Pulmonary Airway Reopening: Effects of Non-Newtonian Fluid Viscosity

1997 ◽  
Vol 119 (3) ◽  
pp. 298-308 ◽  
Author(s):  
H. T. Low ◽  
Y. T. Chew ◽  
C. W. Zhou
Keyword(s):  
Surface Tension ◽  
Film Thickness ◽  
Yield Stress ◽  
Newtonian Fluid ◽  
Shear Thinning ◽  
Fluid Viscosity ◽  
Polyethylene Tube ◽  
Airway Reopening ◽  
Airway Opening ◽  
Fluid Film Thickness

This paper considers the effects of non-Newtonian lining-fluid viscosity, particularly shear thinning and yield stress, on the reopening of the airways. The airway was simulated by a very thin, circular polyethylene tube, which collapsed into a ribbonlike configuration. The non-Newtonian fluid viscosity was described by the powerlaw and Herschel-Buckley models. The speed of airway opening was determined under various opening pressures. These results were collapsed into dimensionless pressure-velocity relationships, based on an assumed shear rate γ˙ = U/(0.5 H), where U and H are the opening velocity and fluid film thickness, respectively. It was found that yield stress, like surface tension, increases the yield pressure and opening time. However, shear thinning reduces the opening time. An increased film thickness of the non-Newtonian lining fluid generally impedes airway reopening; a higher pressure is needed to initiate the airway reopening and a longer time is required to complete the opening process.

Interaction between airway lining fluid forces and parenchymal tethering during pulmonary airway reopening

1995 ◽  
Vol 79 (5) ◽  
pp. 1717-1728 ◽  
Author(s):  
M. L. Perun ◽  
D. P. Gaver
Keyword(s):  
Surface Tension ◽  
Fluid Viscosity ◽  
Polyethylene Tube ◽  
Airway Patency ◽  
Airway Reopening ◽  
Fluid Forces ◽  
Disease States ◽  
Open Cell Foam ◽  
Pulmonary Airway ◽  
Airway Walls

In this study, our goal is to identify the interaction between airway lining fluid viscous and surface forces and parenchymal tethering forces during pulmonary airway reopening. The type of closure we modeled occurs when the airway walls and surrounding parenchyma collapse and are held in apposition by the lining fluid. We mimicked this system with a polyethylene tube coated with a Newtonian lining fluid supported by open-cell foam. Reopening occurs when a finger of air travels through the collapsed region. We measured the airway pressure (Paw) required to open the airway at a constant velocity (U). Increasing the foam stiffness (K), lining fluid viscosity (mu), and surface tension (gamma) results in an increase in Paw. Furthermore, increasing the downstream suction pressure (Pds), through tethering, causes an equivalent reduction in Paw. The upstream radius is the primary length scale, and fluid forces are represented by the capillary number: Ca = microU/gamma. On the basis of these results, we predicted the likelihood that tethering would begin to reopen collapsed airways in various disease states. This analysis showed that the ratio of tethering to fluid forces determines airway patency, which is defined as follows: lambda = PTrans/(gamma/R), where PTrans = Paw-Pds and R is airway radius. Finally, lung volume-dependent surface tension appears to be necessary to stabilize the lung.

Effects of surface tension and viscosity on airway reopening

1990 ◽  
Vol 69 (1) ◽  
pp. 74-85 ◽  
Author(s):  
D. P. Gaver ◽  
R. W. Samsel ◽  
J. Solway
Keyword(s):  
Surface Tension ◽  
Fluid Viscosity ◽  
Opening Pressure ◽  
Viscous Forces ◽  
Considerable Portion ◽  
Airway Opening ◽  
Wall Compliance ◽  
Large Opening ◽  
Surface Tension Forces ◽  
The Relationship

We studied airway opening in a benchtop model intended to mimic bronchial walls held in apposition by airway lining fluid. We measured the relationship between the airway opening velocity (U) and the applied airway opening pressure in thin-walled polyethylene tubes of different radii (R) using lining fluids of different surface tensions (gamma) and viscosities (mu). Axial wall tension (T) was applied to modify the apparent wall compliance characteristics, and the lining film thickness (H) was varied. Increasing mu or gamma or decreasing R or T led to an increase in the airway opening pressures. The effect of H depended on T: when T was small, opening pressures increased slightly as H was decreased; when T was large, opening pressure was independent of H. Using dimensional analysis, we found that the relative importance of viscous and surface tension forces depends on the capillary number (Ca = microU/gamma). When Ca is small, the opening pressure is approximately 8 gamma/R and acts as an apparent “yield pressure” that must be exceeded before airway opening can begin. When Ca is large (Ca greater than 0.5), viscous forces add appreciably to the overall opening pressures. Based on these results, predictions of airway opening times suggest that airway closure can persist through a considerable portion of inspiration when lining fluid viscosity or surface tension are elevated.

