The effect of gravity on liquid plug propagation in a two-dimensional channel

The effect of plug propagation speed and gravity on the quasisteady motion of a liquid plug in a two-dimensional liquid-lined channel oriented at an angle αα with respect to gravity is studied. The problem is motivated by the transport of liquid plugs instilled into pulmonary airways in medical treatments such as surfactant replacement therapy, drug delivery, and liquid ventilation. The capillary number Ca is assumed to be small, while the Bond number Bo is arbitrary. Using matched asymptotic expansions and lubrication theory, expressions are obtained for the thickness of the trailing films left behind by the plug and the pressure drop across it as functions of Ca, Bo, αα and the thickness of the precursor films. When the Bond number is small it is found that the trailing film thickness and the flow contribution to the pressure drop scale as Ca2/3Ca2∕3 at leading order with coefficients that depend on Bo and αα. The first correction to the film thickness is found to occur at O(Ca)O(Ca) compared to O(Ca4/3)O(Ca4∕3) in the Bo = 0Bo=0 case. Asymmetry in the liquid distribution is quantified by calculating the ratio of liquid volumes above and below the centerline of the channel, VṘ. VR = 1VR=1 at Bo = 0Bo=0, indicating a symmetric distribution, and decreases with Bo and Ca, but increases with the plug length LpLp. The decrease of VRVR with Ca suggests that higher propagation speeds in small airways may result in less homogenous liquid distribution, which is in contrast to the expected effect in large airways. For given values of the other parameters, a maximum capillary number CacCac is identified above which the plug will eventually rupture. When the Bond number becomes equal to an orientation-dependent critical value BocBoc, it is found that the scaling of the film thickness and pressure drop change to Ca1/2Ca1∕2 and Ca1/6Ca1∕6, respectively. It is shown that this scaling is valid for small increments of the Bond number over its critical value, Bo = Boc+BCa1/6Bo=Boc+BCa1∕6, but for higher Bond numbers the asymptotic approach breaks down.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87914/2/031507_1.pd

The propagation of a surfactant laden liquid plug in a capillary tube

This paper considers the propagation of a liquid plug, forced by a driving pressure ΔP, within a rigid tube. The tube is already lined with a liquid precursor film of thickness 2.h̄2. Both the plug and the precursor film, as well as the interface, contain small amounts of surfactant whose concentrations are assumed to be near equilibrium. Since the motions are slow, we seek asymptotic solutions for small capillary number, Ca≪1,Ca≪1, and also assume that sorption kinetics control the surfactant flux to the interface compared to bulk diffusion. An additional asymptotic assumption is that the Stanton number, St, is sufficiently large such that β∝Ca1/3/St≪1,β∝Ca1/3/St≪1, which relates the importance of sorption kinetics to convection. The surfactant strength is measured by the surface elasticity, E = M/βE=M/β where M is the Marangoni number. The results of the analysis are that, for a given plug Ca, ΔP increases with increasing E but decreases with increasing 2.h̄2. The trailing film thickness, 1,h̄1, increases with ΔP, but at a slower rate when E is larger. For 1<2,h̄1<h̄2, criteria for plug rupture are established. This model is relevant to delivery of surfactants into the lung by direct instillation into the bronchial network as is done in surfactant replacement therapy and the use of surfactant solutions to carry other substances (e.g., genetic material) into the airways. © 2002 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69965/2/PHFLE6-14-2-471-1.pd

Liquid plug formation in an airway closure model

The closure of a human lung airway is modeled as an instability of a two-phase flow in a pipe coated internally with a Newtonian liquid. For a thick enough coating, the Plateau-Rayleigh instability creates a liquid plug which blocks the airway, halting distal gas exchange. Owing to a bifrontal plug growth, this airway closure flow induces high stress levels on the wall, which is the location of airway epithelial cells. A parametric numerical study is carried out simulating relevant conditions for human lungs, in either ordinary or pathological situations. Our simulations can represent the physical process from pre- to postcoalescence phases. Previous studies have been limited to precoalescence only. The topological change during coalescence induces a high level of stress and stress gradients on the epithelial cells, which are large enough to damage them, causing sublethal or lethal responses. We find that postcoalescence wall stresses can be in the range of 300% to 600% greater than precoalescence values and so introduce an important source of mechanical perturbation to the cells

Pulmonary Fluid Flow Challenges for Experimental and Mathematical Modeling

Modeling the flow of fluid in the lungs, even under baseline healthy conditions, presents many challenges. The complex rheology of the fluids, interaction between fluids and structures, and complicated multi-scale geometry all add to the complexity of the problem. We provide a brief overview of approaches used to model three aspects of pulmonary fluid and flow: the surfactant layer in the deep branches of the lung, the mucus layer in the upper airway branches, and closure/reopening of the airway. We discuss models of each aspect, the potential to capture biological and therapeutic information, and open questions worthy of further investigation. We hope to promote multi-disciplinary collaboration by providing insights into mathematical descriptions of fluid-mechanics in the lung and the kinds of predictions these models can make

