Some features of oscillatory flow in a model bifurcation.

Oscillatory flow in the lung is studied using an order-of-magnitude analysis and flow visualization experiments in a single bifurcation with lung-like geometry. The results are used to obtain a classification scheme that identifies three major flow regimes, distinguished on the basis of whether the flow is dominated by unsteadiness, viscous effects, or the effects of convective acceleration. The unsteady regime is found to exist for values of a dimensionless stroke length (L/a, i.e., stroke volume/local cross-sectional area) less than or equal to 3 and for values of a dimensionless frequency (alpha 2 = alpha 2 omega/nu, where alpha is airway radius, omega the oscillatory frequency, and nu the kinematic viscosity) less than or equal to 10 in basic agreement with previous studies. The viscous regime is found when alpha 2(L/a)(a/R)1/2 less than 10 and alpha 2 less than 10 where R is the local radius of curvature in the bifurcation; the convective regime is found when alpha 2(L/a)(a/R)1/2 greater than 10 and L/a greater than 3. This same approach yields scaling laws for the magnitude of secondary flow velocities and shows that the ratio of secondary-to-axial velocity is small everywhere outside of the convective regime where it scales with (a/R)1/2. Comparison of these results to related simple flows shows that many of the features observed can be attributed to the effects of curvature, suggesting that the influence of the flow divider and of area change may be of lesser importance than previously thought.

Filling of partially collapsed compliant tubes.

Filling of a thin-walled, highly compliant tube in a partially collapsed condition is studied. The theory, based on one-dimensional flow, takes account of friction, longitudinal tension, and the highly nonlinear pressure-area law for the tube. Various aspects of filling behavior are revealed by alternative calculations using: (i) the method of characteristics; (ii) numerical integration of the continuity, momentum, and tube-law equations; and (iii) a crude but simple lumped-element capacitance-inertance-resistance model. Varied phenomena appear. At high Reynolds number, these include dispersive wave trains associated with circumferential bending stiffness and longitudinal tension, nonlinear changes of wave form, development of highly asymmetrical wave reflections, and sloshing. At low Reynolds number, the area changes with time in a diffusivelike manner. The experiments exhibited the dispersive phenomena predicted by the theory.