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The fundamental study of blood flow past a circular cylinder filled with an oxygen source is investigated as a building block for an artificial lung. The Casson constitutive equation is used to describe the shear-thinning and yield stress properties of blood. The presence of hemoglobin is also considered. Far from the cylinder, a pulsatile blood flow in the x direction is prescribed, represented by a time periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest for the characterization of the flow and transport are the steady Reynolds number (Re), Womersley parameter (alpha), pulsation amplitude (A), and the Schmidt number (Sc). The Hill equation is used to describe the saturation curve of hemoglobin with oxygen. Two different feed-gas mixtures were considered: pure O(2) and air. The flow and concentration fields were computed for Re=5, 10, and 40, 0< or =A< or =0.75, alpha=0.25, 0.4, and Schmidt number, Sc=1000. The Casson fluid properties result in reduced recirculations (when present) downstream of the cylinder as compared to a Newtonian fluid. These vortices oscillate in size and strength as A and alpha are varied. Hemoglobin enhances mass transport and is especially important for an air feed which is dominated by oxyhemoglobin dispersion near the cylinder. For a pure O(2) feed, oxygen transport in the plasma dominates near the cylinder. Maximum oxygen transport is achieved by operating near steady flow (small A) for both feed-gas mixtures. The time averaged Sherwood number, Sh, is found to be largely influenced by the steady Reynolds number, increasing as Re increases and decreasing with A. Little change is observed with varying alpha for the ranges investigated. The effect of pulsatility on Sh is greater at larger Re. Increasing Re aids transport, but yields a higher cylinder drag force and shear stresses on the cylinder surface which are potentially undesirable.

Fluid dynamics of mucus plug rupture is important to understand mucus clearance in lung airways and potential effects of mucus plug rupture on epithelial cells at lung airway walls. We established a microfluidic model to study mucus plug rupture in a collapsed airway of the 12th generation. Mucus plugs were simulated using Carbopol 940 (C940) gels at concentrations of 0.15%, 0.2%, 0.25%, and 0.3%, which have non-Newtonian properties close to healthy and diseased lung mucus. The airway was modeled with a polydimethylsiloxane microfluidic channel. Plug motion was driven by pressurized air. Global strain rates and shear stress were defined to quantitatively describe plug deformation and rupture. Results show that a plug needs to overcome yield stress before deformation and rupture. The plug takes relatively long time to yield at the high Bingham number. Plug length shortening is the more significant deformation than shearing at gel concentration higher than 0.15%. Although strain rates increase dramatically at rupture, the transient shear stress drops due to the shear-thinning effect of the C940 gels. Dimensionless time-averaged shear stress, T xy , linearly increases from 3.7 to 5.6 times the Bingham number as the Bingham number varies from 0.018 to 0.1. The dimensionless time-averaged shear rate simply equals to T xy /2. In dimension, shear stress magnitude is about one order lower than the pressure drop, and one order higher than yield stress. Mucus with high yield stress leads to high shear stress, and therefore would be more likely to cause epithelial cell damage. Crackling sounds produced with plug rupture might be more detectable for gels with higher concentration.

The pulsatile flow and gas transport of a Newtonian passive fluid across an array of cylindrical microfibers are numerically investigated. It is related to an implantable, artificial lung where the blood flow is driven by the right heart. The fibers are modeled as either squared or staggered arrays. The pulsatile flow inputs considered in this study are a steady flow with a sinusoidal perturbation and a cardiac flow. The aims of this study are twofold: identifying favorable array geometry/spacing and system conditions that enhance gas transport; and providing pressure drop data that indicate the degree of flow resistance or the demand on the right heart in driving the flow through the fiber bundle. The results show that pulsatile flow improves the gas transfer to the fluid compared to steady flow. The degree of enhancement is found to be significant when the oscillation frequency is large, when the void fraction of the fiber bundle is decreased, and when the Reynolds number is increased; the use of a cardiac flow input can also improve gas transfer. In terms of array geometry, the staggered array gives both a better gas transfer per fiber (for relatively large void fraction) and a smaller pressure drop (for all cases). For most cases shown, an increase in gas transfer is accompanied by a higher pressure drop required to power the flow through the device.

Flow limitation during pressure-driven expiration in liquid-filled lungs was examined in intact, euthanized New Zealand white rabbits. The aim of this study was to further characterize expiratory flow limitation during gravitational drainage of perfluorocarbon liquids from the lungs, and to study the effect of perfluorocarbon type and negative mouth pressure on this phenomenon. Four different perfluorocarbons (PP4, perfluorodecalin, perfluoro-octyl-bromide, and FC-77) were used to examine the effects of density and kinematic viscosity on volume recovered and maximum expiratory flow. It was demonstrated that flow limitation occurs during gravitational drainage when the airway pressure is < or = -15 cm H(2)O, and that this critical value of pressure did not depend on mouth pressure or perfluorocarbon type. The perfluorocarbon properties affect the volume recovered, maximum expiratory flow, and the time to drain, with the most viscous perfluorocarbon (perfluorodecalin) taking the longest time to drain and resulting in lowest maximum expiratory flow. Perfluoro-octyl-bromide resulted in the highest recovered volume. The findings of this study are relevant to the selection of perfluorocarbons to reduce the occurrence of flow limitation and provide adequate minute ventilation during total liquid ventilation.

Many medical therapies require liquid plugs to be instilled into and delivered throughout the pulmonary airways. Improving these treatments requires a better understanding of how liquid distributes throughout these airways. In this study, gravitational and surface mechanisms determining the distribution of instilled liquids are examined experimentally using a bench-top model of a symmetrically bifurcating airway. A liquid plug was instilled into the parent tube and driven through the bifurcation by a syringe pump. The effect of gravity was adjusted by changing the roll angle (phi) and pitch angle (gamma) of the bifurcation (phi = gamma =0 deg was isogravitational). Phi determines the relative gravitational orientation of the two daughter tubes: when phi not equal to 0 deg, one daughter tube was lower (gravitationally favored) compared to the other. Gamma determines the component of gravity acting along the axial direction of the parent tube: when gamma not equal to 0 deg, a nonzero component of gravity acts along the axial direction of the parent tube. A splitting ratio Rs, is defined as the ratio of the liquid volume in the upper daughter to the lower just after plug splitting. We measured the splitting ratio, Rs, as a function of: the parent-tube capillary number (Cap); the Bond number (Bo); phi; gamma; and the presence of pre-existing plugs initially blocking either daughter tube. A critical capillary number (Cac) was found to exist below which no liquid entered the upper daughter (Rs = 0), and above which Rs increased and leveled off with Cap. Cac increased while Rs decreased with increasing phi, gamma, and Bo for blocked and unblocked cases at a given Cap > Ca,. Compared to the nonblockage cases, Rs decreased (increased) at a given Cap while Cac increased (decreased) with an upper (lower) liquid blockage. More liquid entered the unblocked daughter with a blockage in one daughter tube, and this effect was larger with larger gravity effect. A simple theoretical model that predicts Rs and Cac is in qualitative agreement with the experiments over a wide range of parameters.

