diffusion studies in humic gels
DESCRIPTION
Marek Burian Martina Klučáková Miloslav Pekař. Diffusion studies in humic gels. Institute of Physical and Applied Chemistry Faculty of Chemistry Brno University of Technology Purkyňova 118 612 00 Brno Czech Republic. why study diffusion of metal ions in humic gels?. - PowerPoint PPT PresentationTRANSCRIPT
Diffusion studies in humic gelsDiffusion studies in humic gels
Marek BurianMarek BurianMartina KlučákováMartina Klučáková
Miloslav PekařMiloslav Pekař
Institute of Physical and Applied ChemistryFaculty of Chemistry
Brno University of TechnologyPurkyňova 118
612 00 BrnoCzech Republic
why study diffusion of metal ions why study diffusion of metal ions in humic gels?in humic gels?
HA form very easily complexes with ions of HA form very easily complexes with ions of transition metalstransition metals
rate of interaction in sol rate of interaction in sol >> >> rate of interaction rate of interaction in solidin solid
strongly diffusion-effected interaction with strongly diffusion-effected interaction with solid HAsolid HA
diffusion effect in heterogenous systemdiffusion effect in heterogenous system
model system for diffusion studymodel system for diffusion study= humic gel = humic gel
experimentally more tractableexperimentally more tractable simple suppression of convective and thermal simple suppression of convective and thermal
mixingmixing close to water environmentclose to water environment relation to real (natural) systemsrelation to real (natural) systems
non-stationary diffusionnon-stationary diffusion
11 cgradDdivtc
Fick law: one-dimensional problem; Fick law: one-dimensional problem; DD DD ((cc11))
211
x
cD
t
c
diffusion of Codiffusion of Co2+2+ ions into humic ions into humic gels (experimental arrangement)gels (experimental arrangement)
diffusion from constant sourcediffusion from constant source
Dt
xerfc
c
c
s 4,1
1 Dt
cm s,12
tt = 0 = 0 xx 0; 0; LL cc11 = 0 = 0
tt 0 0 xx = 0 = 0 cc11 = const. = const.
t t 0 0 xx = = LL / 2 / 2 cc11 / / xx = 0 = 0
diffusion from constant source diffusion from constant source (supersaturated solution) (supersaturated solution)
0
5
10
15
20
25
0 10 20 30 40 50
x [mm]
c [m
ol/d
m3 ]
y = 0.9512x
R2 = 0.9986
0
100
200
300
0 100 200 300
time1/2 [s1/2]to
tal f
lux
[mol
/m2 ]
DDnumnum , m , m22/s/s DDpubpub , m , m22/s/s
7.987.981010-10-10 1.461.461010-9-9
diffusion from time-variable sourcediffusion from time-variable source
tD
xerfc
DD
cc
121
0,21
4/1
tD
DD
cm 1
21
0,2
/1
2
tt = 0 = 0 xx 0; 0; LL cc11 = 0 = 0
t t = 0= 0 xx << 0; 0; xx > > LL cc22 = = cc2,02,0
tt 0 0 xx = 0 = 0 DD11 cc11 / / xx = = DD22 cc2 2 / / xx
tt 0 0 xx = = LL / 2 / 2 cc22 / / xx = 0 = 0
tt x x = 0= 0 = = cc11 / / cc22
diffusion from time-variable source diffusion from time-variable source (decrease of solution concentration)(decrease of solution concentration)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
x [mm]
c [m
mol
/gH
K]
0.01M 0.05M 0.20M 0.40M
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
x [mm]
c [m
mol
/gH
K]
10min 30min 6h 24h
diffusion from time-variable source diffusion from time-variable source (decrease of solution concentration)(decrease of solution concentration)
y = 5.51E-02x
R2 = 9.83E-01
y = 1.03E-02x
R2 = 9.88E-01
0
5
10
15
20
0 100 200 300 400
t1/2 [s1/2]
tota
l flu
x [m
mol
/ m2 g]
gel HA
y = 12.652x + 3.5773
R2 = 0.9825
y = 21.875x + 6.6392
R2 = 0.9873
0
5
10
15
20
0 0.1 0.2 0.3 0.4 0.5
cin [mol/dm3]
slop
e [m
mol
/ m
2 g]
gel HA
diffusion with chemical reactiondiffusion with chemical reaction
first order reactionfirst order reaction: A : A products products
121
21 kc
x
cD
t
c
tt = 0 = 0 xx 0; 0; LL cc11 = 0 = 0
tt 0 0 xx = 0 = 0 cc11 = = cc1,0 1,0 expexp - -ktkt
tt 0 0 xx = = LL / 2 / 2 cc11 / / xx = 0 = 0
interaction Cointeraction Co2+2+ with humic gel with humic gel
summary reactionsummary reaction: Co: Co2+2+ + H + H22R R CoR + 2H CoR + 2H++
0
0.01
0.02
0.03
0.04
0 200 400 600
time [s]
cond
ucti
vity
[m
S]
0.01M 0.05M 0.10M 0.20M
5
10
15
0 200 400 600
time [s]
cond
ucti
vity
[m
S]
1
2
3
pH
conductivity pH
diffusion with chemical reactiondiffusion with chemical reaction
1,1 cc im
t
c
x
cD
t
c im
,1
21
21
21
21
1 x
cD
t
c
1
D
Def
211
x
cD
t
c
diffusion with chemical reactiondiffusion with chemical reaction
0.0
0.5
1.0
1.5
0 200 400 600
time [s]
c [m
ol/d
m3 ]
D-pub. D-exp.
0
1
2
3
0 1 2 3
x [cm]
c [m
ol/d
m3 ]
1h-exp. 24h-exp. 1h-calc. 24h-calc.
conclusionsconclusions
simple but effective method
effect of chemical reaction!
numerical analysis inevitable
future directionsfuture directions
other elements
diffusion from saturated gel