The formation of a liquid plug inside a human airway, known as airway closure, is computationally studied by considering the elastoviscoplastic (EVP) properties of the pulmonary mucus covering the airway walls for a range of liquid film thicknesses and Laplace numbers. The airway is modeled as a rigid tube lined with a single layer of an EVP liquid. The Saramito-Herschel-Bulkley (Saramito-HB) model is coupled with an Isotropic Kinematic Hardening model (Saramito-HB-IKH) to allow energy dissipation at low strain rates. The rheological model is fitted to the experimental data under healthy and cystic fibrosis (CF) conditions. Yielded/unyielded regions and stresses on the airway wall are examined throughout the closure process. Yielding is found to begin near the closure in the Saramito-HB model, whereas it occurs noticeably earlier in the Saramito-HB-IKH model. The kinematic hardening is seen to have a notable effect on the closure time, especially for the CF case, with the effect being more pronounced at low Laplace numbers and initial film thicknesses. Finally, standalone effects of rheological properties on wall stresses are examined considering their physiological values as baseline.

Gastric mucus is a polyelectrolyte gel that serves as the primary defense of the stomach lining against acid and digestive enzymes. Mucus is released from granules in specialized cells where it is stored at very high concentration. Experiments show that such a dense mucus gel may swell explosively within a short time period, and that this is accompanied by a massive transport of monovalent cations from the extracellular environment into the densely packed mucus in exchange for divalent calcium that had crosslinked the negatively-charged mucus fibers. We propose a 2D computational method for simulating mucus swelling with a two-fluid model. The model includes electro-diffusive transport of ionic species, the coupled motion of the glycoprotein network and hydrating fluid, and chemical interactions between the network and dissolved ions. Each ionic species in the solvent phase is subject to a Nernst-Planck type equation. Together with the electro-neutrality constraint, these equations constitute a system of non-linear parabolic PDEs subject to an algebraic constraint. The discretized system is solved by a Schur complement reduction scheme. Numerical results indicate that the method is very efficient, robust and accurate, even for problems which exhibit large spatial gradients in the concentration of ions. The new method is combined with our previously-published numerical methods for solving the coupled momentum equations of the solvent and network, extended to account for the chemical forces determined from the distribution of ions between solvent and network and in space. The computational effectiveness of the new methods is demonstrated through accuracy and efficiency metrics and through investigation of some of the factors that influence swelling dynamics.

The moving contact line of a thin fluid film can often corrugate into fingers, which is also known as a fingering instability. Although the fingering instability of Newtonian fluids has been studied extensively, there are few studies published on contact line fingering instability of non-Newtonian fluids. In particular, it is still unknown how shear-thinning rheological properties can affect the formation, growth, and shape of a contact line instability. Our previous study (Hu and Kieweg, 2012) showed a decreased capillary ridge formation for more shear-thinning fluids in a 2D model (i.e. 1D thin film spreading within the scope of lubrication theory). Those results motivated this study's hypothesis: more shear-thinning fluids should have suppressed finger growth and longer finger wavelength, and this should be evident in linear stability analysis (LSA) and 3D (i.e. 2D spreading) numerical simulations. In this study, we developed a LSA model for the gravity-driven flow of shear-thinning films, and carried out a parametric study to investigate the impact of shear-thinning on the growth rate of the emerging fingering pattern. A fully 3D model was also developed to compare and verify the LSA results using single perturbations, and to explore the result of multiple-mode, randomly imposed perturbations. Both the LSA and 3D numerical results confirmed that the contact line fingers grow faster for Newtonian fluids than the shear-thinning fluids on both vertical and inclined planes. In addition, both the LSA and 3D model indicated that the Newtonian fluids form fingers with shorter wavelengths than the shear-thinning fluids when the plane is inclined; no difference in the most unstable (i.e. emerging) wavelength was observed at vertical. This study also showed that the distance between emerging fingers was smaller on a vertical plane than on a less-inclined plane for shear-thinning fluids, as previously shown for Newtonian fluids. For the first time for shear-thinning fluids, these results connect trends in capillary ridge and contact line finger formation in 2D models, LSA, and 3D simulations. The results can provide us insights on how to optimize non-Newtonian fluid properties to minimize a fingering instability in many industrial and biological applications.

