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Research Papers

Computational Analysis of Microbubble Flows in Bifurcating Airways: Role of Gravity, Inertia, and Surface Tension

[+] Author and Article Information
Xiaodong Chen, Rachel Zielinski

Department of Biomedical Engineering,
The Ohio State University,
Columbus, OH 43210

Samir N. Ghadiali

Department of Biomedical Engineering,
The Ohio State University,
Columbus, OH 43210
Department of Internal Medicine,
Division of Pulmonary, Allergy, Critical Care and
Sleep Medicine,
Dorothy M. Davis Heart &
Lung Research Institute,
The Ohio State University,
Columbus, OH 43210
e-mail: ghadiali.1@osu.edu

1Corresponding author.

Manuscript received October 10, 2013; final manuscript received July 20, 2014; accepted manuscript posted July 30, 2014; published online August 12, 2014. Assoc. Editor: Alison Marsden.

J Biomech Eng 136(10), 101007 (Aug 12, 2014) (11 pages) Paper No: BIO-13-1478; doi: 10.1115/1.4028097 History: Received October 10, 2013; Revised July 20, 2014; Accepted July 30, 2014

Although mechanical ventilation is a life-saving therapy for patients with severe lung disorders, the microbubble flows generated during ventilation generate hydrodynamic stresses, including pressure and shear stress gradients, which damage the pulmonary epithelium. In this study, we used computational fluid dynamics to investigate how gravity, inertia, and surface tension influence both microbubble flow patterns in bifurcating airways and the magnitude/distribution of hydrodynamic stresses on the airway wall. Direct interface tracking and finite element techniques were used to simulate bubble propagation in a two-dimensional (2D) liquid-filled bifurcating airway. Computational solutions of the full incompressible Navier–Stokes equation were used to investigate how inertia, gravity, and surface tension forces as characterized by the Reynolds (Re), Bond (Bo), and Capillary (Ca) numbers influence pressure and shear stress gradients at the airway wall. Gravity had a significant impact on flow patterns and hydrodynamic stress magnitudes where Bo > 1 led to dramatic changes in bubble shape and increased pressure and shear stress gradients in the upper daughter airway. Interestingly, increased pressure gradients near the bifurcation point (i.e., carina) were only elevated during asymmetric bubble splitting. Although changes in pressure gradient magnitudes were generally more sensitive to Ca, under large Re conditions, both Re and Ca significantly altered the pressure gradient magnitude. We conclude that inertia, gravity, and surface tension can all have a significant impact on microbubble flow patterns and hydrodynamic stresses in bifurcating airways.

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Figures

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Fig. 1

Schematic view of microbubble propagation in a two-generation bifurcating airway. Curved lines indicate locations for hydrodynamic stress evaluation and represent the upper, lower, and middle interior airway walls.

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Fig. 2

Comparison of bubble shapes during propagation with fixed Ca = 0.082 and Re = 2.66 and varying Bond numbers: (a) Bo = 0.068, (t = 0, 0.005, 0.01, 0.015, 0.02, 0.03, 0.048 s) (b) Bo = 0.136 (t = 0, 0.005, 0.01, 0.015, 0.02, 0.03, 0.05 s), (c) Bo = 0.68 (t = 0, 0.005, 0.01, 0.015, 0.02, 0.03, 0.045 s), and (d) Bo = 1.36 (t = 0, 0.005, 0.01, 0.015, 0.02, 0.03, 0.04 s)

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Fig. 3

Velocity fields and pressure distribution within the fluid during bubble propagation with fixed Ca = 0.082 and Re = 2.66 and varying Bond numbers: (a) Bo = 0.068 (t = 0.048 s), (b) Bo = 0.136 (t = 0.05 s), (c) Bo = 0.68 (t = 0.045 s), and (d) Bo = 1.36 (t = 0.04 s)

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Fig. 4

Pressure and shear stress gradients along the upper and lower daughter airway wall as a function of Bond number. Data were obtained for different Bond numbers at fixed Ca = 0.082 and Re = 2.66 at t = 0.04 s. (a) Pressure gradients in the upper daughter airway, (b) pressure gradients in the lower daughter airway, (c) shear stress gradients in upper daughter airway, and (d) shear stress gradients in lower daughter airway.

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Fig. 5

Maximum pressure gradients along the upper, lower, and middle interior walls as a function of Bo. At low Bo, maximum pressure gradient is comparable on the upper, lower, and middle interior walls while at higher Bo, maximum pressure gradient is higher on the upper and middle interior wall.

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Fig. 6

Pressure and shear stress gradients along the upper and lower daughter airway wall as a function of Reynolds number. Data was obtained for different Reynolds numbers at fixed Ca = 0.082 and Bo = 0.136. (a) Pressure gradients in the upper daughter airway, (b) pressure gradients in the lower daughter airway, (c) shear stress gradients in upper daughter airway, and (d) shear stress gradients in lower daughter airway.

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Fig. 7

Maximum pressure gradient calculations at fixed Capillary number (Ca = 0.082) by varying Bond numbers (Bo = 0.068, Bo = 0.136, Bo = 0.68, Bo = 1.36) and Reynolds numbers (Re = 2.66, Re = 26.6, Re = 53.2, Re = 133) for (a) upper daughter airway and (b) lower daughter airway wall

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Fig. 8

Pressure and shear stress gradients along the upper and lower daughter airway walls as a function of Capillary number. Data were obtained for different Capillary numbers at fixed Re = 2.66 and Bo = 0.136. (a) Pressure gradients in the upper daughter airway, (b) pressure gradients in the lower daughter airway, (c) shear stress gradients in upper daughter airway, and (d) and shear stress gradients in lower daughter airway.

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Fig. 9

Maximum pressure gradient calculations at fixed Reynolds number (Re = 2.66) by varying Bond numbers (Bo = 0.068, Bo = 0.136, Bo = 0.68, Bo = 1.36) and Capillary numbers (Ca = 0.82, Ca = 0.082, Ca = 0.008, Ca = 0.0008) for (a) upper daughter airway and (b) lower daughter airway

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Fig. 10

Sensitivity of maximum pressure gradient to changes in Re, Ca, and Bo for different baseline values of Re. (a) Represents data from the upper daughter airway and (b) represents data from the lower daughter airway.

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Fig. 11

(a) Velocity field and bubble shape during propagation in a straight 2D channel. Solid line is the initial bubble shape. (b) Comparison of the dimensionless film thickness obtained with current finite element technique (triangles) with Bretherton's asymptotic predictions (dashed line) and BEM simulations (solid line).

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