2017/04/05 by Tobin A. Driscoll, Driscoll, Tobin A., Richard Braun +3
Chemistry · Engineering · Medicine · Physics and Astronomy · #FOS: Mathematics #Fluid Dynamics and Thin Films #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Ocular Surface and Contact Lens #Surfactants and Colloidal Systems
paper · pdf · doi:10.48550/arxiv.1704.01618
openalex publication_date 2017/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
During the upstroke of a normal eye blink, the upper lid moves and paints a\nthin tear film over the exposed corneal and conjunctival surfaces. This thin\ntear film may be modeled by a nonlinear fourth-order PDE derived from\nlubrication theory. A challenge in the numerical simulation of this model is to\ninclude both the geometry of the eye and the movement of the eyelid. A pair of\northogonal and conformal maps transform a square into an approximate\nrepresentation of the exposed ocular surface of a human eye. A spectral\ncollocation method on the square produces relatively efficient solutions on the\neye-shaped domain via these maps. The method is demonstrated on linear and\nnonlinear second-order diffusion equations and shown to have excellent accuracy\nas measured pointwise or by conservation checks. Future work will use the\nmethod for thin-film equations on the same type of domain.\n