A mathematical model is presented for surfactant-driven thin weakly viscoelastic film flows on a flat, impermeable plane. The Oldroyd-B constitutive relation is used to model the viscoelastic fluid. Lubrication theory and a perturbation expansion in powers of the Weissenberg number (We) are employed, which give rise to non-linear coupled evolution equations governing the transport of insoluble surfactant and thin liquid film thickness. Spreading on a Newtonian film is recovered to leading order and corrections to viscoelasticity are obtained at order We. These equations are solved numerically over a wide range of viscosity ratio (ratio of solvent viscosity to the sum of solvent and polymeric viscosities), pre-existing surfactant level and Peclet number (Pe). The effect of viscoelasticity on surfactant transport and fluid flow is investigated and the mechanisms underlying this effect are explored. Shear stress, streamwise normal stress and the temporal rate of change of extra shear stress generated from gradients in surfactant concentration dominate thin viscoelastic film flows whereas only shear stresses play a role in Newtonian thin film flows. Our results also reveal that, for weak viscoelasticity, the influence of viscosity ratio on the evolution of surfactant concentration and film thickness can be significant and varies considerably, depending on the concentration of pre-existing surfactant and surfactant surface diffusivity.

We investigate the rupture mechanism of a precorneal thin mucus coating sandwiched between the aqueous tear film and the corneal epithelial surface with a monolayer of surfactant overlying the aqueous layer. The Ostwald constitutive relation is employed to model mucus and a linear equation of state describing the relationship between surface tension and surfactant concentration is adopted. Three nonlinear coupled evolution equations governing the transport of surfactant, mucus, and total liquid layer thicknesses, based on lubrication theory and a perturbation expansion technique, have been derived. The resulting equations are solved numerically in order to explore the influence of the rheological properties of mucus, aqueous-mucus thickness ratio, aqueous-mucus interfacial tension, Marangoni number, and surfactant concentration on both the onset of instability and tear film evolution in the presence of van der Waals interactions, which could rupture the tear film. Our results reveal that the influence of rheological properties, aqueous–mucus thickness ratio, and interfacial tension on the time required for film rupture can be significant and varies considerably, depending on the magnitude of the Hamaker constants governing the strength of the van der Waals forces.

Both for tear films and along the airways within the lung, one has an extremely thin fluid layer overlying a biological substrate; in both cases surfactants either of natural origin, or artificially introduced, are important in driving fluid flows. There is evidence that slip can occur when hydrophilic liquids, similar to mucus or aqueous tear films, overlie hydrophobic epithelium. Utilizing results from recent experimental findings we examine the possible influence of slip upon tear film rupture, important in so-called dry eye, and upon surfactant-induced flows within the lung, used in surfactant replacement therapy.

The results of an experimental study on both pulsating and steady Newtonian fluid flow in an initially stretched rubber tube subjected to external vibration are reported. A circulating loop system was designed to maintain constant hydrostatic pressure throughout the tests so that the influence of external excitation on the fluid flow could be properly distinguished. The effects of fluid flow velocity and initial stretch rates on the dynamicrespon se and damping of the tube conveying fluid were examined, and it was observed that damping ratios increase with increasing flow velocities, and generally decrease with increasing initial stretch rates for the tube conveying fluid. It was also noted that dynamic responses increase with increasing initial stretch rates, and decrease with increasing flow velocities. The effect of external vibration on fluid flow rates is small in a tube with a thickness-to-radius ratio

A mathematical model is developed for lung injury treatments involving the delivery of therapeutic chemicals, such as drugs and gene vectors, into the lung using simultaneous tracheal instillation of exogenous pulmonary surfactant. The influence of exogenous surfactant dose, flow rate, bulk liquid viscosity, pulmonary absorption rate and chemical molecular diffusivity on the chemical delivery to the lung is investigated. Our results reveal that different pulmonary absorption rates lead to significantly different distribution patterns and change the time taken for the total amount of chemical to be absorbed along the airways. The various factors can also influence where the majority of the chemical is placed within the lung and this is relevant to the targeting of drugs to particular lung generations.