Effects of elastoviscoplastic properties of mucus on airway closure in healthy and pathological conditions

Airway mucus is a complex material with both viscoelastic and viscoplastic properties that vary with healthy and pathological conditions of the lung. In this study, the effects of these conditions on airway closure are examined in a model problem, where an elastoviscoplastic (EVP) single liquid layer lines the inner wall of a rigid pipe and surrounds the air core. The EVP liquid layer is modelled using the Saramito-HB model. The parameters for the model are obtained for the mucus in healthy, asthma, chronic obstructive pulmonary disease (COPD), and cystic fibrosis (CF) conditions by fitting the rheological model to the experimental data. Then the liquid plug formation is studied by varying the Laplace number and undisturbed liquid film thickness. Airway closure is a surface-tension-driven phenomenon that occurs when the ratio of the pulmonary liquid layer thickness to the airway radius exceeds a certain threshold. In previous studies, it has been found that airway epithelial cells can be lethally or sublethally damaged due to the high peak of the wall stresses and stress gradients during the liquid plug formation. Here we demonstrate that these stresses are also related to the EVP features of the liquid layer. Yielded zones of the liquid layer are investigated for the different mucus conditions, and it is found that the liquid layer is in a chiefly unyielded state before the closure, which indicates that this phase is dominated by the elastic behavior and solvent viscosity. This is further confirmed by showing that the elastic coefficient is one of the most critical parameters determining whether the closure occurs. This parameter also largely affects the closure time. The wall stresses are also investigated for the pathological and healthy cases. Their peaks for COPD and CF are found to be the highest due to the viscoelastic extra stress contribution. Contrary to the Newtonian case, the wall stresses for COPD and CF do not smoothly relax after closure, as they rather remain effectively almost as high as the Newtonian peak. Moreover, the local normal wall stress gradients are smaller for the COPD and CF liquid layer due to their higher stiffness causing a smaller curvature at the capillary wave. The local tangential wall stress gradients are also shown to be smaller for these cases because of the slower accumulation of the liquid at the bulge

A viscoelastic deadly fluid in carnivorous pitcher plants

Background : The carnivorous plants of the genus Nepenthes, widely distributed in the Asian tropics, rely mostly on nutrients derived from arthropods trapped in their pitcher-shaped leaves and digested by their enzymatic fluid. The genus exhibits a great diversity of prey and pitcher forms and its mechanism of trapping has long intrigued scientists. The slippery inner surfaces of the pitchers, which can be waxy or highly wettable, have so far been considered as the key trapping devices. However, the occurrence of species lacking such epidermal specializations but still effective at trapping insects suggests the possible implication of other mechanisms. Methodology/Principal Findings : Using a combination of insect bioassays, high-speed video and rheological measurements, we show that the digestive fluid of Nepenthes rafflesiana is highly viscoelastic and that this physical property is crucial for the retention of insects in its traps. Trapping efficiency is shown to remain strong even when the fluid is highly diluted by water, as long as the elastic relaxation time of the fluid is higher than the typical time scale of insect movements. Conclusions/Significance : This finding challenges the common classification of Nepenthes pitchers as simple passive traps and is of great adaptive significance for these tropical plants, which are often submitted to high rainfalls and variations in fluid concentration. The viscoelastic trap constitutes a cryptic but potentially widespread adaptation of Nepenthes species and could be a homologous trait shared through common ancestry with the sundew (Drosera) flypaper plants. Such large production of a highly viscoelastic biopolymer fluid in permanent pools is nevertheless unique in the plant kingdom and suggests novel applications for pest control

Impact of resilience enhancing programs on youth surviving the Beslan school siege

The objective of this study was to evaluate a resilience-enhancing program for youth (mean age = 13.32 years) from Beslan, North Ossetia, in the Russian Federation. The program, offered in the summer of 2006, combined recreation, sport, and psychosocial rehabilitation activities for 94 participants, 46 of who were taken hostage in the 2004 school tragedy and experienced those events first hand. Self-reported resilience, as measured by the CD-RISC, was compared within subjects at the study baseline and at two follow-up assessments: immediately after the program and 6 months later. We also compared changes in resilience levels across groups that differed in their traumatic experiences. The results indicate a significant intra-participant mean increase in resilience at both follow-up assessments, and greater self-reported improvements in resilience processes for participants who experienced more trauma events