Rheological Behaviors of Pressure-Driven Radial Flow

2007 ◽  
Author(s):  
Z. Xie ◽  
Q. Zou ◽  
D. Yao
Keyword(s):  
Film Thickness ◽  
Radial Flow ◽  
Practical Interest ◽  
Fluid Film ◽  
Fluid Viscosity ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Shear Dependent Viscosity ◽  
Fluid Film Thickness ◽  
Pressure Driven

The characteristics of fluid flows confined within microscale space are of theoretical and practical interest [1]. Such flow includes the thin lubrication films, the liquid flow between biological cells, and the flow of polymer melts in a micro-injection molding machines, etc. A pressure-driven radial flow microrheometry (PDRFM) is used to characterize high-shear microscale fluids. The shear-dependent viscosity of the pressure-driven radial flow is modeled to investigate the possible size effect on the fluid viscosity. In the modeling, the surface shear rate and surface shear stress at the edge of the radial flow are expressed in terms of three measurable parameters, i.e. the flow rate, the loading force, and the fluid film thickness. By decreasing the fluid film thickness to microscale level, this model can be used to study the microscale effect of any homogeneous fluids. The analysis has been verified by using CFD simulations as digital testing platforms. Furthermore, the preliminary experimental results of Newtonian and non-Newtonian flows also proved the rheological modeling.

An Experimental Model Investigation of the Opening of a Collapsed Untethered Pulmonary Airway

1995 ◽  
Vol 117 (3) ◽  
pp. 245-253 ◽  
Author(s):  
Matthew L. Perun ◽  
Donald P. Gaver
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Structural Characteristics ◽  
Stable Steady State ◽  
Effective Diameter ◽  
Fluid Viscosity ◽  
Two Dimensional ◽  
Fluid Properties ◽  
Wall Deformation ◽  
Fluid Film Thickness

We developed an essentially two-dimensional planar benchtop model of an untethered collapsed airway to investigate the influence of fluid properties (viscosity, μ and surface tension, γ) and the structural characteristics (effective diameter, D, longitudinal tension, T, and fluid film thickness, H) on airway reopening. This simplified model was used to quantify the relationship between wall deformation and meniscus curvature during reopening. We measured the pressure (P) required to move the meniscus at a constant velocity (U), and found the dimensionless post-startup pressure (PD/γ) increased monotonically with the capillary number (Ca = μU/γ). Startup pressures depend on the fluid viscosity and piston acceleration, and may significantly increase reopening pressures. Consistently stable steady-state pressures existed when Ca > 0.5. D was the most dominant structural characteristic, which caused an increase in the post-startup pressure (P) for a decrease in D. An increase in H caused a slight decrease in the reopening pressure, but a spatial variation in H resulted in only a transient increase in pressure. T did not significantly affect the reopening pressure. From our planar two-dimensional experiments an effective yield pressure of 3.69 γ/D was extrapolated from the steady-state pressures. Based on these results, we predicted airway pressures and reopening times for axisymmetrically collapsed airways under various disease states. These predictions indicate that increasing surface tension (as occurs in Respiratory Distress Syndrome) increases the yield pressure necessary to reopen the airways, and increasing viscosity (as in cystic fibrosis) increases the time to reopen once the yield pressure has been exceeded.

scholarly journals Yield-stress fluid deposition in circular channels

2017 ◽  
Vol 818 ◽  
pp. 838-851 ◽  
Author(s):  
Benoît Laborie ◽  
Florence Rouyer ◽  
Dan E. Angelescu ◽  
Elise Lorenceau
Keyword(s):  
Yield Stress ◽  
Newtonian Fluid ◽  
Capillary Number ◽  
Pure Shear ◽  
Scaling Law ◽  
Classical Problem ◽  
Nonlinear Effects ◽  
Shear Thinning ◽  
Quantitative Agreement ◽  
Yield Stress Fluid

