ORIGINAL ARTICLE Effect of Viscosity on Tear Drainage and Ocular Residence Time HENG ZHU, PhD, and ANUJ CHAUHAN, PhD University of Florida, Chemical Engineering Department, Gainesville, Florida ABSTRACT Purpose. An increase in residence time of dry eye medications including artificial tears will likely enhance therapeutic benefits. The drainage rates and the residence time of eye drops depend on the viscosity of the instilled fluids. However, a quantitative understanding of the dependence of drainage rates and the residence time on viscosity is lacking. The current study aims to develop a mathematical model for the drainage of Newtonian fluids and also for power-law non-Newtonian fluids of different viscosities. Methods. This study is an extension of our previous study on the mathematical model of tear drainage. The tear drainage model is modified to describe the drainage of Newtonian fluids with viscosities higher than the tear viscosity and power-law non-Newtonian fluids with rheological parameters obtained from fitting experimental data in literature. The drainage rate through canaliculi was derived from the modified drainage model and was incorporated into a tear mass balance to calculate the transients of total solute quantity in ocular fluids and the bioavailability of instilled drugs. Results. For Newtonian fluids, increasing the viscosity does not affect the drainage rate unless the viscosity exceeds a critical value of about 4.4 cp. The viscosity has a maximum impact on drainage rate around a value of about 100 cp. The trends are similar for shear thinning power law fluids. The transients of total solute quantity, and the residence time agrees at least qualitatively with experimental studies. Conclusions. A mathematical model has been developed for the drainage of Newtonian fluids and power-law fluids through canaliculi. The model can quantitatively explain different experimental observations on the effect of viscosity on the residence of instilled fluids on the ocular surface. The current study is helpful for understanding the mechanism of fluid drainage from the ocular surface and for improving the design of dry eye treatments. (Optom Vis Sci 2008;85:E715–E725) Key Words: canaliculi, model, tear balance, tear drainage, viscosity, shear-thinning E ye drops are commonly instilled to treat a variety of ocular problems, such as dry eyes, glaucoma, infections, allergies, etc. The fluid instillation results in an increase in tear vol- ume, and it slowly returns to its steady value due to tear drainage through canaliculi, and also fluid loss through other means such as evaporation or transport across the ocular epithelia. 1 In fact, if the instilled fluid has a viscosity similar to that of tears, which is about 1.5 mPa  s, the instilled fluids or solutes are eliminated from the tears in a few minutes. 2–4 As a result, the fluids or solutes have a short contact time with the eye surface, which results in reduced effects for artificial tears or low bioavailability for ophthalmic drugs. To increase the duration of comfort after drop instillation and to increase the bioavailability of the drugs delivered via eye drops, it is desirable to prolong the residence time for the instilled fluid. It has been suggested and also shown in a number of clinical and animal studies that increasing the viscosity of the instilled fluid leads to an increase in the retention time. Zaki et al. 5 studied the clearance of solutions with viscosities from 10 to 100 mPa  s from the precorneal surface. These experiments showed a rather inter- esting effect of viscosity: the retention began to increase only after the fluid viscosity exceeded a critical value of about 10 mPa  s and also the relative increase in retention became smaller at very high viscosities. Although increasing fluid viscosity increases the resi- dence time, it may also cause discomfort and damage to ocular epithelia due to an increase in the shear stresses during blinking. Shear thinning fluids such as sodium hyaluronate (NaHA) solu- tions can be used to obtain the beneficial effect of an increase in retention and yet avoid excessive stresses during blinking. 2 The likely reason is that the shear rates during blinking are very high and at such high shear rates these shear-thinning fluids exhibit low viscosity but during the interblink which is the period during which tear drainage occurs, these fluids act as high viscosity fluids 1040-5488/08/8508-0715/0 VOL. 85, NO. 8, PP. E715–E725 OPTOMETRY AND VISION SCIENCE Copyright © 2008 American Academy of Optometry Optometry and Vision Science, Vol. 85, No. 8, August 2008