Changes in the cerebral blood flow (CBF) baseline produce significant changes to the hemodynamic response. This work shows that increases in the baseline blood flow level produce blood oxygenation-level dependent (BOLD) and blood flow responses that are slower and lower in amplitude, while decreases in the baseline blood flow level produce faster and higher amplitude hemodynamic responses. This effect was characterized using a vascular model of the hemodynamic response that separated arterial blood flow response from the venous blood volume response and linked the input stimulus to the vascular response. The model predicted the baseline blood flow level effects to be dominated by changes in the arterial vasculature. Specifically, it predicted changes in the arterial blood flow time constant and venous blood volume time constant parameters of +294% and −24%, respectively, for a 27% increase in the baseline blood flow. The vascular model performance was compared to an empirical model of the hemodynamic response. The vascular and empirical hemodynamic models captured most of the baseline blood flow level effects observed and can be used to correct for these effects in fMRI data. While the empirical hemodynamic model is easy to implement, it did not incorporate any explicit physiological information.

In partial liquid ventilation (PLV), perfluorocarbon (PFC) acts as a diffusion barrier to gas transport in the alveolar space since the diffusivities of oxygen and carbon dioxide in this medium are four orders of magnitude lower than in air. Therefore convection in the PFC layer resulting from the oscillatory motions of the alveolar sac during ventilation can significantly affect gas transport. For example, a typical value of the Peclet number in air ventilation is Pe approximately 0.01, whereas in PLV it is Pe approximately 20. To study the importance of convection, a single terminal alveolar sac is modeled as an oscillating spherical shell with gas, PFC, tissue and capillary blood compartments. Differential equations describing mass conservation within each compartment are derived and solved to obtain time periodic partial pressures. Significant partial pressure gradients in the PFC layer and partial pressure differences between the capillary and gas compartments (P(C)-Pg) are found to exist. Because Pe>> 1, temporal phase differences are found to exist between P(C)-Pg and the ventilatory cycle that cannot be adequately described by existing non-convective models of gas exchange in PLV The mass transfer rate is nearly constant throughout the breath when Pe>>1, but when Pe<

Expiratory flow limitation occurs during total liquid ventilation (TLV), and is characterized by the sudden development of excessively negative intratracheal pressures without increases in flow. The purpose of this study was to identify a dynamic signal for the servoregulation of expiratory flow (Ve), by determining the range of dynamic intratracheal pressures [P(T)], which mark the onset of flow limitation during liquid expiration, where choke occurs at the critical pressure (Pc). The lungs of rabbits were filled with perflurocarbon to an end-inspiratory lung volume (EILV) of 20, 30, or 40cc/kg and connected to a piston driven liquid ventilator, which removed perfluorocarbon at a rate (Vs) of 2.5, 5.0, or 7.5 ml/s. Nine animals per EILV group were used (27 animals total), and within each EILV group each (Vs) was used three times. P(T) and (Ve) (T) were measured at the tracheostomy tube, and dP/dT was calculated from P(T). Pc was determined within each EILV/(Vs) group by examining the average dP/dT curve for the first significant change from baseline. Pc ranged from -6.02 +/- 1.83 to -9.02 +/- 3.2 mm Hg. In general, the higher the EILV, the more negative the Pc. We conclude that Pc during TLV varies within a limited range in rabbits. These data may be used to maximize expired volume during TLV by sequentially tapering flow rates as this critical range of pressures is approached.

This paper analyzes the effect of surfactant on the linear stability of an annular film in a capillary undergoing a time-periodic pressure gradient force. The annular film is thin compared to the radius of the tube. An asymptotic analysis yields a coupled set of equations with time-periodic coefficients for the perturbed fluid-fluid interface and the interfacial surfactant concentration. Wei and Rumschitzki (submitted for publication) previously showed that the interaction between a surfactant and a steady base flow could induce a more severe instability than a stationary base state. The present work demonstrates that time-periodic base flows can modify the features of the steady-flow-based instability, depending on surface tension, surfactant activity, and oscillatory frequency. For an oscillatory base flow (with zero mean), the growth rate decreases monotonically as the frequency increases. In the low-frequency limit, the growth rate approaches a maximum corresponding to the growth rate of a steady base flow having the same amplitude. In the high-frequency limit, the growth rate reaches a minimum corresponding to the growth rate in the limit of a stationary base state. The underlying mechanisms are explained in detail, and extension to other time-periodic forms is further exploited.

The flow rate of a liquid drainage from the lungs is limited because of the elastic nature of the airways. This study was designed to clarify the relationship between intrapulmonary liquid volume and the development of the flow limitation or choked flow phenomenon as a function of expiratory flow rate during total liquid ventilation with perflubron.Prospective animal study.University research laboratory.Rabbits with a weight of 3.2 +/- 0.3 kg.After the rabbits were killed, the lungs were filled to functional residual capacity with perflubron, followed by administration of an additional volume of 30, 45, or 60 mL of perflubron (initial volume = functional residual capacity + additional volume).In one set of five animals, the intratracheal pressure at the occurrence of choked flow was established at -20 mm Hg. In another set of six animals, we demonstrated that the volume remaining in the lung at the point of development of choked flow (Vch) was stable for the first 40 mins after the animals were killed. Flow rates of 1.25, 2.5, 3.75, 5.0, 7.5, 10.0, and 12.5 mL/sec were then applied at an additional volume of 30, 45, or 60 mL to 34 animals. Vch approximately doubled as the flow rate increased from 1.25 mL/sec to 12.5 mL/sec (p.001). At the same flow, Vch was higher for an additional volume of 60 mL than 30 mL when the flow wasor =2.5 mL/sec.From these data, we conclude that choked flow occurs at intratracheal pressure of less than -20 mm Hg, that Vch is stable for the first 40 mins after the animals are killed, and that Vch is a function of flow rate and initial volume.

