Biomedical Engineering Reference
In-Depth Information
At ambient pressure and temperature, the mean free path of a gas molecule
such as oxygen, nitrogen or carbon dioxide is about 70 nm (before it collides
with other gas molecules). The so-called Knudsen number, K =d
p
(where
mean free path and d
p
pore diameter) is thus small. Considering the pore
sizes quoted by the manufacturers
8
in the region of 0.1m 100 nm the
Knudsen number is close to 1 or somewhat lower. Below K 1, one assumes
increasing so-called Knudsen diffusion, where the interaction and collisions with
the borders (here the walls of the pores) gain importance over the bare diffusion.
These collisions are determined by the pore size, the tortuosity () of the pores
and the porosity of the medium. Since the walls between the pores of a highly
porous medium are very thin and many pores will have dead ends, the solution
diffusion through the polymer medium also plays a role.
A method to determine how much of the gas transport occurs by diffusion
and how much by convection
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analyses the transport through the membrane at
different pressure gradients and extrapolates the data to a pressure difference of
zero. This value at zero pressure difference represents the bare diffusion part,
whereas the slope of the curve gives the convection part. As the pressure
difference across a membrane for blood oxygenation must be kept low, this
represents an interesting method to characterise the membranes and to illustrate
the flow conditions, but has no direct meaning for the process of blood
oxygenation itself.
In composite membranes with both a microporous backbone and a non-
porous skin, the membrane forms two phases with two permeabilities. The
overall permeability of the composite membrane cannot be larger than the
permeability of the layer with the lower permeability, which is almost always
the non-porous layer. Composite membranes therefore have a very thin non-
porous layer on a (micro)porous backbone, which serves as a scaffold for the
skin and is only needed for sufficient mechanical stability. If the skin is
sufficiently thin, the composite membrane can reach the permeability and
performance of a microporous membrane.
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Table 1.1 shows the permeabilities of different polymers for oxygen and
carbon dioxide. Blood oxygenation membranes from PP are microporous; their
permeability therefore mostly depends on the pore geometry. Membranes for
longer-term use as artificial lungs should have a non-porous outer surface to
Table 1.1 Permeability of different polymers for breathing gases
(in Barrer10
ÿ10
cm
3
cm/(s cm
2
cmHg))
11,12
Oxygen
Carbon dioxide
Silicone (polysiloxane)
600
3200
PP (polypropylene)
2.2
9.2
PMP (polymethylpentene)
32.2
92.6
