Analysis of tear film rupture: effect of non-Newtonian rheology

Zhang, Yong Liang; Matar, Omar; Craster, Richard V.

doi:10.1016/s0021-9797(03)00200-5

Cited by 77 publications

(59 citation statements)

References 58 publications

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“…The pronounced effects of slip have been observed for thinner liquid layers. This has motivated Zhang et al [58] to examine the possible role of slip on tear film rupture (due to evidence that slip occurs when hydrophilic liquids, similar to mucus or aqueous tear films, overlie hydrophobic epithelium) and on surfactant-induced flows within the lung, used in surfactant replacement therapy. Based on the physical constants associated with airways and with a tear film, the typical values of the dimensionless numbers have been presented [58] and the dimensionless slip parameter, in these applications, is shown to range between 0 and 0.2.…”

Section: Introductionmentioning

confidence: 99%

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Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

Anjalaiah

Usha

2015

Acta Mech

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This manuscript provides a theoretical stability analysis for the configuration of two-layer immiscible flow down an inclined plane with velocity slip along the incline in the limit of zero Reynolds number. Surfactants may be present at the air-liquid interface, liquid-liquid interface, or both. In addition to an Orr-Sommerfeld analysis (again at zero Reynolds number), a long wavelength stability analysis is performed and the results are shown to be consistent. The interface mode, namely the mode of instability that arises because of viscosity stratification, is examined. Stability results (growth rates as a function of slip parameter and neutral stability boundaries) for various configurations of viscosity, surfactant placement, and layer thickness are compared with those of the previous literature and found to agree. It is found that velocity slip along the inclined plane reduces the maximum growth rate of instabilities in configurations where they occur, and the range of unstable wave numbers shrinks as well, indicating that slip has a promise for stabilization. This suggests that there is a possibility of using this favourably as a control option for two-layer flows in the absence or presence of surfactants, in relevant applications by designing the substrate to be a porous substrate with small permeability or a slippery substrate or a rough substrate or a hydrophobic substrate which can be modelled as substrates with velocity slip.

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Section: Introductionmentioning

confidence: 99%

“…However, the study by Sharma et al [61] suggests that, under certain circumstances, the mucus layer causes a slip for the aqueous layer. In view of this, investigations or tear film dynamics have incorporated slip at the surface of the cornea [58,62].…”

Section: Introductionmentioning

confidence: 99%

Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

Anjalaiah

Usha

2015

Acta Mech

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“…Then both, the liquid-liquid and the liquid-gas interface are free to move and their evolution has to be described by coupled evolution equations. Models were derived, for instance, assuming a lower liquid layer that is much thicker than the upper layer 39 , and for two-layer systems with surfactants (and non-newtonian behaviour) 40,41,42 or including evaporation 43,44,45 . A two-layer system under the solely influence of molecular interactions is studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

Morphology changes in the evolution of liquid two-layer films

Pototsky

Bestehorn

Merkt

et al. 2005

The Journal of Chemical Physics

163

202

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We consider a thin film consisting of two layers of immiscible liquids on a solid horizontal (heated) substrate. Both, the free liquid-liquid and the liquid-gas interface of such a bilayer liquid film may be unstable due to effective molecular interactions relevant for ultrathin layers below 100 nm thickness, or due to temperature-gradient caused Marangoni flows in the heated case. Using a long wave approximation we derive coupled evolution equations for the interface profiles for the general non-isothermal situation allowing for slip at the substrate. Linear and nonlinear analyses of the short-and long-time film evolution are performed for isothermal ultrathin layers taking into account destabilizing long-range and stabilizing short-range molecular interactions. It is shown that the initial instability can be of a varicose, zigzag or mixed type. However, in the nonlinear stage of the evolution the mode type and therefore the pattern morphology can change via switching between two different branches of stationary solutions or via coarsening along a single branch.

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“…The stability of a bi-layer liquid film on a solid substrate (with two fluid-fluid interfaces) bears many similarities to the experimental system outlined above, where the layers can exhibit dewetting and rupture, with application to the flow of mucus on the lining of the airways (Craster & Matar 2000;Matar et al 2002), the tear film (Zhang et al 2003) or to industrial coating processes (Pototsky et al 2004(Pototsky et al , 2005Fisher & Golovin 2005). The stability of this bi-layer system to van der Waals attractions has been widely studied, where the system exhibits two temporal branches, one or both of which can be unstable (Pototsky et al 2004;Fisher & Golovin 2005).…”

Section: Introductionmentioning

confidence: 89%

Stability of a bi-layer free film: simultaneous or individual rupture events?

et al. 2015

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We consider the stability of a long free film of liquid composed of two immiscible layers of differing viscosities, where each layer experiences a van der Waals force between its interfaces. We analyse the different ways the system can exhibit interfacial instability when the liquid layers are sufficiently thin. For an excess of surfactant on one gas-liquid interface the coupling between the layers is relatively weak and the instability manifests as temporally separated rupture events in each layer. Conversely, in the absence of surfactant the coupling between the layers is much stronger and the instability manifests as rupture of both layers simultaneously. These features are consistent with recent experimental observations.

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Analysis of tear film rupture: effect of non-Newtonian rheology

Cited by 77 publications

References 58 publications

Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

Morphology changes in the evolution of liquid two-layer films

Stability of a bi-layer free film: simultaneous or individual rupture events?

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