Reports experimental studies on air-liquid two-phase stratified flows in polymeric microfluidic channels for volume-efficient and cost-effective flow cytometry. Different flow behaviors of liquid core streams sheathed by air flows were investigated by varying surface chemistry and geometry of poly(dimethylsiloxane) (PDMS) channels. Fluorescent beads and myoblast cells carried by stable liquid flows were analyzed by a digital photo-multiplier tube (PMT)-based optical detection system to analyze the number of particles in a sample.

Presents an experimental investigation of the stability phenomena of an air-liquid two-phase microfluidic system in air-sheath-driven flow cytometry. High-speed thin liquid jets interacting with air-sheath flows and polymeric microfluidic channel walls show different flow behaviors in response to channel geometry, surface chemistry, and flow rates of liquid and air. We studied the variation of flow structure and stability of liquid jets in hydrophobic channels having different thickness to identify the effect of device geometry on microscale air-liquid two-phase flows.

Describes a new type of gravity-driven polymeric microfluidic cell sorter developed for low-power, low-cost, and rapid cell separation. The device takes advantage of size-based differential migration of cells/particles in flows where widening of flow streamlines amplifies the separation between sample particles. We studied the migration and separation of polystyrene microbeads, red blood cells, and perfluorocarbon droplets used for ultrasound imaging and therapy having different sizes in the novel cell sorter. Compared to other conventional cell separation systems, microHYCS reduces power and cost requirements, and is advantageous for the development of easy-to-use sample separation and diagnostics tools.

Using the biphasic theory of Biot (1941), we examine the evolution of deformations of a poroelastic layer, secured at its base to a rigid plane and having a stress-free, impermeable upper surface. By identifying a limit in which the layer is very thin but the wavelength of disturbances is very long, we show how nonlinear effects due to the finite slope of the free surface cause local elevations of the free surface to decay more slowly than depressions.

A finite-length liquid plug may be present in an airway due to disease, airway closure, or by direct instillation for medical therapy. Air forced by ventilation propagates the plug through the airways, where it deposits fluid onto the airway walls. The plug may encounter single or bifurcating airways, an airway surface liquid, and other liquid plugs in nearby airways. In order to understand how these flow situations influence plug transport, benchtop experiments are performed for liquid plug flow in: Case (i) straight dry tubes, Case (ii) straight pre-wetted tubes, Case (iii) bifurcating dry tubes, and Case (iv) bifurcating tubes with a liquid blockage in one daughter. Data are obtained for the trailing film thickness and plug splitting ratio as a function of capillary number and plug volumes. For Case (i), the finite length plug in a dry tube has similar behavior to a semi-infinite plug. For Case (ii), the trailing film thickness is dependent upon the plug capillary number (Ca) and not the precursor film thickness, although the shortening or lengthening of the liquid plug is influenced by the precursor film. For Case (iii), the plug splits evenly between the two daughters and the deposited film thickness depends on the local plug Ca, except for a small discrepancy that may be due to an entrance effect or from curvature of the tubes. For Case (iv), a plug passing from the parent to daughters will deliver more liquid to the unblocked daughter (nearly double, consistently) and then the plug will then travel at greater Ca in the unblocked daughter as the blocked. The flow asymmetry is enhanced for a larger blockage volume and diminished for a larger parent plug volume and parent-Ca.

Both theoretical and experimental studies of pleural fluid dynamics and lung buoyancy during steady-state, apneic conditions are presented. The theory shows that steady-state, top-to-bottom pleural-liquid flow creates a pressure distribution that opposes lung buoyancy. These two forces may balance, permitting dynamic lung floating, but when they do not, pleural–pleural contact is required. The animal experiments examine pleural-liquid pressure distributions in response to simulated reduced gravity, achieved by lung inflation with perfluorocarbon liquid as compared to air. The resulting decrease in lung buoyancy modifies the force balance in the pleural fluid, which is reflected in its vertical pressure gradient. The data and model show that the decrease in buoyancy with perfluorocarbon inflation causes the vertical pressure gradient to approach hydrostatic. In the microgravity analogue, the pleural pressures would be toward a more uniform distribution, consistent with ventilation studies during space flight. The pleural liquid turnover predicted by the model is computed and found to be comparable to experimental values from the literature. The model provides the flow field, which can be used to develop a full transport theory for molecular and cellular constituents that are found in pleural fluid.

This paper reports on the design and initial experimental investigation of a disposable air-liquid two-phase microfluidic system for use in microscale flow cytometry (µFC). Air sheath flow is advantageous in developing miniaturized and integrated flow cytometers because it reduces volume and power requirements. Air-liquid two-phase stratified flow was achieved by a combination of suction (vacuum pump) and injection (syringe pump) in a thin polymeric microfluidic channel. A photo-multiplier tube (PMT)-based detection system mounted on an inverted epi-fluorescence microscope was used to demonstrate counting of the number of fluorescent particles passing through the observation channel.

A simplified model of alveolar liquid lining dynamics is developed using a stretchable two-dimensional slot and an insoluble surfactant. Using lubrication theory, a coupled set of evolution equations is derived that describes the film height and interfacial surfactant distribution during the oscillation cycle. This system is solved asymptotically in the limit of small stretching amplitudes. The unsteady flow field is characterized by vortices at the end positions of the oscillation cycle. The cycle-averaged flow field also contains vortical structures, whose number and size vary over parameter space. For large molecular species, like proteins and surfactants, the bulk Peclet numbers can be large, indicating the importance of this liquid layer in the transport process. This may have an impact on the effectiveness and optimization of several medical treatment modalities. Also, since the liquid lining covers many cells within an alveolus, the predicted flow/transport patterns can allow a communication pathway among cells of the same alveolus.

