The role of lipid abnormalities, aqueous and mucus deficiencies in the tear film breakup, and implications for tear substitutes and contact lens tolerance

Instability and rupture of surfactant-laden bilayer thin liquid films

The stability of surfactant-laden bilayer thin films, where the top layer is subject to van der Waals driven breakup, is of particular relevance to applications where one thin liquid layer is spread on another, such as film-forming firefighting foams and multilayer coatings. Although there has been much prior modeling work on the stability of thin liquid bilayers, additional physical effects and assumptions were incorporated in those studies, making it difficult to isolate the influence of surfactant on the rupture of the top layer. The present work addresses this issue through application of the lubrication approximation to derive a coupled system of nonlinear evolution equations describing the perturbations to the liquid-liquid and liquid-air interfaces and the surfactant interfacial concentrations. The surfactant is assumed to be insoluble and can be present at each interface. Linear stability analysis suggests, and nonlinear simulations confirm, that by using surfactant that adsorbs to both interfaces, the rupture time can be increased by an order of magnitude relative to the surfactant-free case. However, we find it crucial to have the right amount of surfactant to generate strongly stabilizing Marangoni stresses without reducing the interfacial tension too much. Nonlinear simulations and linear stability analysis provide insight into the mechanisms of the delayed rupture and show how the direction and strength of the Marangoni stresses strongly depend on the viscosity ratio of the layers. These results can help guide the choice and design of surfactants to achieve more effective firefighting foams and more stable liquid coatings.

Dynamics and mechanisms for tear breakup (TBU) on the ocular surface

The human tear film is rapidly established after each blink, and is essential for clear vision and eye health. This paper reviews mathematical models and theories for the human tear film on the ocular surface, with an emphasis on localized flows where the tear film may fail. The models attempt to identify the important physical processes, and their parameters, governing the tear film in health and disease.

On tear film breakup (TBU): dynamics and imaging

We report the results of some recent experiments to visualize tear film dynamics. We then study a mathematical model for tear film thinning and tear film breakup (TBU), a term from the ocular surface literature. The thinning is driven by an imposed tear film thinning rate which is input from in vivo measurements. Solutes representing osmolarity and fluorescein are included in the model. Osmolarity causes osmosis from the model ocular surface, and the fluorescein is used to compute the intensity corresponding closely to in vivo observations. The imposed thinning can be either one-dimensional or axisymmetric, leading to streaks or spots of TBU, respectively. For a spatially-uniform (flat) film, osmosis would cease thinning and balance mass lost due to evaporation; for these space-dependent evaporation profiles TBU does occur because osmolarity diffuses out of the TBU into the surrounding tear film, in agreement with previous results. The intensity pattern predicted based on the fluorescein concentration is compared with the computed thickness profiles; this comparison is important for interpreting in vivo observations. The non-dimensionalization introduced leads to insight about the relative importance of the competing processes; it leads to a classification of large vs small TBU regions in which different physical effects are dominant. Many regions of TBU may be considered small, revealing that the flow inside the film has an appreciable influence on fluorescence imaging of the tear film.

Effect of an insoluble surfactant on the dynamics of a thin liquid film flowing over a non-uniformly heated substrate

The stability analysis of a gravity-driven thin liquid film with an insoluble surfactant flowing over a surface with embedded, regularly spaced heaters is investigated. At the leading edge of a heater, the presence of a temperature gradient induces an opposing Marangoni stress at the interface leading to the formation of a capillary ridge. This ridge has been shown to be susceptible to thermocapillary (oscillating in the flow direction) and rivulet (spanwise periodic pattern) instabilities. The presence of an insoluble surfactant is shown to have a stabilizing effect on this system. The governing equations for the evolution of the film thickness and surfactant concentration are obtained within the lubrication approximation. The coupled two-dimensional base solutions for the film thickness and surfactant concentration show that there is no significant change in the height of the capillary ridge at the subsequent heaters downstream. The height of the capillary ridge is reduced by the presence of the surfactant. For very small Peclet number, the presence of multiple heaters has almost no significant effect on the film stability as compared to a single heater and similar trends are observed between the two configurations in the presence of the surfactant as for the case of a clean interface. However, for large Peclet number, the effect was observed on both types of instabilities for certain heater configurations. The Biot number is shown to have a strong effect on the stability results wherein the dominant mode of instability is altered (from rivulet to thermocapillary instability) for a passive or no surfactant case with increase in the Biot number. For an active surfactant thermocapillary instability is found to remain the dominant mode of instability for all the values of the Biot number. It is shown that increasing the number of heaters beyond a couple does not further affect the stability results.

