Development of a Oxygen Sensor for Marine ... - DTU Nanotech

3.1. CHEMISTRY OF THE CLARK SENSOR 19
The pressure profile within the membrane and the current output under
steady state conditions can then be obtained from Eq. 3.5 and Eq. 3.8:
and
p
p0
= x
dm
I = NF A Pm
dm
· p0
(3.9)
(3.10)
At steady state, the pressure profile is linear and the current output is
proportional to the oxygen partial pressure in the bulk liquid, where Eq. 3.10
forms the basis for DO measurement by the sensor. The response time of the
sensor as seen from Eq. 3.8 is:
τ = d2 m
Dm
(3.11)
Where τ determines how fast the sensor responds, due to the thickness
of the membrane or a high Dm. However these conditions tend to weaken
the assumption of membrane-controlled diffusion. Therefore, a compromise
has to be made for optimum sensor performance. Changing dm (rather than
Dm) is more effective in adjusting τ (since it depends on the square of dm).
Eq. 3.10 and Eq. 3.11 gives the indication, that the design variables for a
DO sensor is Pm, dm, Dm, and A.
3.1.2 Two layer model
The problem is, however, that the second assumption, made earlier in this
chapter, is not entirely accurate. A stagnant liquid film will almost always
exists right outside the membrane even at high liquid velocities.[28] Hence
a more realistic model have to be made, in order to account for this film as
shown on Figure 3.4. This take into consideration the effect of the film, as
it slows down the diffusion through the membrane.
The effect of the liquid layer on the sensor current can be calculated by
expanding the previous model, at steady state the oxygen flux J through
each layer should be the same.