The airways of the lungs are coated with a thin viscous film. Often, especially in disease, the liquid film can form a plug that obstructs airflow. The formation of the liquid plug is due to capillary driven instabilities that can arise in the lining, causing the lining to close up [1–4]. Airflow can also be obstructed if the airway wall collapses. This occurs when the elastic forces of the tube are not large enough to sustain the negative fluid pressures inside the tube. The phenomenon of airway closure occurs in many normal and pathological situations. It can occur in premature neonates who do not produce enough surfactant to keep the surface-tension sufficiently low. A clinical treatment is to deliver exogenous surfactant to these neonates in the form of a liquid bolus. In order to facilitate breathing they are also placed on mechanical ventilators. The amplitude (tidal volume) and frequency settings are two key parameters at the disposal of clinicians. Frequencies may range from normal breathing to high frequency ventilation at 5 Hz or more [6–7]. Airway obstruction and hypercapnea (build up of carbon dioxide in the lungs) are two examples of the manifestation of chronic obstructive pulmonary disease that may also occur in adults. In order to reduce breathlessness in patients with obstructive airway disease, chest wall vibrators are placed around the patients rib cage, which oscillate at frequencies up to 100 Hz [8]. Airway closure is also an issue in the microgravity environment of outer space since there is marked decrease in ventilatory inhomogeneity. It has been shown using the single nitrogen breath washout test that even though closing volumes are not affected by microgravity, there is considerable variability [9]. Their investigations suggest that some airways may close above residual volume, and that other factors besides gravity, such as the mechanical properties of the airway walls, are important factors on whether airway closure occurs.

The mesothelial cells that form the visceral pleura of the lung are subjected to physical forces such as stretch due to lung expansion and fluid shear stress due to the sliding motion of the lung against the chest wall. In this study, the effect of mechanical forces on the production of growth factors by mesothelial cells was investigated. Rat visceral pleura mesothelial (RVPM) cells were exposed to fluid shear stress by perfusing a column of cell-covered beads. RVPM cells grown on a silicone elastomer were subjected to cyclic strain by applying an oscillating vacuum to the bottom of the wells using the Flexercell apparatus. Fluid shear stress (5.2-15.7 dyn/cm2) stimulated the release of endothelin-1 (ET-1) by RVPM cells two- to fivefold over static cells. ET-1 secretion by RVPM cells was also stimulated approximately twofold by cyclic stretch (20% maximum strain, 30 cycles/min). RVPM cells released significant levels of platelet-derived growth factor (PDGF), but there was no effect of either shear stress or cyclic strain on PDGF release. These results suggest that the production of growth factors by pleural mesothelial cells is regulated in part by physical forces.

The sliding motion of the lung against the chest wall creates a shear stress in the pleural space, which can be as high as 60 dyn/cm2, depending on the respiration rate. Such shear stresses may affect the mesothelial cells that line the pleural space on the lung (visceral pleura) and chest wall (parietal pleura). When exposed to shear stress (17 dyn/cm2) in a parallel-plate flow chamber for 22 h, rat visceral pleura mesothelial cells were not altered morphologically and did not align in the direction of flow, in contrast to the shape changes observed for bovine aortic endothelial cells. By using mesothelial cells cultured on porous microcarrier beads, we measured the permeability of the cells at different flows in a cell-column chromatography assay. The permeabilities to sodium fluorescein and cyanocobalamin increased from 8.2 +/- 1.0 and 7.8 +/- 0.7 x 10(-5) cm/s to 22.5 +/- 1.2 and 21.8 +/- 3.0 x 10(-5) cm/s, respectively, when the flow was increased from 0.9 to 3.5 ml/min (corresponding to average shear stresses of 4.7-18.4 dyn/cm2). The permeabilities returned to baseline values when the flow was reduced. Cytochalasin D stimulated an increase in permeability that was not augmented by a subsequent increase in shear stress. These results suggest that the barrier function of mesothelial cells is responsive to changes in fluid shear stress.

OBJECTIVE: To survey the current state of scientific knowledge of gas flow and mixing in pulmonary airways, especially at high frequencies. DATA SOURCES: Results from the authors' own laboratory studies and Western bioengineering literature on respiratory fluid mechanics. STUDY SELECTION: This survey concentrates on understanding the principal physical mechanisms that underlie the enhancement of airway gas transport in high-frequency oscillation. The results of experimental, computational, and mathematical studies are described. DATA SYNTHESIS: The topic was covered by seven presenters at the Munster Meeting on High Frequency Ventilation, January 31 to February 2, 1993. Six of these presentations are summarized in the six sections of this paper under the following headings: Introductory Survey; Three-Dimensional Numerical Simulation of Inspiratory and Expiratory Flows in Small Airways; Computational and Experimental Models of High-Frequency Oscillation; Unsteady Gas Mixing in Airways; Gas Dispersion From the Lagrangian Viewpoint; and Soluble Gas Mass Transfer in Tubes and Airways. CONCLUSIONS: The dominant mechanism for the enhancement of gas transport along airways at high frequency is likely to lie in the coupling of the secondary motions caused by airway curvature with the oscillatory longitudinal flow. However, laboratory experiments and theoretical analyses have led only to an accurate simulation of the phenomena in idealized geometries, not in real lungs.

This article covers several aspects of respiratory fluid mechanics that have been actively investigated by our group over the years. For the most part, the topics involve two-phase flows in the respiratory system with applications to normal and diseased lungs, as well as therapeutic interventions. Specifically, the topics include liquid plug flow in airways and at airway bifurcations as it relates to surfactant, drug, gene, or stem cell delivery into the lung; liquid plug rupture and its damaging effects on underlying airway epithelial cells as well as a source of crackling sounds in the lung; airway closure from "capillary-elastic instabilities," as well as nonlinear stabilization from oscillatory core flow which we call the "oscillating butter knife;" liquid film, and surfactant dynamics in an oscillating alveolus and the steady streaming, and surfactant spreading on thin viscous films including our discovery of the Grotberg-Borgas-Gaver shock.

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)(t), 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 epsilon, the closure time, t(c), increases slightly with We, while for moderate values of epsilon, 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 epsilon0.18, indicating the strong influence of surface tension. The film thickness parameter epsilon and the Weissenberg number We also have a significant effect on the maximum shear stress on tube wall, max(tau(w)), and thus, potentially, an impact on cell damage. Max(tau(w)) increases with epsilon for fixed We, and it decreases with increasing We for small We provided the solvent viscosity parameter is sufficiently small. For large epsilon approximately 0.2, there is no significant difference between the Newtonian flow case and the large We cases.

