Kinetics of capillary tear flow in the Schirmer strip

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Abstract
The popular Schirmer test of tearing ability heretofore has never been analyzed kinetically and the interpretation of the results is usually based on implicit, often erroneous assumptions. We have analyzed the capillary flow of fluids in filter paper strips in vitro systems for the cases of unlimited supply and limited supply at constant rates, and in vivo using human subjects, who kinetically corresponded to limited supply having variable rates. The effects of evaporation, surface tension, viscosity, paper pore-size, and the wettability of the cellulose fibers in the paper were also studied. The results show that in the case of unlimited supply, the fluid absorption is kinetically identical to fluid uptake by a horizontal capillary. This implies that the paper strip can absorb fluids only at a certain maximum rate which decreases with time. At lower secretion rates, the rate of wetting length increase is linearly proportional to the secretion rate provided that evaporation is prevented. Evaporation increases with increased wetting length until a steady state is reached where the length of wetting remains constant in time. As long as the secretion rate remains below the maximum uptake rate of the paper strip, the paper and fluid characteristics have a negligible influence on the wetting rate thus the rate of wetting can provide quantitative information on the secretion rate. Wetting length versus time curves obtained in vivo can be best described mathematically by assuming that the initially high secretion rate exponentially decays to a lower, final value. From the data, the magnitude of the initial and final tear secretion rates as well as the secretion rate decay coefficient can be calculated. These physiologically relevant values quantitatively characterize the functioning of the lacrimal system and may have diagnostic value in detecting marginal lacrimal deficiencies and predicting poor contact lens tolerance.
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