Surfactant - Tissue Functioning and Remodeling in the Circulatory and Ventilatory Systems - page 796

Surfactants affect the normal stress balance, as they reduce T s ,butalsothe
tangential stress balance, as they generate Marangoni stresses. Tangential surface
stresses can only be balanced by viscous stresses associated with fluid motion.
Surfactant brings an effective elasticity to the interface. In a fluid motion
associated with a radial surface motion, the presence of surfactant provokes the
redistribution of surfactant. Whatever the evolution of the surfactant concentration,
either surfactant accumulation or drops, the resulting Marangoni stress aims at
suppressing the surface motion, resisting it through an effective surface elasticity.
When surfactant accumulates, Marangoni stresses again resist to the wall movement.
Surfactant is aimed at avoiding interface collapse and rupture.
Mass transfer of surfactant in thin, viscous layers such as airway surface liquid
at constant temperature along an interface between 2 fluids depends on the surface
tension gradient caused by a concentration gradient. Surfactant creates a type of
Marangoni flow.
The transient spreading of an insoluble surfactant on an interface causes motion
in the direction of higher surface tension, i.e., lower surfactant concentration [ 1618 ].
When the surface diffusion and gravity are negligible, a large change in film height
and surface tension over a very short distance can appear. The film thickens and
thins downstream with possible rupture.
The evolving concentration of surfactant on a free surface ( c s ) is governed by the
surfactant surface transport equation :

∂ t c s + ∇ · ( c s v s )+ c s ( ∇ s · v s )( v · n )= D s ∇ s c s + J ( c s , C s ) , (13.8)

n ∂
∂

≡ ( − ) · ≡ ( − ) · ∇ = ∇ −

where v s I nn v is the surface velocity, ∇ I nn ( ∇

n )

s s

the surface gradient operator ( I : identity tensor), D s the surface diffusivity of the

surfactant, J flux of surfactant from the source to the interface associated with
adsorption onto or desorption from the surface that depends on both the surface
surfactant concentration and the bulk concentration ( C s ).
Other governing equations include the Navier-Stokes equations (mass and
momentum conservation) and conservation of surfactant species in the bulk phase
( surfactant bulk transport equation ):

2 C s ,

∂ t C s + ∇ · ( C s v )= D ∇ (13.9)

where is the bulk diffusivity.

In surfactant replacement therapy, several factors influence the transport: the
bolus volume, its injection rate, dose, instillation site, physical properties (viscosity,
density, and surface tension) of the injected fluid, gravity, ventilation mode, clear-
ance of instilled surfactant, and treatment history. Surfactant delivery comprises
4 stages of instilled bolus transport, starting from a liquid plug that possibly occludes
the large airways, progression with a trailing film to a deposited layer along large
airway walls that moves under the influence of gravity, spreading in smaller airways
due to Marangoni flows, and arriving in alveoli, where surfactant lipids and proteins

D