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

xc

Dtc

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

Dtxerfc

cc

s 4,1

1 Dtcm 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 = 0.9512xR2 = 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

tDxerfc

DDc

c121

0,21 4/1

tDDD

cm 1

21

0,2

/12

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-02xR2 = 9.83E-01

y = 1.03E-02xR2 = 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 + 3.5773R2 = 0.9825

y = 21.875x + 6.6392R2 = 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

/ m2 g]

gel HA

diffusion with chemical reactiondiffusion with chemical reaction

first order reactionfirst order reaction: A : A products products

121

21 kc

xc

Dtc

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 600time [s]

cond

uctiv

ity [m

S]

0.01M 0.05M 0.10M 0.20M

5

10

15

0 200 400 600time [s]

cond

uctiv

ity [m

S]1

2

3

pH

conductivity pH

diffusion with chemical reactiondiffusion with chemical reaction

1,1 cc im

tc

xc

Dtc im

,1

21

21

21

21

1 xcD

tc

1

DDef

211

xc

Dtc

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