Respiratory insufficiency patients who need only partial ventilatory support are, nevertheless, intubated and connected to a respirator. In search of a partial respiratory assistance method we evaluated the gas exchange, mechanisms, and hemodynamic effects of intratracheal insufflation (ITI) via a narrow (0.2-cm) catheter. The effects of flow rate (0.05-0.2 liter/min per kg), catheter tip position (carina, bronchus, and trachea), and superimposed chest vibration at 22 Hz were studied in seven anesthetized and partially paralyzed dogs. ITI in the carina induced CO2 removal (VCO2) of 48 +/- 16 ml/min in the periods between breaths, which was 39% of the control VCO2. CO2 removal rates between breaths with ITI in a bronchus and in the trachea were 63 and 28% of control, respectively (P < 0.05). ITI at 0.15-0.2 liter/min per kg augmented total VCO2 by > 50% over control (P < 0.05) and decreased PaCO2 by 10% (P < 0.05) despite a 28% fall in VE and 32% lower work of breathing (P < 0.05). Adding vibration to ITI at 0.15 liter/min per kg induced VCO2 of 162 +/- 34 ml/min, which was significantly greater than control, while PaCO2 fell from 69 +/- 24 to 47 +/- 6 mmHg (P < 0.05), despite complete cessation of spontaneous breathing. ITI with or without vibration did not cause any hemodynamic changes, except for a fall in the shunt fraction from 14.6 +/- 9.9% to 5.8 +/- 2.8% with vibration. Thus, ITI at low flow rates can support respiration with no hemodynamic side effects. Adding chest vibration further enhances gas exchange and can provide total ventilation.

The influence of time-dependent flows on oxygen and carbon dioxide transport for blood flow past fiber arrays arranged in in-line and staggered configurations was computationally investigated as a model for an artificial lung. Both a pulsatile flow, which mimics the flow leaving the right heart and passing through a compliance chamber before entering the artificial lung, and a right ventricular flow, which mimics flow leaving the right heart and directly entering the artificial lung, were considered in addition to a steady flow. The pulsatile flow was modeled as a sinusoidal perturbation superimposed on a steady flow while the right ventricular flow was modeled to accurately depict the period of flow acceleration (increasing flow) and deceleration (decreasing flow) during systole followed by zero flow during diastole. It was observed that the pulsatile flow yielded similar gas transport as compared to the steady flow, while the right ventricular flow resulted in smaller gas transport, with the decrease in...

We have developed a method to characterize fluid transport through the perialveolar interstitium using micropuncture techniques. In 10 experiments we established isolated perfused rat lung preparations. The lungs were initially isogravimetric at 10 cmH2O arterial pressure, 2 cmH2O venous pressure, and 5 cmH2O alveolar pressure. Perialveolar interstitial pressure was determined by micropuncture at alveolar junctions by use of the servo-null technique. Simultaneously a second micropipette was placed in an alveolar junction 20-40 microns away, and a bolus of albumin solution (3.5 g/100 ml) was injected. The resulting pressure transient was recorded for injection durations of 1 and 4 s in nonedematous lungs. The measurements were repeated after gross edema formation induced by elevated perfusion pressure. We model the interstitium as a homogeneous linearly poroelastic material and assume the initial pressure distribution due to the injection to be Gaussian. The pressure decay is inversely proportional to time, with time constant T, where T is a measure of the ratio of interstitial tissue stiffness to interstitial resistance to fluid flow. A linear regression was performed on the reciprocal of the pressure for the decaying portion of the transients to determine T. Comparing pressure transients in nonedematous and edematous lungs, we found that T was 4.0 +/- 1.4 and 1.4 +/- 0.6 s, respectively. We have shown that fluid transport through the pulmonary interstitium on a local level is sensitive to changes in interstitial stiffness and resistance. These results are consistent with the decreased stiffness and resistance in the perialveolar interstitium that accompany increased hydration.

The lung is comprised of a network of bifurcating airway tubes which are coated with a thin viscous film. Often times, especially in the case of disease, the liquid film can form a meniscus which blocks the tube, thus obstructing airflow. The formation of the liquid meniscus is due to capillary driven instabilities which can arise in the lining, causing the lining to close up. In addition, airflow can also be obstructed if the airway tube collapses in on itself. This occurs when the elastic forces of the tube are not large enough to sustain the negative fluid pressures caused by the surface-tension of the airliquid interface. Premature babies, whose lungs haven’t developed sufficient surfactant to maintain the surface tension of the lung at a sufficiently low level for healthy functioning, are especially predisposed to problems caused by airway closure. In such cases, the patients are sometimes put on high frequency ventilation machines to improve gas exchange (Heldt et al. 1992, Patel 1995, Paulson it el al. 1996). The frequency of the breathing cycle, as well as the tidal volume, are two control parameters at the disposal of the clinician. Little is known, however, of the effect that these two parameters can have on the occurrence of airway closure. Indeed, if airways can be kept open by using some given machine frequency, then this would be of vital importance in the treatment of such patients. The present work examines and quantifies these particular issues.

This paper considers the propagation of a liquid plug driven by a constant pressure within a rigid axisymmetric tube whose inner surface is coated by a thin liquid film. The Navier-Stokes equations are solved using the finite-volume method and the SIMPLEST algorithm. The effects of precursor film thickness, initial plug length, pressure drop across the plug, and constant surface tension on the plug behavior and tube wall mechanical stresses are investigated. As a plug propagates through a liquid-lined tube, the plug gains liquid from the leading front film, and it deposits liquid into the trailing film. If the trailing film is thicker (thinner) than the precursor film, the plug volume decreases (increases) as it propagates. For a decreasing volume, eventually the plug ruptures. Under a specific set of conditions, the trailing film thickness equals the precursor film thickness, which leads to steady state results. The plug speed decreases as the precursor film thins because the resistance to the moving front meniscus increases. As the pressure drop across the plug decreases, the plug speed decreases resulting in thinning of the trailing film. As the plug length becomes longer, the viscous resistance in the plug core region increases, which slows the plug and causes the trailing film to become even thinner. The magnitude of the pressure and shear stress at the tube inner wall is maximum in the front meniscus region, and it increases with a thinner precursor film. As the surface tension increases, the plug propagation speed decreases, the strength of the wall pressure in the front meniscus region increases, and the pressure gradient around the peak pressure becomes steeper.

