Dispersive mixing in the posterior tear film under a soft contact lens

This paper is a first attempt to model mixing in the tear layer of the eye sandwiched between the cornea and a soft contact lens (i.e., the post-lens tear film-or POTF). The proposed driving force for mixing is lateral diffusion enhanced by the periodic lateral (up-down) and squeezing (in-out) motion of the contact lens during blinking. In a mechanism similar to Taylor dispersion, the classical diffusion equation emerges at long times when concentration gradients smooth, but with a mechanical dispersion coefficient, D*, rather than-a molecular diffusion coefficient, D. Calculated values of the dispersion coefficient are orders of magnitude larger than molecular diffusivities permitting mixing in the POTF on time scales much shorter than that of pure diffusion, L-2/D, where L is the lens radius. The dispersive-mixing model is tested against clinical experiments of fluorescein-labeled dextran decay from the POTF on 23 human subjects, each with soft contact lenses of four different diameters. Comparison between theory and experiment for the nonreactive dye is reasonable, especially considering the fact that accurate measurements of several parameters are not available, such as the transverse lens travel and the tear-film thickness. The model captures the essential physics involved in the mixing process but requires modification to improve quantitative prediction. Further, the proposed dispersive-mixing theory for flushing of the POTF serves as a foundation for predicting the mixing behavior of reactive solutes, such as oxygen, carbon dioxide, and bacteria.