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Electrochemical diagnostics of dissolved oxygen diffusion
Kamil Wichterle and Jana Wichterlová
Department of Chemistry, VSB-Technical University of Ostrava Ostrava, Czech Republic
COST F2 Conference
”Electrochemical Sensors for Flow Diagnostics”Florence, Italy
November 2001, 7th-9th
O2 + 2 H2O + 4e- 4 OH-
[C/mol]]m[
[A]
sm
mol22 FzS
iM
Electric current
Faraday constant
Area of the cathode
Stoichiometric coefficient
Oxygen flow
• Convection in a shear flow layer (Lévēque)
• Convection in a critical point (Levich)• Unsteady diffusion to the semiinfinite
space (Cotrel)• Steady diffusion through a finite layer• Unsteady diffusion through a finite layer
Convection in a shear flow layer (Lévēque)
Concentration c0
Shear rate
Circular cathode, zero concentration
Velocity profile
vxγ = dv/dx
31
32
0865.0
d
DM
c
Diffusion coefficient
Concentration
Shear rate
Cathode diameter
Oxygen flow
Convection in a shear flow layer (Lévēque)
Convection in a critical point (Levich)
Concentration c0
Rotation speed Ω
Concentration 0
Rotating disc electrode
Density
Convection in a critical point (Levich)
ConcentrationRotation speed
Viscosity
Rotating disc electrode
216
1
32
06205.0
DM c
Diffusion coefficient
Oxygen flow
0
5
10
15
20
25
30
-1.2-1-0.8-0.6-0.4-0.20
V (SCE)
A/m2
3000 RPM
2000 RPM
1000 RPM
400 RPM
100 RPM
Rotating disc electrode (RDE)
H2O2 + 2e- 2 OH-
O2 + 2 H2O + 2e- H2O2 + 2 OH-
O2 + 2 H2O + 4e- 4 OH-
2 H2O + 2e- H2 + 2 OH-
1
2
3
4
0 10 20 30 40 50 60T [oC]
D [10-9
m2/s]
Diffusivity of oxygen
RDA measurement
● water saturated by oxygen
● water saturated by air
Unsteady diffusion to the semiinfinite space (Cotrel)
Time t=0, concentration c0 everywhere
Time t>0, polarization, concentration c=0 at the cathode
Time t=0, switching the electrochemical cell - on
Diffusion starts, decreasing electric current
Unsteady diffusion to the semiinfinite space (Cotrel)
21
0564.0
tD
M c
Initial concentration
Diffusion coefficient
Time
Oxygen flow
Steady diffusion through a finite layer(Fick)
hDiffusion coefficient D
concentration c=0 at the cathode
concentration c0* in the environment
concentration c0 at outer layer boundary
h
cDM 0
Oxygen flow
Partial pressure p0* in the environment
h
pPM
*0
Permeability P
oxygensample
tissue soaked by KCl solution comunicating with the anodic space
Au cathode
Determination of permeability by Fatt (thin samples)
Unsteady diffusion through a finite layerFatt method
1
10
100
1000
0.01 0.1 1 10 100 1000t [s]
i [A]
Diffusion in the electrolyte layer
D ~h2/ttransition
Diffusion in the sample layer
c0 D ~i t1/2
Diffusion through the sample layer
P p0*/h ~ i
Thin samples
• + high current signal
• + short time if saturation
• - significant effect of electrolyte layer
Thick samples• + minor effect of electrolyte layer
• - low current signal
• - long time if saturation
• - inhomogeneous concentration field
Determination of permeability (thick samples)
Electrode driven oxygen diffusion
Oxygen
Determination of permeability (thick samples)
Electrode and inert driven oxygen diffusion
Oxygen
Inert Nitrogen
Au cathode insulation
resin
body of the electrode
polyamide tissue
sample
water saturated by oxygen
grid
sealing
electrolyte 0.01-n K2SO4 saturated by nitrogen
Determination of permeability (thick samples)
Au cathode insulation
resin
body of the electrode
polyamide tissue
sample
water saturated by oxygen
grid
sealing
electrolyte 0.01-n K2SO4 saturated by nitrogen
Determination of permeability (thick samples)
Unsteady diffusion through a finite layer
hDiffusion coefficient D
concentration c=0 at the cathode
concentration c0* in the environment
concentration c0 at outer layer boundary
Oxygen flow for t>0
Partial pressure p0* in the environment
Permeability P
Time t<0 Time t>0
p1*c1*c1
02
22
01
0 exp)1(21k
k th
DkMM
MM
SAMPLE LAYER
Unsteady diffusion through a finite layer
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20t [min]
i *
2/1
2
1388.0th
D
Diffusion coefficient D can be determined from the half time
01
0
MM
MM
t [min]
t1/2
Why not oxygen ?
•low current signal (and background currents)
•variable concentration (temperature, pressure)
•strange reactions (slow response, hysteresis)
•electrode poisoning
Low current signal
due to limited concentration of oxygen
solubility of oxygen at normal pressure :
~ 0.25 mol/m3 from air
~ 1.25 mol/m3 from pure oxygen
(100 times lower than for common salts !)
Background reactions
due to complicated mechanism of oxygen reduction !
due to trace of impurities !
Does the reduction of oxygen correspond to the difference of signals given for mass transfer driven by oxygen and blind current without oxygen ?
icorr = iOxygen - iNitrogen
?
icorr = iOxygen - iNitrogen
YES ?NO ?
O2 + 2 H2O + 4e- 4 OH-
0
5
10
15
20
-1.4-1.2-1-0.8-0.6-0.4-0.20
V (SCE)
A/m2
pH = 7
pH = 2pH = 3
pH = 11
pH = 12
O2 + 2 H2O + 4e- 4 OH-
O2 + 2 H2O + 2e- H2O2 + 2 OH-
2 H2O + 2e- H2 + 2 OH-
Effect of OH- ions
Au cathode insulation
resin
body of the electrode
polyamide tissue
sample
water saturated by oxygen
grid
sealing
electrolyte 0.01-n K2SO4 saturated by nitrogen
High signal in inert atmosphere !!!
Probably:2 H2O + 2e- H2 + 2 OH-
In absence of:O2 + 2 H2O + 4e- 4 OH-
Electrode treatment
• Gold? Platinum? Silver?
• Acids? Bases?
• Polarization +- ?
• Emery paper?
Conclusions
• Oxygen works !
• Less accurate results !
• Random impurities cause random behavior !
• Periodical checking of the system is strongly recommended !
Electrochemical diagnostics of oxygen mass transfer suitable for determination of :
• oxygen concentration
• oxygen diffusivity
• oxygen permeability
• oxygen solubility
• essential properties of liquid flow
Thank you for your attention
Kamil Wichterle and Jana Wichterlová
VSB-Technical University of Ostrava Ostrava, Czech Republic