A mathematical model of ozone absorption, or for any soluble gas that has similar transport properties, is developed for a branching network of liquid-lined cylinders. In particular, we investigate specific flow regimes for finite length tubes where boundary layer phenomena and entrance effects exist in high Reynolds and Peclet (Pe) number airways. The smaller airways which have lower Reynolds and Peclet number flows are modelled by incorporating the detailed analysis found in [10] and modifying it for airways which have alveolated surfaces. We also consider a reacting gas and treat specific regimes where the reaction front is located at the air-liquid interface, within the liquid or at the liquid-tissue interface. Asymptotic methods are used in regions of the tracheobronchial tree where Pe much less than 1 and Pe much greater than 1. In addition, the fact that the radial transport parameter gamma much less than 1 for this toxin, and others such as nitrous oxides, is employed to simplify the analysis. The ozone concentrations, airway absorption and tissue dose are examined as a function of airway generation for several values of the governing parameters. The general result is a maximal dosing in airway generations 17 to 18 that is much larger (up to an order of magnitude) than the predictions of previous theories.

The primary function of the lung is the exchange of oxygen and carbon dioxide. Other substances, such as anesthetics, aerosols, and toxins, are delivered and removed from the lungs by a similar process. Mass transport in the lung depends on convection, diffusion, and their interaction during oscillatory flow. High frequency ventilation (HFV) is an alternative type of ventilation under investigation (Bohn et al. 1980). In HFV, relatively small tidal volumes of air (35–150 ml) are delivered at high frequencies (5–30 Hz), so that pulmonary barotrauma and cardiac impairment are avoided.

Liquid plugs may form in pulmonary airways during the process of liquid instillation or removal in many clinical treatments. Studies have shown that the effectiveness of these treatments may depend on how liquids distribute in the lung. Better understanding of the fundamental fluid mechanics of liquid plug transport will facilitate treatment strategies. In this paper, we develop a numerical model of steady plug propagation driven by gravity and pressure in a two-dimensional liquid-lined channel oriented at an angle α with respect to gravity. We investigate the effects of gravity through the Bond number, Bo, and α; the plug propagation speed through the capillary number, Ca, or the Reynolds number, Re; the plug length LP, and the surfactant concentration C0. Without gravity, i.e., Bo=0, the plug is symmetric, and there are two regimes for the flow: two wall layers and two trapped vortices in the core. There is no flow interaction between the upper and lower half plug domains. When Bo≠0 and α≠0, π, fluid is...

The mass transport of a pulsatile free-stream flow past a single circular cylinder is investigated as a building block for an artificial lung device. The free stream far from the cylinder is represented by a time-periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest are the steady Reynolds number (Re), Womersley parameter (α), sinusoidal amplitude (A), and the Schmidt number (Sc). The ranges investigated in this study are 5⩽Re⩽40, 0.25⩽α⩽4, 0.25⩽A⩽0.75, and Sc=1000. A pair of vortices downstream of the cylinder is observed in almost all cases investigated. These vortices oscillate in size and strength as α and A are varied. For α αc, the vortex is attached to the cylinder only during part of a time cycle (intermittent). The time-averaged Sherwood number, Sh, is found to be largely influenced by the steady Reynolds number, increasing approximately as...

In this study, we investigate the steady propagation of a liquid plug in a two-dimensional channel lined by a uniform, thin liquid film. The liquid contains soluble surfactant that can exist both in the bulk fluid and on the air-liquid interface. The Navier-Stokes equations with free-surface boundary conditions and the surfactant transport equations are solved using a finite volume numerical scheme. The adsorption/desorption process of the surfactant is modeled based on pulmonary surfactant properties. As the plug propagates, the front meniscus sweeps preexisting interfacial surfactant from the precursor film, and the surfactant accumulates on the front meniscus interface. As the front meniscus converges on the precursor film from the region where the interfacial surfactant concentration is maximized, the Marangoni stress opposes the flow. In this region, the Marangoni stress results in nearly zero surface velocity, which causes the precursor film thickness near the meniscus to be thicker than the leading film thickness. Since the peaks of wall pressure and wall shear stress occur due to narrowing of the film thickness, the observed increase of the minimum film thickness weakens these stresses. In the thicker film region, however, the drag forces increase due to an increase in the surfactant concentration. This causes the overall pressure drop across the plug to increase as a result of the increasing surfactant concentration. A recirculation flow forms inside the plug core and is skewed toward the rear meniscus as the Reynolds number increases. When no surfactant exists, the recirculation flow is in contact with both the front and the rear interfaces. As the surfactant concentration increases, the Marangoni stress begins to rigidify the front interface and forces the recirculation flow away from the front interface. Subsequently, the recirculation flow is directed away from the rear interface in a manner similar to that for the front interface. When the plug length is shorter, this change in recirculation pattern occurs at a smaller surfactant concentration.

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 α 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, α 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∕3 at leading order with coefficients that depend on Bo and α. The first correction to the film thickness is found to occur at O(Ca) compared to O(Ca4∕3) in the Bo=0 case. Asymmetry in the liquid distribution is quantified by calculating the ratio of liquid volumes above and below the centerline of the channel, VR. VR=1 at Bo=0, indicating a symmetric distribution, and decreases with Bo and Ca, but increases with the plug length Lp. The decrease of VR 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 Cac is identified above which the plug will eventually rupture. When the Bond number becomes equal to an orientation-dependent critical value Boc, it is found that the scaling of the film thickness and pressure drop change to Ca1∕2 and Ca1∕6, respectively. It is shown that this scaling is valid for small increments of the Bond number over its critical value, Bo=Boc+BCa1∕6, but for higher Bond numbers the asymptotic approach breaks down.

The flow and transport in an alveolus are of fundamental importance to partial liquid ventilation, surfactant transport, pulmonary drug administration, cell-cell signaling pathways, and gene therapy. We model the system in which an alveolus is partially filled with liquid in the presence of surfactants. By assuming a circular interface due to sufficiently strong surface tension and small surfactant activity, we combine semianalytical and numerical techniques to solve the Stokes flow and the surfactant transport equations. In the absence of surfactants, there is no steady streaming because of reversibility of Stokes flow. The presence of surfactants, however, induces a nontrivial cycle-averaged surfactant concentration gradient along the interface that generates steady streaming. The steady streaming patterns (e.g., number of vortices) particularly depend on the ratio of inspiration to expiration periods (I:E ratio) and the sorption parameter K. For an insoluble surfactant, a single vortex is formed when t...

