The effect of viscoelasticity on the stability of a pulmonary airway liquid layer

Abstract

The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer, which may cause the lung's airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid, which is modeled using the Oldroyd-B constitutive equation or as a Jeffreys fluid. To examine the role of mucus alone, a single layer of a viscoelastic fluid is considered. A system of nonlinear evolution equations is derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate g for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Closure occurs if the minimum core radius, R min ͑t͒, reaches zero within one breath. Solutions of the nonlinear evolution equations reveal that R min normally decreases to zero faster with increasing relaxation time parameter, the Weissenberg number We. For small values of the dimensionless film thickness parameter , the closure time, t c , increases slightly with We, while for moderate values of , ranging from 14% to 18% of the tube radius, t c decreases rapidly with We provided the solvent viscosity is sufficiently small. Viscoelasticity was found to have little effect for Ͼ0.18, indicating the strong influence of surface tension. The film thickness parameter and the Weissenberg number We also have a significant effect on the maximum shear stress on tube wall, max͑ w ͒, and thus, potentially, an impact on cell damage. Max͑ w ͒ increases with for fixed We, and it decreases with increasing We for small We provided the solvent viscosity parameter is sufficiently small. For large Ϸ 0.2, there is no significant difference between the Newtonian flow case and the large We cases.

Numerical study of flow fields in an airway closure model

“…Figure 4 shows comparisons of the dimensionless histories of the maximum interfacial velocity and R min (the minimum distance between the interface and the centreline) between the lubrication theory model (Halpern, Fujioka & Grotberg 2010) and the SIM with L = 9.0, ε = 0.2 and Re = 1.0. Results shown in figure 4 demonstrate good agreement between both approaches until t = 18, and an increasing deviation occurs between them after t = 18.…”

Role of Airway Recruitment and Derecruitment in Lung Injury

“…Finally, Grotberg and colleagues have developed several models to account for liquid plug formation, motion, and rupture. 98–101 Although these biophysical models have significantly advanced our understanding of the fluid mechanics of airway recruitment/derecruitment, they do not directly simulate cellular deformation during reopening, and can therefore only infer potential injury mechanisms. Since the injury response of epithelial cells is clearly related to the amount of deformation, our laboratory has developed several unique and sophisticated models of cellular deformation during airway reopening that account for complex morphological, biomechanical, and fluid-structure interactions.…”

Liquid plug formation in an airway closure model

“…The Marangoni stresses induced by uneven distribution of interfacial surfactant concentration oppose the closure ow. Halpern et al [20], using lubrication theory, showed that viscoelasticity does not strongly aect the critical lm thickness h c /a, and for h c /a < 0.119 airway closure does not occur within a breathing cycle. On the other hand, if 14% ≤ h/a ≤ 18%, increasing the Weissenberg number speeds up the growth rate when the viscoelastic uid exhibits a shear-thinning behavior.…”