The thin film lubrication approximation has been studied extensively for moving contact lines of Newtonian fluids. However, many industrial and biological applications of the thin film equation involve shear-thinning fluids, which often also exhibit a Newtonian plateau at low shear. This study presents new numerical simulations of the three-dimensional (i.e. two-dimensional spreading), constant-volume, gravity-driven, free surface flow of an Ellis fluid. The numerical solution was validated with a new similarity solution, compared to previous experiments, and then used in a parametric study. The parametric study centered around rheological data for an example biological application of thin film flow: topical drug delivery of anti-HIV microbicide formulations, e.g. hydroxyethylcellulose (HEC) polymer solutions. The parametric study evaluated how spreading length and front velocity saturation depend on Ellis parameters. A lower concentration polymer solution with smaller zero shear viscosity (), , and values spread further. However, when comparing two fluids with any possible combinations of Ellis parameters, the impact of changing one parameter on spreading length depends on the direction and magnitude of changes in the other two parameters. In addition, the isolated effect of the shear-thinning parameter, , on the front velocity saturation depended on . This study highlighted the relative effects of the individual Ellis parameters, and showed that the shear rates in this flow were in both the shear-thinning and plateau regions of rheological behavior, emphasizing the importance of characterizing the full range of shear-rates in rheological measurements. The validated numerical model and parametric study provides a useful tool for future steps to optimize flow of a fluid with rheological behavior well-described by the Ellis constitutive model, in a range of industrial and biological applications.

Drug delivery of topical microbicidal molecules against HIV offers promise as a modality to prevent sexual transmission of the virus. Success of any microbicide product depends, in an interactive way, upon its drug (the microbicide active pharmaceutical ingredient, API) and its delivery system (e.g. a gel, film or intravaginal ring). There is a widespread agreement that more effective drug delivery vehicles, as well as better APIs, must be developed to improve the efficacy of microbicide products. Non-Newtonian gels are primary microbicide vehicles, but those to date have been created with limited understanding of how their properties govern their spreading and retention in the vagina, which, in turn, govern successful drug delivery. Here, we apply fundamental fluid mechanical and physicochemical transport theory to help better understand how successful microbicide API delivery depends upon properties of a gel and the vaginal environment. We address several critical components of this complex process, including: elastohydrodynamic flow of the bolus of a non-Newtonian fluid; and mass transfer due to inhomogeneous dilution of the gel by vaginal fluid contacting it along a moving boundary (the locally deforming vaginal epithelial surface). Local dilution of gel alters local rheological properties. We evaluated this experimentally, delin-eating the way that constitutive parameters of a shear-thinning gel are modified by dilution. We supplement the Reynolds lubrication equation with a mass conservation equation to model diluting fluid movement across the moving vaginal epithelial surface and into the gel bolus. This is a physicochemically complex phenomenon that is not well understood. We implement a boundary flux model based upon the elevated hydrodynamic pressures in the cells. Results show that this model produces fluxes that lie within the range of mean values that have been reported. Further experimental characterization of the vaginal wall is required for a more precise set of parameters and a more sophisticated theoretical treatment of epithelium.

A recent study in South Africa has confirmed, for the first time, that a vaginal gel formulation of the antiretroviral drug Tenofovir, when applied topically, significantly inhibits sexual HIV transmission to women [10]. However the gel for this drug, and anti-HIV microbicide gels in general, have not been designed using full understanding of how gel spreading and retention in the vagina govern successful drug delivery. Elastohydrodynamic lubrication theory can be applied to model such spreading of microbicide gels, which are inherently non-Newtonian [13,15]. A yield stress is emerging as one of the important properties of microbicide gel vehicle deployment, as this may improve retention within the vaginal canal. On the other hand, a yield stress may decrease the initial extent of the coating flow. Here, we first explain a certain yield stress paradox observed generally in many lubrication flows. Four conditions are determined, via scaling analysis, which mitigate the inconsistency in the use of lubrication theory to analyze the specific problem of elastic wall squeezing flow of yield stress fluid. Parameters characterizing these conditions are obtained experimentally for a test gel. Using them, it is shown that the lubrication approximation may be applied to the elastic wall-squeezing problem for this gel.

The classical oscillatory shear wave model of Ferry et al. [J. Polym. Sci. 2:593-611, (1947)] is extended for active linear and nonlinear microrheology. In the Ferry protocol, oscillation and attenuation lengths of the shear wave measured from strobe photographs determine storage and loss moduli at each frequency of plate oscillation. The microliter volumes typical in biology require modifications of experimental method and theory. Microbead tracking replaces strobe photographs. Reflection from the top boundary yields counterpropagating modes which are modeled here for linear and nonlinear viscoelastic constitutive laws. Furthermore, bulk imposed strain is easily controlled, and we explore the onset of normal stress generation and shear thinning using nonlinear viscoelastic models. For this paper, we present the theory, exact linear and nonlinear solutions where possible, and simulation tools more generally. We then illustrate errors in inverse characterization by application of the Ferry formulas, due to both suppression of wave reflection and nonlinearity, even if there were no experimental error. This shear wave method presents an active and nonlinear analog of the two-point microrheology of Crocker et al. [Phys. Rev. Lett. 85: 888 - 891 (2000)]. Nonlocal (spatially extended) deformations and stresses are propagated through a small volume sample, on wavelengths long relative to bead size. The setup is ideal for exploration of nonlinear threshold behavior.