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Modelling of interfacial mass transfer in microfluidic solvent extraction: part II. Heterogeneous transport with chemical reaction

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Abstract

The use of a microfluidic device in determining the extraction kinetics of CoII ions by di-(2-ethylhexyl) phosphoric acid (DEHPA) was demonstrated. Experimental data obtained using a Y-Y-shaped microchannel were modelled using a finite volume method. The contributions of diffusion and reaction transport resistances to the overall rate of mass transfer were obtained. A diffusion-controlled transfer assumption could not account for the experimental data, confirming that transport occurs under a mixed reaction–diffusion resistance regime. The reaction rate constant was determined to be \((2.4 \pm 0.6) \times 10^{-10}\) m/s, in good agreement with corresponding Lewis cell measurements from the literature.

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Abbreviations

A :

Kinetic rate constant (m/s)

Bo :

Bond number (\({Bo} = \Updelta \rho g D_{\rm h} ^2/\gamma \))

c :

Local species concentration (mM)

\({\fancyscript{D}} \) :

Diffusivity (m2/s)

\(D_{\rm h}\) :

Hydraulic diameter of microchannel half-volume (m)

F :

Volumetric flow rate (m3/s)

g :

Gravitational acceleration (m/s2)

I :

Total initial ionic strength (mM)

k 1, k −1, k 2 :

Interfacial reaction rate constants (m/s)

k f, k b :

Forwards/backwards reaction rate constant

K 2 :

Dimerisation constant \(([(\text{HL})_2]_{\rm org}/[\text{HL}]^2_{\rm org})\) (mM−1)

K d :

Distribution constant (\([\text{HL}]_{\rm org}/[\text{HL}]_{\rm aq}\))

K eq :

Equilibrium constant

MAPEexp :

Mean Absolute Percentage Error (experimental reference)

R :

Extraction rate per unit area (mol/m2 s)

RSS:

Residual sum of squares (mM2)

u :

Fluid velocity (m/s)

V N :

Molar volume of solute at normal boiling point (m3/kmol)

x, y, z :

Cartesian coordinates (m)

γ:

Interfacial tension (N/m)

ε:

Molar absorptivity (M−1 cm−1)

ρ:

Fluid density (kg/m3)

μ:

Dynamic viscosity (Pa s)

ν:

Stoichiometric coefficient

0:

Initial

aq:

Aqueous phase

exp:

Experiment

i :

ith phase

int:

Interface

j :

jth species

org:

Organic phase

sim:

Simulation

Ac :

Acetate

AcH:

Acetic acid

CFD:

Computational fluid dynamics

DEHPA:

Di-(2-ethylhexyl) phosphoric acid

DHBA:

2,2′-Dihydroazobenzene

HL:

Condensed notation for DEHPA

(HL)2 :

Condensed notation for the dimeric form of DEHPA

HTCO:

1,4,7,10,13,16-Hexathiacyclooctadecane

Kelex 100:

7-(4-Ethyl-1-methyloctyl)-8-hydroxyquinoline

L :

Condensed notation for the deprotonated form of DEHPA

LIX 84:

2-Hydroxy-5-nonylacetophenone oxime

MAPE:

Mean Absolute Percentage Error

MTWCR:

Mass Transfer With Chemical Reaction

PC-88A:

2-Ethylhexyl phosphonic acid mono 2-ethylhexyl ester

TBP:

Tri-n-butylphosphate

SX:

Solvent extraction

μSX:

Microfluidic solvent extraction

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Acknowledgments

Support from the Australian Research Council and the Particulate Fluids Processing Centre is gratefully acknowledged.

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Ciceri, D., Mason, L.R., Harvie, D.J.E. et al. Modelling of interfacial mass transfer in microfluidic solvent extraction: part II. Heterogeneous transport with chemical reaction. Microfluid Nanofluid 14, 213–224 (2013). https://doi.org/10.1007/s10404-012-1039-y

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  • DOI: https://doi.org/10.1007/s10404-012-1039-y

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