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Revealing mass transfer and hydrodynamic effects in a PRDC column by using the integration of extraction and separation for molybdenum and tungsten ions from aqueous solution

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The present work is performed to assess the hydrodynamic parameters and mass transfer coefficients in a PRDC column for the chemical reaction systems. By considering the selective extraction of molybdenum from tungsten, the extraction parameters and synergistic enhancement factor were interpreted at the batch experiments. In the column experiments, the impacts of operating conditions such as the agitation rate, inlet solvent phase velocity as well as inlet aqueous phase velocity were studied on the drop behavior, overall mass transfer coefficients, and extraction efficiencies. The modified correlations by using relationship of dimensionless numbers were illustrated to estimate the hydrodynamic factors (holdup value and the Sauter mean drop diameter) under the physical and reactive systems. The mass transfer coefficients for the continuous phase were evaluated by the axial diffusion method in both extraction and stripping stages. It was observed that the column performance was primarily affected by the agitation speed and mass transfer direction, but this phenomenon slightly changes with the inlet phase velocities. The previous empirical models were compared with the obtained mass transfer data, and the available models were failed to precisely anticipate the experimental data due to chemical reaction conditions. Finally, two new models based on the dimensionless numbers were derived for calculating the overall Sherwood number. The value of separation factor in the extractor indicated the column capacity with the excellent separation for molybdenum from tungsten in the sulfate solution.

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Average absolute relative error (-)

a :

Interfacial area (m2/m3)

d 32 :

Sauter mean drop diameter (m)

D :

Distribution coefficient (-)

D col :

Column diameter (m)

D c :

Molecular diffusivity of continuous phase (m2/s)

D R :

Disk diameter (m)

D S :

Stator ring diameter (m)

E :

Axial mixing coefficient (m2/s)


Extraction efficiency (-)

g :

Acceleration due to gravity (m/s2)

H :

Effective height of the column (m)

h c :

Compartment height (m)

K oc :

Overall continuous mass transfer coefficient (m/s)

K c :

Continuous mass transfer coefficient (m/s)

K d :

Dispersed mass transfer coefficient (m/s)

m :

Distribution ratio (-)

N :

Agitation speed (1/s)

N oc :

Number of ‘true’ transfer unit (-)


Reynolds number (-)


Schmitt number (-)


Péclet number (-)

P n org log :

Probability of number density (-) for normal or logarithmic function

Pec :

Continuous-phase Péclet number (= d32Vs/Dc)


Concentration of metal ions (mg/L)

[M]aq, s :

Concentration of metal ions in the stripping solution (mg/L)

V org :

Volume of organic phase (ml)

V aq :

Volume of aqueous phase (ml)

V aq, s :

Volume of aqueous phase in the stripping solution (ml)

d e :

Equivalent diameter (m)

d i :

Droplet diameter (m)

n i :

Number of droplets of mean diameter di (-)


Separation factor (-)


Synergistic enhancement factor (-)


Sherwood number (-)


Stripping efficiency (-)


Number values of data points

V :

Superficial velocity (m/s)


Specific volume (m3)

\(\overline{V}_{\text{c}}\) :

Continuous phase true velocity (m/s)

V s :

Slip velocity (m/s)

x :

Mass fraction of elements in continuous phase (-)

x * :

Equilibrium mass fraction (-)

y :

Mass fraction of elements in dispersed phase (-)

α :

Constant parameter of probability of density function (-)

β :

Constant parameter of probability of density function (-)

ρ c :

Density of continuous phase (Kg/m3)

ρ d :

Density of dispersed phase (Kg/m3)

µ d :

Viscosity of dispersed phase (pa.s)

µ c :

Viscosity of continuous phase (pa.s)

φ :

Dispersed phase holdup (-)

σ :

Interfacial tension (N/m)

κ :

Viscosity ratio of µdc


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This work was not supported by any funding.

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Correspondence to Mehdi Asadollahzadeh.

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Shakib, B., Torkaman, R., Torab-Mostaedi, M. et al. Revealing mass transfer and hydrodynamic effects in a PRDC column by using the integration of extraction and separation for molybdenum and tungsten ions from aqueous solution. Chem. Pap. 74, 4295–4313 (2020).

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