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Experimental investigation of terminal velocity and Sherwood number of rising droplet in an extraction column

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Abstract

Mass transfer and terminal velocity of toluene drops rising in an extraction column was studied experimentally. The impact of packing was investigated by inserting a structured packing in three different heights of 10, 25 and 40 cm inside the column. The effect of packing height, flow rate and drop size on terminal velocity and Sherwood number were investigated and the results were also compared with the case of non-packed column. It was discussed that a 30% increase in Sherwood number could be achieved using the packing with 40 cm in height. It was also found that for Eötvös number, Eö, higher than 0.4, the deformation of drops and velocity oscillation appeared, which affected the terminal velocity. Finally, two correlations were proposed, which permitted the prediction of deformation and extraction ratio versus the dimensionless numbers of Reynolds, Eötvös and the packing height ratio.

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Abbreviations

AR:

Aspect ratio of drop, (dvert./dhor)

\(c\) :

Solute concentration in dispersed phase (kg/m3)

\(c_{0}\) :

Initial concentration of solute in dispersed phase (kg/m3)

\(c^{*}\) :

Equilibrium concentration of solute in dispersed phase (kg/m3)

\(d\) :

Drop size (m)

\(d_{N}\) :

Needle size of nozzle (mm)

\(D\) :

Molecular diffusivity (m2/s)

E:

Extraction ratio (–)

Eö:

Eötvös number \((\frac{{(\rho_{c} - \rho_{d} )gd^{2} }}{\gamma })\)

h:

Rising distance (cm)

hp:

Packing height (cm)

\(k\) :

Mass transfer coefficient (m/s)

M:

Molecular weight of solvent (kg/kmol)

Q:

Volumetric flow rate of dispersed phase (ml/min)

Re:

Reynolds number \(\left( {\frac{{\rho_{c} u_{t} d}}{{\mu_{c} }}} \right)\)

Sh:

Sherwood number \(\left( { = \frac{{k_{d} d}}{{D_{A,m} }}} \right)\)

t:

Rising time (s)

T:

Temperature (K)

\(u_{t}\) :

Terminal velocity of a single drop (m/s)

V:

Molar volume at normal boiling temperature (m3/kmol)

We:

Weber number, \(\left( {\frac{{\rho_{c} u_{t}^{2} d}}{\gamma }} \right)\)

\(\gamma\) :

Interfacial tension (N/m)

\(\mu\) :

Viscosity (Pa.s)

\(\varphi\) :

Association factor of the solvent (= 2.6 for water)

\(\rho\) :

Density (kg/m3)

\(\Delta \rho\) :

Density difference (ρc- ρd), (kg/m3)

A:

Solute

\(c\) :

Continuous phase

crit:

Critical

d :

Dispersed phase

hor.:

Horizontal

i:

Counter

m:

Mixture

np:

Non-Packed

o:

Overall

p:

Packed

vert.:

Vertical

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Azizi, Z. Experimental investigation of terminal velocity and Sherwood number of rising droplet in an extraction column. Heat Mass Transfer 53, 3027–3035 (2017). https://doi.org/10.1007/s00231-017-2037-0

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