Since the pioneering works of Taylor and Bretherton, the thickness $h$ of the film deposited behind a long bubble invading a Newtonian fluid is known to increase with the capillary number power $2/3$ ($h\sim RCa^{2/3}$), where $R$ is the radius of the circular tube and $Ca$ is the capillary number, comparing the viscous and capillary effects. This law, known as Bretherton’s law, is valid only in the limit of $Ca<0.01$ and negligible inertia and gravity. We revisit this classical problem when the fluid is a yield-stress fluid (YSF) exhibiting both a yield stress and a shear-thinning behaviour. First, we provide quantitative measurement of the thickness of the deposited layer for Carbopol, a Herschel–Bulkley fluid, in the limit where the yield stress is of a similar order of magnitude to the capillary pressure and for $0.1<Ca<1$. To understand our observations, we use scaling arguments to extend the analytical expression of Bretherton’s law to YSFs in circular tubes. In the limit of $Ca<0.1$, our scaling law, in which the adjustable parameters are set using previous results concerning non-Newtonian fluids, successfully retrieves several features of the literature. First, it shows that (i) the thickness deposited behind a Bingham YSF (exhibiting a yield stress only) is larger than for a Newtonian fluid and (ii) the deposited layer increases with the amplitude of the yield stress. This is in quantitative agreement with previous numerical results concerning Bingham fluids. It also agrees with results concerning pure shear-thinning fluids in the absence of yield stress: the shear-thinning behaviour of the fluid reduces the deposited thickness as previously observed. Last, in the limit of vanishing velocity, our scaling law predicts that the thickness of the deposited YSF converges towards a finite value, which presumably depends on the microstructure of the YSF, in agreement with previous research on the topic performed in different geometries. For $0.1<Ca<1$, the scaling law fails to describe the data. In this limit, nonlinear effects must be taken into account.

Three-dimensional airway reopening: the steady propagation of a semi-infinite bubble into a buckled elastic tube

2003 ◽  
Vol 478 ◽  
pp. 47-70 ◽  
Author(s):  
ANDREW L. HAZEL ◽  
MATTHIAS HEIL
Keyword(s):  
Surface Tension ◽  
Three Dimensional ◽  
Propagation Speed ◽  
Elastic Tube ◽  
Shear Stresses ◽  
Fluid Viscosity ◽  
Flow Topology ◽  
Airway Reopening ◽  
Bubble Pressure ◽  
Steady Propagation

We consider the steady propagation of an air finger into a buckled elastic tube initially filled with viscous fluid. This study is motivated by the physiological problem of pulmonary airway reopening. The system is modelled using geometrically nonlinear Kirchhoff–Love shell theory coupled to the free-surface Stokes equations. The resulting three-dimensional fluid–structure-interaction problem is solved numerically by a fully coupled finite element method.The system is governed by three dimensionless parameters: (i) the capillary number, Ca=μU/σ*, represents the ratio of viscous to surface-tension forces, where μ is the fluid viscosity, U is the finger's propagation speed and σ* is the surface tension at the air–liquid interface; (ii) σ=σ*/(RK) represents the ratio of surface tension to elastic forces, where R is the undeformed radius of the tube and K its bending modulus; and (iii) A∞=A*∞/(4R2), characterizes the initial degree of tube collapse, where A*∞ is the cross-sectional area of the tube far ahead of the bubble.The generic behaviour of the system is found to be very similar to that observed in previous two-dimensional models (Gaver et al. 1996; Heil 2000). In particular, we find a two-branch behaviour in the relationship between dimensionless propagation speed, Ca, and dimensionless bubble pressure, p*b/(σ*/R). At low Ca, a decrease in p*b is required to increase the propagation speed. We present a simple model that explains this behaviour and why it occurs in both two and three dimensions. At high Ca, p*b increases monotonically with propagation speed and p*b/(σ*/R) ∝ Ca for sufficiently large values of σ and Ca. In a frame of reference moving with the finger velocity, an open vortex develops ahead of the bubble tip at low Ca, but as Ca increases, the flow topology changes and the vortex disappears.An increase in dimensional surface tension, σ*, causes an increase in the bubble pressure required to drive the air finger at a given speed; p*b also increases with A*∞ and higher bubble pressures are required to open less strongly buckled tubes. This unexpected finding could have important physiological ramifications. If σ* is sufficiently small, steady airway reopening can occur when the bubble pressure is lower than the external (pleural) pressure, in which case the airway remains buckled (non-axisymmetric) after the passage of the air finger. Furthermore, we find that the maximum wall shear stresses exerted on the airways during reopening may be large enough to damage the lung tissue.

