusion, suffer a tendency to adhere to the cornea.…”

Section: Introductionmentioning

confidence: 99%

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The Effect of Water Hydraulic Permeability on the Settling of a Soft Contact Lens on the Eye

Monticelli

Chauhan

Radke

2005

Current Eye Research

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“…For typical values of the permeability for three different soft contact lenses (all approximately 10 −8 μm 2 ), their results indicate a negligible influence of the permeability on the settling rate during a blink. The influence of deformation of the contact lens, modeled as a thin elastic shell, during multiple blink cycles and the question of a balance, or lack thereof, between the loss/gain of fluid in the post-lens tear film over a blink cycle has also been assessed (Chauhan and Radke [25]). …”

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confidence: 99%

Thin Film Evolution over a Thin Porous Layer: Modeling a Tear Film on a Contact Lens

Nong¹,

Anderson²

2010

SIAM J. Appl. Math.

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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. [5], and Cher [6]) suggest a somewhat more complex system. In particular, the current view replaces the mucus and aqueous layers with a mucoaqueous layer in which mucins secreted from goblet cells are distributed throughout the bulk of the tear film and epithelial mucins form a complex barrier at the corneal surface. Measurements of the overall thickness of a human tear film range from a few microns to as many as 40 (see the review by Bron et al. [5]). The corneal surface itself has 100-nm-scale microbumps and rod-like mucins of length 200-500 nm that extend into the tear film [4]. These mucins have multiple functions ranging from cleanup and removal of debris from the tear film, stabilization of the tear film, and, with particular attention to the membrane-associated mucins, maintaining wettability at the corneal surface. The lipid layer, whose thickness has been estimated to range between 13-100 nm, serves to further stabilize the film and to slow evaporative mass loss (Bron et al. [5]).Dry eye syndrome is a common disorder of the human tear film that results from decreased tear production, excessive tear evaporation, and/or an abnormality in the

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Settling and Deformation of a Thin Elastic Shell on a Thin Fluid Layer Lying on a Solid Surface

Cited by 30 publications

References 8 publications

Elastohydrodynamics of the Eyelid Wiper

Elastohydrodynamics of the Eyelid Wiper

The Effect of Water Hydraulic Permeability on the Settling of a Soft Contact Lens on the Eye

Thin Film Evolution over a Thin Porous Layer: Modeling a Tear Film on a Contact Lens

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