Mechanisms of Particle Deposition - Aerosols: Measurement, Dosimetry, and Health Effects - page 56

3.6.1 F undaMentals oF F low
A discussion of the dynamics of airlow in the respiratory airways requires the introduction of some
basic low considerations.

3.6.1.1 Steady versus Unsteady Flow
If the luid properties (e.g., density, velocity) at each point in a prescribed low ield are time invari-
ant, then the low is considered steady. In contrast, in unsteady low the luid properties at each
point in the low ield vary with time. In some circumstances, when the time-dependent changes in
luid properties are very small, the low may be assumed to be quasi-steady. During normal respira-
tion, the low in the lung airways can be considered quasi-steady. However, under high-frequency
breathing or forced expiration, low in the airways is unsteady. 73 It is important for investigators
to recognize the potential signiicance of transient, time-dependent, phenomena when analyzing
airlow patterns in their particular studies.

3.6.1.2 Laminar versus Turbulent Flow
Flow in airways may be either laminar or turbulent. Simply stated, in laminar low, the luid motion
occurs in smooth layers (laminae), and there is no luid mixing between adjacent layers. In the
turbulent regime, the low structure is random and characterized by the chaotic motion of luid
particles within the larger structure of the mean luid low. In this case, mixing of luid between
layers may be initiated locally and propagated to downstream regions.
Flows in an idealized cylindrical passage can be characterized as either laminar or turbulent by
calculating the value of dimensionless Reynolds number:

Re = ρ

dV

a a

(3.20)

μ

In general, the low in idealized tubes will be laminar for Re < 2300. 74 Idealized tubes (i.e., those
being straight and having smooth, rigid walls, circular cross sections, and constant diameters) are
rarely observed in vivo .
Table 3.3 provides estimated Reynolds numbers in 24 different airway generations for two differ-
ent respiratory rates. We note that the Re values predict laminar low in every airway at a ventilation
rate of 15 L/min, but predict turbulent low in the larger airways at a rate of 60 L/min. However, it
has been determined that due to disturbances in the inlow of air to the lungs caused by the larynx
and the cartilaginous rings, turbulent low is usually observed in the large airways, 73 and thus, care
must be exercised when attempting to relate Re values with in vivo low conditions. 75

3.6.2 F low in i dealized t ubes
A straightforward way of simulating airlow within respiratory passageways is to consider airways
as idealized tubes, as deined earlier. Flow in such an airway under both laminar and turbulent
conditions is shown in Figure 3.2. As low enters, the velocity of the luid V 0 is uniform within the
cross section of the tube. This type of velocity pattern is called plug low. As the low proceeds,
the velocity is retarded by the shear force that the boundary surface of the tube imparts on the
airlow. The no-slip condition exists at the tube surface, so the velocity of low at the wall is zero.
The axial distribution of low velocity is called the velocity proile. The region of the low where
V < V 0 is called the boundary layer. As the luid moves along the tube, pressure and shear forces
within the luid will equilibrate, and a fully developed velocity proile will be attained. The distance
from the entrance of the tube to the point where the laminar velocity proile is fully developed is