Why biofluid mechanics? It is a fair question since Physics of Fluids embarked on this special section of papers dedicated to the subject. After some thought, my answer is the relatively simple view that life is a wet and sticky business, to be sure. And to our knowledge it is mostly immersed in our earthly atmosphere. So as long as people and other organisms strive to live, reproduce, and interact with who and what is around them, biofluid mechanics will have a steady stream of challenges. The vast scope of fluid physics, from nano/micro to galactic scales, is certainly understood by the audience of this journal. Biofluid mechanics, while not stretched to such a range of characteristic lengths, is equally vast in its richness of complex fluid properties and unique boundary conditions. For example, phonation derives from the interplay of airflow through the vocal cords, the results varying from love songs to crying to lectures in introductory fluid mechanics. The coupling of air vibrations to the cochlear apparatus of the ear gives the speaker/singer an audience. And it is the homeostatic balance of fluid flow in the eye that lets the reader read. Without healthy biofluid mechanics, we are all potentially deaf, dumb, and blind. By the way, biofluid mechanics researchers are busy in developing diagnostic and assistive modalities for those who do face such obstacles in their daily life. The field of biofluid mechanics is a growing area of research and Physics of Fluids welcomes original contributions. One clear indicator of the increasing interest and activity in this field is the rapid expansion of presentations witnessed at the 57th Annual Meeting of the Division of Fluid Dynamics during 21–23 November 2004 in Seattle, Washington. There were 10 sessions entitled Bio-Fluid Dynamics I–X over the three-day conference period. In addition to the 94 talks in those sessions, there were many others involving biological flows scattered elsewhere in the program. The list of treated topics is quite broad, including flows related to: aneurysms, stenotic blood vessels, stents, flapping flight, experimental methods, dispersion, biomimetics, bioreactors, microfluidics, microcirculation, lab-on-chip devices, animal-on-chip devices, large blood vessels, heart valves, fluid-elastic interactions, non-Newtonian flows, respiration, vocalization, artificial lungs, swimming by animals and actuated models, walking on water with feet or tails, collapsible tubes as conduits or as pumps, interactions with cells, and the mosquito proboscis. The range of applications was perhaps best seen in one of the sessions where “Measuring vortex breakdown flows within open cylindrical bioreactors using stereoscopic particle image velocimetry” was immediately followed by “Sniffers.” The collection of papers in this special section of Physics of Fluids is dedicated to biofluid mechanics and is representative of those seeking new fluid physics in the biological realm. From this interface, one hopes that there is both new fluid mechanics and new biology. These goals often go handin-hand. The papers cover interesting aspects of two-phase flow and stability in the lung where moving and elastic wall boundaries interact with surface tension and flow dynamics, cell–cell and cell–wall interactions in blood flow with complex cell and wall models to account for micro and molecular structure and function, and swimming of spirochetes. I wish to express my thanks to these authors for sharing this work with us. PHYSICS OF FLUIDS 17, 031401 s2005d

Surfactant spreading phenomena on thin films is a fundamental problem in a number of fields including biomedical and chemical engineering. Coating processes, film drainage, and paint technology are all examples of technological applications. Research in this area has experienced a recent surge of activity, partly due to the biomedical applications of surfactant replacement therapy in prematurely born infants. A brief review of the surfactant spreading literature is given in this letter.

We performed a theoretical investigation of the progression of a finger of air through a liquid-filled flexible-walled channel - an initial model of pulmonary airway reopening. Positive pressure, Pb* drives the bubble forward, and separates flexible walls that are modelled as membranes under tension, T, supported by linearly elastic springs with elasticity K. The gap width between the walls under stress-free conditions is 2H, and the liquid has constant surface tension, γ, and viscosity, μ. Three parameters define the state of the system: Ca = μU/γ is a dimensionless velocity that represents the ratio of viscous to capillary stresses; η = T/γ is the wall tension to surface tension ratio, and γ = KH2/γ is the wall elastance parameter. We examined steady-state solutions as a function of these parameters using lubrication analysis and the boundary element method.These studies showed multiple-branch behaviour in the Pb-Ca relationship, where Pb = Pb*/(γ/H) is the dimensionless bubble pressure. Low Ca flows (Ca [Lt ] min (1, (Γ3/η)1/2)) are dominated by the coupling of surface tension and elastic stresses. In this regime, Pb decreases as Ca increases owing to a reduction in the downstream resistance to flow, caused by the shortening of the section connecting the open end of the channel to the fully collapsed region. High Ca behaviour (max (1, (γ3/η)1/2) [Lt ] Ca [Lt ] η) is dominated by the balance between fluid viscous and longitudinal wall tension forces, resulting in a monotonically increasing Pb–Ca relationship. Increasing η or decreasing Γ reduces the Ca associated with the transition from one branch to the other. Low Ca streamlines show closed vortices at the bubble tip, which disappear with increasing Ca.Start-up yield pressures are predicted to range from 1 [les ] Pyield*/(γ/L*) [les ] 2, which is less than the minimum pressure for steady-state reopening, Pmin/(γ/L*), where L* is the upstream channel width. Since Pyield* < Pmin*, the theory implies that low Ca reopening may be unsteady, a behaviour that has been observed experimentally. Our results are consistent with experimental observations showing that Pb* in highly compliant channels scales with γ/L*. In contrast, we find that wall shear stress scales with γ/H. These results imply that wall shear and normal stresses during reopening are potentially very large and may be physiologically significant.

The dynamics of a thin film of Newtonian fluid coating the inner surface of an elastic circular tube is analysed. This problem is motivated by an interest in the closure of small airways of the lungs either by formation of a liquid bridge, the collapse of the airway wall or a combination of both processes. Liquid bridge formation is due to the destabilization of the liquid film that coats the inner surface of airways, while wall collapse can be due to either the high surface tension of the air–liquid interface or the flexibility of the wall.Nonlinear evolution equations for the film thickness and wall position are derived using lubrication theory, but an accurate representation of the curvatures of both the liquid and wall interfaces is employed which is valid for thick films. These approximations allow closure to be predicted. In addition, these approximations are justified by comparison with rigid-wall results obtained by solving the full Navier–Stokes equations and because fluid inertia only becomes important in the very late stages of closure. The linear stability of these equations is examined using normal-mode analysis for infinitesimal disturbances and the nonlinear stability is investigated by solving the governing equations numerically using the method of lines. Solutions show that there is a critical film thickness, strongly dependent on fluid and wall properties, above which unstable waves grow to form liquid bridges. The critical film thickness decreases with increasing surface tension or wall compliance since waves grow faster. Even for relatively stiff airways, the volume of fluid in the liquid lining required for closure can be approximately 70% of the volume for the rigid-tube case. Wall damping is an important effect only when the airway is sufficiently compliant. Airway closure occurs more rapidly with increasing unperturbed film thickness, surface tension and wall flexibility and decreasing wall damping.

