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Compound threads and jets consist of a core liquid surrounded by an annulus of a second immiscible liquid. Capillary forces derived from axisymmetric disturbances in the circumferential curvatures of the two interfaces destabilize cylindrical base states of compound threads and jets (with inner and outer radii R1 and aR1 respectively). The capillary instability causes breakup into drops; the presence of the annular phase allows both the annular- and core-phase properties to influence the drop size. Of technological interest is breakup where the core snaps first, and then the annulus. This results in compound drops. With jets, this pattern can form composite particles, or if the annular fluid is evaporatively removed, single drops whose size is modulated by both fluids.This paper is a study of the linear temporal instability of compound threads and jets to understand how annular fluid properties control drop size in jet breakup, and to determine conditions which favour compound drop formation. The temporal dispersion equation is solved numerically for non-dimensional annular thicknesses a of order one, and analytically for thin annuli (a – 1 = ε [Lt ] 1) by asymptotic expansion in ε. There are two temporally growing modes: a stretching mode, unstable for wavelengths greater than the undisturbed inner circumference 2πR1, in which the two interfaces grow in phase; and a squeezing mode, unstable for wavelengths greater than 2πaR1, which grows exactly out of phase. Growth rates are always real, indicating that in jetting configurations disturbances convect downstream with the base velocity. For order-one thicknesses, the growth rate of the stretching mode is higher for the entire range of system parameters examined. The drop size scales with the wavenumber of the maximally growing wave (kmax). We find that for the dominant stretching mode and a = 2, variations from 0.1 to 10 in the ratios of the annulus to core viscosity, or the tension of the outer surface to that of the inner interface, can result in changes in kmax by a factor of approximately 2. However, for these changes in the system ratios, the growth rate (smax) and the ratio of the amplitude of the outer to the inner interface (Amax) for the fastest growing wave only change marginally, with Amax near one. The system appears most sensitive to the ratio of the density of the annulus to the core fluid. For a variation between 0.1 and 10, kmax again changes by a factor of 2, but Amax and smax vary more significantly with large amplitude ratios for low density ratios. The amplitude ratio of the stretching mode at the maximally growing wave (Amax) indicates whether the film or core will break first. When this ratio is near one, linear theory predicts that the core breaks with the annulus intact, forming compound drops. Except for low values of the density ratio, our results indicate that most system conditions promote compound drop formation.For thin annuli, the growth rate disparity between modes becomes even greater. In the limit ε → 0, the squeezing growth rate is roughly proportional to ε2 while the stretching mode growth rate is roughly proportional to ε0 and asymptotes to a single jet with radius R1 and tension equal to the sum of the two tensions. Thus, in this limit the growth rate and kmax are independent of the film density and viscosity. The amplitude ratio of the stretching mode becomes equal to one for all wavenumbers; so thin films break as compound drops. Our results compare favourably with previously published measurements on unstable waves in compound jets.

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Among all non-invasive alternatives, contact lenses offer the highest bioavailability to the cornea due to the location of the lens in the immediate vicinity of the cornea. Several approaches have been patented to improve contact lens design for an extended release duration of drugs. Many technologies have successfully integrated suitable drug release profiles into contact lenses, but drug-eluting contacts are not yet commercialized likely due to regulatory challenges, including the high costs of clinical trials.

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.

Ophthalmic drug for the anterior chamber diseases are delivered into tears by either eye drops or by extended release devices placed in the eyes. The instilled drug exits the eye through various routes including tear drainage into the nose through the canaliculi and transport across various ocular membranes. Understanding the mechanisms relevant to each route can be useful in predicting the dependency of ocular bioavailability on various formulation parameters, such as drug concentration, salinity, viscosity, etc. Mathematical modeling has been developed for each of the routes and validated by comparison with experiments. The individual models can be combined into a system model to predict the fraction of the instilled drug that reaches the target. This review summarizes the individual models for the transport of drugs across the cornea and conjunctiva and the canaliculi tear drainage. It also summarizes the combined tear dynamics model that can predict the ocular bioavailability of drugs instilled as eye drops. The predictions from the individual models and the combined model are in good agreement with experimental data. Both experiments and models predict that the corneal bioavailability for drugs delivered through eye drops is less than 5% due to the small area of the cornea in comparison to the conjunctiva, and the rapid clearance of the instilled solution by tear drainage. A contact lens is a natural choice for delivering drugs to the cornea due to the placement of the contact in the immediate vicinity of the cornea. The drug released by the contact towards the cornea surface is trapped in the post lens tear film for extended duration of at least 30min allowing transport of a large portion into the cornea. The model predictions backed by in vivo animal and clinical data show that the bioavailability increases to about 50% with contact lenses. This realization has encouraged considerable research towards delivering ocular drugs by contact lenses. Commercial contacts are, however, not ideal for drug delivery due to the short release durations which may necessitate wearing multiple lenses each day, reducing the viability of this approach. Recent research has focused on designing contacts that retain all critical properties while increasing the release durations to a few hours or a few days. Beagle dog studies with contact lenses containing vitamin E nanobarriers to attenuate drug transport have shown promising results. Human studies using contacts for drug delivery have also been conducted for allergy therapy but drug eluting contacts are not available in the market for any therapy.

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