The fluid mechanics of shear-thinning tear substitutes

Tear substitutes are used to treat dry eye syndrome. Shear-thinning should help to delay the appearance of dry spots and improve comfort. This article discusses a numerical model study of the spreading of shear-thinning tear substitutes during blinking. The Ellis model, which takes account of the Newtonian plateau at low shear rate, was chosen. Flow is governed by the capillary number Ca, the shear-thinning index of the fluid α, and a third dimensionless number L2, representing surface tension effects in relation to shear-thinning effects. The numerical solution was validated by scaling laws and by results found in the literature for the Newtonian case. An optimisation process was applied to determine the ranges of Ca, α, and L2, that would ensure greater stability of the tear film than with Newtonian substitutes. The results obtained are illustrated with the cases of two substitutes.