Lubrication theory and similarity methods are used to determine the spreading rate of a localized monolayer of insoluble surfactant on the surface of a thin viscous film, in the limit of weak capillarity and weak surface diffusion. If the total mass of surfactant increases as t(alpha), then at early times, when spreading is driven predominantly by Marangoni forces, a planar (axisymmetric) region of surfactant is shown to spread as t(1 + alpha)/3 (t(1 + alpha)/4) . A shock exists at the leading edge of the monolayer; asymptotic methods are used to show that a wavetrain due to capillary forces exists ahead of the shock at small times, but that after a finite time it is swamped by diffusive effects. For alpha < 1/2 (alpha < 1), the diffusive lengthscale at the shock grows faster than the length of the monolayer, ultimately destroying the shock; subsequently, spreading is driven by diffusion, and proceeds as t1/2. The asymptotic results are shown to be good approximations of numerical solutions of the governing partial differential equations in the appropriate limits. Additional forces are also considered: weak vertical gravity can also destroy the shock in finite time, while effects usually neglected from lubrication theory are important only early in spreading. Experiments have shown that the severe thinning of the film behind the shock can cause it to rupture: the dryout process is modelled by introducing van der Waals forces.

We investigated experimentally the flows induced by a localized surfactant (oleic acid) on thin glycerol films. The oleic acid creates surface-tension gradients, which drive convention on the surface and within the film. Qualitative descriptions of the Lagrangian flow field were provided by flow-visualization experiments. Quantitative measurements of surface flows were conducted using dyed glycerol markers, where the initial motion of these markers is used to define the position of the timedependent ‘ convection front ’. The flow characteristics were found to depend largely upon the magnitude of a gravitational parameter, G, representing the ratio of gravitational to surface-tension gradient (Marangoni) forces. Small G (G 0. For this reason, surface markers may not be used to measure accurately the position of the droplet’s leading edge. Finally, simulations of the Lagrangian flows conducted using the theory of Gaver & Grotberg (1990) compare favourably with these experimental results in the limit of dilute surfactant concentrations, and thus experimental verification of that theory is provided by this work. The results of this study may be useful for understanding the behaviour of the lung’s thin-film lining after an aerosol droplet of insoluble exogenous surfactant lands upon its surface.

A laser-Doppler velocimeter is used to analyse volume-cycled oscillatory flow of a Newtonian viscous fluid in a straight circular tube. The axial velocity is measured at radial positions across the diameter of the tube for a wide range of amplitude A = stroke distance/tube radius (2.4 [les ] A [les ] 21.6) and Womersley parameter (9 < α < 33). Transition to turbulence is detected during the decelerating phase of fluid motion for 500 < Rδ < 854, where Rδ = αA √2 is the Reynolds number based on Stokes-layer thickness. The turbulence is confined to an annular region which is a few times the Stokes-layer thickness near the wall. Hot-film anemometer measurements indicate the core flow remains stable when the boundary layer becomes turbulent for Rδ up to 1310.

We investigate the flow induced by a localized insoluble surfactant on a thin film. This problem is intended to model the behaviour of the lung's thin-film lining after an aerosol droplet lands on its surface. The surfactant-induced surface-tension gradients drive convection (Marangoni convection) within the film, disrupting the film surface and causing the surfactant to spread. The surfactant may also spread on the film's surface by surface diffusion without inducing convection. Gravity provides a restoring force that decreases film disturbances.Lubrication theory is employed to derive equations that describe the evolution of the film thickness and surfactant concentration. A nonlinear surface-tension equation of state describes the relationship between the surfactant concentration and the surface tension. Solutions of the evolution equations are found numerically using the method of lines and analytically under limiting cases of small and large surface diffusivity. The results elucidate the behaviour of the thin-film/surfactant system.We find that surface-tension-induced convection creates film disturbances that increase the film thickness near the surfactant's leading edge, and thins the film in the central region. Surface diffusion causes more rapid spreading of the surfactant, and decreases the film disturbances. Gravity decreases the film disturbances by creating bi-directional flow in the form of a ring vortex. This behaviour may have implications for the delivery of medications or toxins by aerosol inhalation.

A mathematical analysis of flow through a flexible channel is examined as a model of flow-induced flutter oscillations that pertain to the production of wheezing breath sounds. The model provides predictions for the critical fluid speed that will initiate flutter waves of the wall, as well as their frequency and wavelength. The mathematical results are separated into linear theory (small oscillations) and nonlinear theory (larger oscillations). Linear theory determines the onset of the flutter, whereas nonlinear theory determines the relationships between the fluid speed and both the wave amplitudes and frequencies. The linear theory predictions correlate well with data taken at the onset of flutter and flow limitation during experiments of airflow in thick-walled collapsible tubes. The nonlinear theory predictions correlate well with data taken as these flows are forced to higher velocities while keeping the flow rate constant. Particular ranges of the parameters are selected to investigate and discuss the applications to airway flows. According to this theory, the mechanism of generation of wheezes is based in the interactions of fluid forces and friction and wall elastic-restoring forces and damping. In particular, a phase delay between the fluid pressure and wall motion is necessary. The wave speed theory of flow limitation is discussed with respect to the specific data and the flutter model.

Oscillatory viscous flow in a tapered channel is analysed under conditions of fixed stroke volume. A lubrication theory is developed for small taper and the general result is steady bidirectional drift and an induced steady pressure gradient. The characteristics of the drift profiles change significantly as the Womersley parameter is increased. For large values difficulties arise in the matched asymptotics method which are resolved by introducing a steady drift layer that is much thicker than the Stokes layer. This double boundary layer does not arise in pressure-cycled oscillations. Both Eulerian and Lagrangian drift are examined. The results are compared qualitatively to experimental observations which primarily focus on the application to ventilation in the lung.