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

3.1. CHEMISTRY OF THE CLARK SENSOR 21
Where dL is the liquid film thickness and PL the oxygen permeability of
the liquid film.
When the individual mass transfer resistances are included, the steady
state sensor output becomes:
Where ¯ d is defined as:
I = NF A Pm
¯d p0
dL
¯d = dm + Pm
PL
The time constant τ from Eq. 3.11 can be modified to:
with d defined as:
τ = d2
Dm
d = dm + dL
Dm
DL
(3.15)
(3.16)
(3.17)
(3.18)
The DO sensor, when placed in a stagnant liquid, produces a diffusion
gradient extending outside the membrane and farther into the liquid. When
the liquid is stirred, the diffusion gradient can no longer be extended beyond
the liquid film around the membrane. Since the diffusion gradient becomes
steeper with decreasing liquid film thickness, the current output of the sensor
increases with increase in liquid velocity, also that the response time of the
sensor increases as the liquid velocity decreases. This ’flow sensitivity’ is
greater for a sensor with a larger cathode because the size of the stagnant
diffusion field is proportionally greater with a larger cathode. Hence there
is an advantage in going from macro to micro scale, as the cathode will
naturally be smaller here.
Eq. 3.15 can be written as:
I = NF A p0
dm
Pm
+ dL
PL
(3.19)