Biomedical Engineering Reference
In-Depth Information
2.4
show the diffusion coefficients of typical cations and anions in water at 25
C. However, both anion
and cation together should have the same diffusion coefficient to maintain the charge neutrality. It is
interesting to observe from
Table 2.3
that the diffusion coefficient of proton H
þ
is about five times
larger than other ions. Since the size difference between H
þ
and the other ion is not significant,
H
þ
should have a different diffusion mechanism in water. H
þ
actually does not move through water
but reacts with a water molecule and releases a proton on the other side. This new proton can cause
another reaction. This chain reaction speeds up the transport process and leads to a much higher
diffusion coefficient of H
þ
in water
[7]
.
The diffusion coefficient of amolecule consisting of a cation of charge
z
1
and an anion of charge
z
2
is:
¼
j
z
1
jþj
z
2
j
D
(2.40)
j
D
1
þ
j
z
2
j
z
1
j
D
2
where
D
1
and
D
2
are the diffusion coefficients of the cation and the anion, respectively. According to
(2.40)
, the overall diffusion coefficient is determined by the slower ion. Since the diffusion coefficients
are weighted by the charge, the faster ion with a much smaller charge can dominate the overall
diffusion coefficient.
Example 2.7
(
Diffusion coefficient of sodium chloride
). Determine the diffusion coefficient of
sodium chloride at 25
C.
Solution.
From
Tables 2.3 and 2.4
, the diffusion coefficients of sodium cation and chloride anion
are
D
1
¼
10
9
m
2
/sec and
D
2
¼
10
9
m
2
/sec, respectively. Applying
z
1
¼þ
1.33
2.03
1 and
z
2
¼
1in
(2.40)
results in the diffusion coefficient of sodium chloride:
D ¼
j
z
1
jþj
z
2
j
1
þ
1
10
9
¼
1
:
61
10
9
m
2
¼
=
sec
:
1
1
j
D
1
þ
j
z
2
j
z
1
j
D
2
10
9
þ
:
:
1
33
2
03
The diffusion coefficients of electrolytes in water are about four orders smaller than those of gases
and about two orders larger than those of large molecules.
In many lab-on-a-chip applications, micromixers are needed for mixing proteins. The behavior
of proteins is very complex. A protein molecule consists of chains of amino acids. The molecular
weight is very large and can be on the order of 10
5
. A protein molecule has a large number of side
chains that end in amino (-NH
2
) or carboxylic acid (-COOH) groups. Depending on the pH
concentration, amino groups can be positively charged to become (
NH
3
þ
) and carboxylic acid
groups become negatively charged (-COO
). Therefore, the net charge of a protein can be either
positive or negative. Further, depending on the pH, the protein chains can be folded differently,
resulting in various sizes and shapes. The different charges and shapes make the diffusion coef-
ficient of proteins depend on the pH concentration. Furthermore, the diffusion coefficient of
protein also depends strongly on its concentration and the concentration of electrolytes, such as
NaCl.
Many solute molecules, such as surfactant, also have diffusion coefficients that depend on the
solute concentration. At high concentrations, the molecules can aggregate to form micelles. The
aggregation and the electrostatic interaction cause the strong concentration dependence of the diffu-
sion coefficient.
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