Computed flow and fluorescence over the ocular surface

Fluorescein is perhaps the most commonly used substance to visualize tear film thickness and dynamics; better understanding of this process aids understanding of dry eye syndrome which afflicts millions of people. We study a mathematical model for tear film flow, evaporation, solutal transport and fluorescence over the exposed ocular surface during the interblink. Transport of the fluorescein ion by fluid flow in the tear film affects the intensity of fluorescence via changes in concentration and tear film thickness. Evaporation causes increased osmolarity and potential irritation over the ocular surface; it also alters fluorescein concentration and thus fluorescence. Using thinning rates from in vivo measurements together with thin film equations for flow and transport of multiple solutes, we compute dynamic results for tear film quantities of interest. We compare our computed fluorescent intensity distributions with in vivo observations. A number of experimental features are recovered by the model.

Instability, self-organization and pattern formation in thin soft films

The free surface of a thin soft polymer film is often found to become unstable and self-organizes into various meso-scale structures. In this article we classify the instability of a thin polymer film into three broad categories, which are: category 1: instability of an ultra-thin (<100 nm) viscous film engendered by amplification of thermally excited surface capillary waves due to interfacial dispersive van der Waals forces; category 2: instability arising from the attractive inter-surface interactions between the free surface of a soft film exhibiting room temperature elasticity and another rigid surface in its contact proximity; and category 3: instability caused by an externally applied field such as an electric field or a thermal gradient, observed in both viscous and elastic films. We review the salient features of each instability class and highlight how characteristic length scales, feature morphologies, evolution pathways, etc. depend on initial properties such as film thickness, visco-elasticity (rheology), residual stress, and film preparation conditions. We emphasize various possible strategies for aligning and ordering of the otherwise isotropic structures by combining the essential concepts of bottom-up and top-down approaches. A perspective, including a possible future direction of research, novelty and limitations of the methods, particularly in comparison to the existing patterning techniques, is also presented for each setting.

The precorneal tear film as a fluid shell: the effect of blinking and saccades on tear film distribution and dynamics

We conducted a series of experiments to elucidate the behavior of the human precorneal tear film (PCTF) during blinking and horizontal and vertical saccades. Methodology included video-interferometry with subsequent image cross-correlation (tear film lipid layer [TFLL]) and video-microscopy (mucoaqueous subphase [MAS]). We observed that the TFLL interference pattern deteriorates rapidly with successive blinks and degrades slowly with repeated horizontal saccades during blink suppression when dark arcs of thinning appear in the fluorescein-stained PCTF. Furthermore, after full downgaze and a return to the primary position, a transient horizontal bright band appears, deep to the spreading TFLL. It may be followed by local disturbances in the interference pattern. Two horizontal dark bands form in the stained PCTF after the return saccade. PCTF disruption may occur below the lower band during blink suppression. We concluded that shearing during horizontal saccades is insufficient to disturb the tear film structure greatly. The MAS and TFLL move together as a fluid shell. The dark arcs/bands are caused by meniscus-induced thinning, imprinted onto the PCTF at the lid margin. Their stability during blink suppression suggests that the MAS has gel-like properties. The horizontal bright bands are probably due to transient corneal indentation in downgaze. In downgaze, the disturbance of the TFLL and MAS below the dark bands is possibly due to shearing across the MAS in the return phase. This could cause desiccating stress in everyday activities, such as working at a computer.