scholarly journals Concentric cylinder viscometer flows of Herschel-Bulkley fluids

2019 ◽  
Vol 29 (1) ◽  
pp. 173-181 ◽  
Author(s):  
Hans Joakim Skadsem ◽  
Arild Saasen
Keyword(s):  
Shear Rate ◽  
Yield Stress ◽  
Couette Flow ◽  
Newtonian Fluid ◽  
Shear Thinning ◽  
Newtonian Fluids ◽  
Drilling Fluids ◽  
Concentric Cylinder ◽  
Shear Thinning Fluids ◽  
Cylinder Viscometer

Abstract Drilling fluids and well cements are example non-Newtonian fluids that are used for geothermal and petroleum well construction. Measurement of the non-Newtonian fluid viscosities are normally performed using a concentric cylinder Couette geometry, where one of the cylinders rotates at a controlled speed or under a controlled torque. In this paper we address Couette flow of yield stress shear thinning fluids in concentric cylinder geometries.We focus on typical oilfield viscometers and discuss effects of yield stress and shear thinning on fluid yielding at low viscometer rotational speeds and errors caused by the Newtonian shear rate assumption. We relate these errors to possible implications for typical wellbore flows.

Influence of Ground Slag on the Rheology of Mortar

2013 ◽  
Vol 438-439 ◽  
pp. 67-71
Author(s):  
Qian Qian Zhang ◽  
Jian Zhong Liu ◽  
Jia Ping Liu
Keyword(s):  
Film Thickness ◽  
Specific Surface ◽  
Yield Stress ◽  
Surface Area ◽  
Specific Surface Area ◽  
Water Film ◽  
Plastic Viscosity ◽  
Rheological Parameters ◽  
Water Film Thickness ◽  
Binder Ratio

The effects of ground slag with different specific surface area on the rheology of mortar at water-binder ratio of 0.25, 0.28 and 0.30 were investigated, and the combined effects of packing density and solid surface area on the rheology of mortar were evaluated in terms of the water film thickness. The results show that with the increasing of specific surface area of slag (220 m2/kg-784 m2/kg), plastic viscosity and yield stress decrease. The correlations of yield stress and plastic viscosity to the water film thickness are basically linear with high correlation R2 values. The action of the ground slag on the rheology of mortar can be characterized by water film thickness, and with the increasing of water film thickness the rheological parameters decrease.

scholarly journals Analysis of misaligned journal bearing lubrication performance considering the effect of lubricant couple stress and shear thinning

2021 ◽  
Vol 37 ◽  
pp. 282-290
Author(s):  
Junchao Zhu ◽  
Haiyu Qian ◽  
Huabing Wen ◽  
Liangyan Zheng ◽  
Hanhua Zhu
Keyword(s):  
Film Thickness ◽  
Couple Stress ◽  
Journal Bearing ◽  
Shear Thinning ◽  
Inlet Temperature ◽  
Stress Effect ◽  
Misalignment Angle ◽  
Oil Film ◽  
Stress Coefficient ◽  
Lubrication Performance

ABSTRACT This paper investigates journal bearings, and builds a lubrication model taking into account misalignment, the lubricant couple stress effect and shear thinning. In order to explore the sensitivity of couple stress fluid lubrication performance to oil film thickness, we introduce the critical oil film thickness coefficient. The results show that the sensitivity increases with the increase of the couple stress coefficient, and it is highest in the area of minimum oil film thickness. Compared with a parallel journal, increases in the misalignment angle strengthen the effect of couple stress. Shear thinning also plays an important role in bearing lubrication performance. For a low oil inlet temperature, the effect of shear thinning increases with the increase of the couple stress parameter. For a high oil inlet temperature, the influence is negligible. An increase in the misalignment angle will not further enhance the effect of shear thinning.

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