Biomedical Engineering Reference
In-Depth Information
are discussing transport of a species through the digestive tract, we can concern ourselves
with the transport across a cell membrane, which is typically 7 to 8 nm, or we can be con-
cerned with the transport along the tract, which is approximately 30 m in length. This is
an astounding difference in length scales, which would need to be coupled if solving an
organ transport problem. For a time-scale problem in the digestive tract, molecular trans-
port can occur within a few microseconds or as long as a few days. Therefore, the solu-
tions to these types of problems would need to couple both length and time scales that
vary at a few orders of magnitude. Compartmental modeling is a good way to handle
these types of problems, and it will be presented in Chapter 12.
7.4 ENERGY CONSIDERATIONS
The transfer of nutrients can be classified as an adhesion reaction between the nutrient
and the transporter (e.g., glucose) or as an interaction between the nutrient and water
(e.g., ions). In either case, there is some energy that is required to either maintain that
adhesion or break the adhesion. In other words, there is a force required to break the
adhesive interactions between the two molecules that are involved in the diffusion process
so that one molecule can diffuse away freely. Adhesion forces are typically small, on the
nano- to micro-Newton range, and the adhesive forces increase with a decreasing surface
roughness. It is also typical that flexible surfaces have a larger adhesive force than stiffer
surfaces because the flexible surface can conform to the surface profile of the material that
it is adhering to (therefore there would be a higher contact area). In general, there are four
forces that contribute to adhesion: molecular forces, electrostatic forces, capillary forces,
and excessive charge forces (which will not be discussed because this is not typically
found in common biological systems).
Molecular forces act over the shortest range and are typically the weakest types of
forces that play a role in adhesion. These types of attractive forces typically arise due to
changes in electronic structure of the atoms that comprise the molecules. This means that
electrically neutral molecules can exhibit molecular forces, through transient dipoles cre-
ated by these fluctuations. Also, any molecule that has a permanent dipole (such as water),
will experience molecular forces. This type of interaction is termed a van der Waals inter-
action. Van der Waals forces are composed of two components: an attractive force and a
repulsive force. The attractive force arises from transient dipoles within electrically neutral
molecules. The repulsive component arises because two molecules cannot enter the same
space, and therefore, no matter how strong the attractive force is, the two molecules cannot
exist in one location. The force associated with molecular interactions can be described by
"
#
12
6
d
0
d
d
0
d
-
-
0
Ψ
ðdÞ
5
Ψ
ð
7
:
14
Þ
2
Ψ
0
is the strength of the molecular interactions when the molecules are in contact,
d
is the distance between molecules, and
d
' is the range of the interactions. Therefore, if
d
5
d
0
, then the molecular forces will be equal to zero.
where
Search WWH ::
Custom Search