Airway Surface Liquid and Respiratory Mucus - Tissue Functioning and Remodeling in the Circulatory and Ventilatory Systems - page 781

Table 12.8. Airw ay surface liquid model parameters (Source: [ 1594 ]).

Quantity Symbol Value

Cilium height H c 7 m

Cilium radius R c 0.3 m

Number of cilia per cell N c 4or16

Number of spheres per cilium N s 25

α

Angle between wall and cilium 110 degrees

Distance between-cilium center d c 4 R c

d c √ N c Length of epithelium cell L c

Domain edge length L 12 m

Number of x i -space steps N x i 32

Propulsion duration T p 17 ms

Recovery duration T p 34 ms

Cilia oscillation frequency f 19.6 Hz

viscoelastic properties of mucus are constantly regulated to ensure an efficient
clearance and to maintain sufficient adhesive strength to be retained on the epithelial
surface despite external shearing forces.

12.7.1 Governing Equations

Fluid flow equations are given by laws of mass and momentum conservation and a
convection equation for the dynamic viscosity ( μ ):

∂ t ρ + ∇ · ( ρ v )= 0 ,

∂ t ( ρ v )+ ∇ · ( ρ v ⊗ v ) − ∇ · C = b ,

∂ t μ + v · ∇μ = 0 , (12.1)

where v is the flow velocity vector, C the stress tensor, b the body forces, the third
equation arising from the transport of the mucin mass fraction, and

ρ v ⊗ v = ρ v ( ∇ · v )+ ρ ( v · ∇ ) v +( v · ∇ρ ) v (12.2)

The cilium is represented by a moving, piecewise articulated rode with a given
velocity [ 1594 ].