Evaporation-driven instability of the precorneal tear film

Tear-film instability is widely believed to be a signature of eye health. When an interblink is prolonged, randomly distributed ruptures occur in the tear film. "Black spots" and/or "black streaks" appear in 15 to 40 s for normal individuals. For people who suffer from dry eye, tear-film breakup time (BUT) is typically less than a few seconds. To date, however, there is no satisfactory quantitative explanation for the origin of tear rupture. Recently, it was proposed that tear-film breakup is related to locally high evaporative thinning. A spatial variation in the thickness of the tear-film lipid layer (TFLL) may lead to locally elevated evaporation and subsequent tear-film breakup. We examine the local-evaporation-driven tear-film-rupture hypothesis in a one-dimensional (1-D) model for the evolution of a thin aqueous tear film overriding the cornea subject to locally elevated evaporation at its anterior surface and osmotic water influx at its posterior surface. Evaporation rate depends on mass transfer both through the coating lipid layer and through ambient air. We establish that evaporation-driven tear-film breakup can occur under normal conditions but only for higher aqueous evaporation rates. Predicted roles of environmental conditions, such as wind speed and relative humidity, on tear-film stability agree with clinical observations. More importantly, locally elevated evaporation leads to hyperosmolar spots in the tear film and, hence, vulnerability to epithelial irritation. In addition to evaporation rate, tear-film instability depends on the strength of healing flow from the neighboring region outside the breakup region, which is determined by the surface tension at the tear-film surface and by the repulsive thin-film disjoining pressure. This study provides a physically consistent and quantitative explanation for the formation of black streaks and spots in the human tear film during an interblink.

Undulatory locomotion of Caenorhabditis elegans on wet surfaces

The physical and biomechanical principles that govern undulatory movement on wet surfaces have important applications in physiology, physics, and engineering. The nematode Caenorhabditis elegans, with its highly stereotypical and functionally distinct sinusoidal locomotory gaits, is an excellent system in which to dissect these properties. Measurements of the main forces governing the C. elegans crawling gait on lubricated surfaces have been scarce, primarily due to difficulties in estimating the physical features at the nematode-gel interface. Using kinematic data and a hydrodynamic model based on lubrication theory, we calculate both the surface drag forces and the nematode's bending force while crawling on the surface of agar gels within a preexisting groove. We find that the normal and tangential surface drag coefficients during crawling are ∼222 and 22, respectively, and the drag coefficient ratio is ∼10. During crawling, the calculated internal bending force is time-periodic and spatially complex, exhibiting a phase lag with respect to the nematode's body bending curvature. This phase lag is largely due to viscous drag forces, which are higher during crawling as compared to swimming in an aqueous buffer solution. The spatial patterns of bending force generated during either swimming or crawling correlate well with previously described gait-specific features of calcium signals in muscle. Further, our analysis indicates that one may be able to control the motility gait of C. elegans by judiciously adjusting the magnitude of the surface drag coefficients.

Rupture of thin stagnant films on a solid surface due to random thermal and mechanical perturbations

A generalized formalism for the rupture of a nondraining thin film on a solid support due to imposed random thermal and mechanical perturbations, modeled as a Gaussian white noise, is presented. The evolution of amplitude of perturbation is described by a stochastic differential equation. The average film rupture time is the average time for the amplitude of perturbation to equal to the film thickness and is calculated by employing a first passage time analysis for different amplitudes of imposed perturbations, wavenumbers, film thickness, van der Waals and electrostatic interactions and surface tensions. The results indicate the existence of an optimum wavenumber at which the rupture time is minimum. A critical film thickness is identified based on the sign of the disjoining pressure gradient, below which the film is unstable in that the rupture time is very small. The calculated values of rupture time as well as the optimum wavenumber in the present analysis agree well with the results of linear stability analysis for immobile as well as completely mobile gas-liquid film interfaces. For stable films, the rupture time is found to increase dramatically with film thickness near the critical film thickness. As expected, the average rupture time was found to be higher for smaller amplitudes of imposed perturbations, larger surface potentials, larger surface tensions and smaller Hamaker constants.

Enhanced instability in thin liquid films by improved compatibility

We investigated experimentally the morphological evolution of thin polydimethylsiloxane films sandwiched between a silicon wafer and different bounding liquids with interfacial tensions varying by 2 orders of magnitude. It is shown that increasing the compatibility between film and bounding liquid by adding a few surfactant molecules results in a faster instability of shorter characteristic wavelength. Inversely, based on the characteristic parameters describing the instability we determined extremely small interfacial tensions with a remarkable accuracy.

Meibomian gland dysfunction

Blepharitis is probably the most common disease entity seen in the general ophthalmologist's office. A significant proportion of these cases are secondary to meibomian gland disease. This review outlines our knowledge of the histopathology, lipid abnormalities and role of microorganisms in meibomian gland dysfunction. We will also review the physiology of meibomian gland secretion and present models of meibomian gland dysfunction which have enhanced our knowledge of this condition. The importance of diagnosing associated conditions such as aqueous tear deficiency, contact lens intolerance, rosacea, and seborrheic dermatitis is emphasized. Although this condition causes significant morbidity in the population, there are effective treatments available and these will be discussed.