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The effect of thermodynamic properties on sublation performance was illustrated by plotting the fractional removal versus the enhancement factor, H, which accounts for the surface-active nature of compounds. It was shown that large enhancement factors have favorable effects on fractional removal for nonvolatile compounds. However, as the volatility increases, the effect of the enhancement factor becomes less important.

Finally, the effects of design variables were discussed. It was shown that small improvements in sparger design (i.e., producing smaller bubbles) can have a significant, favorable effect on sublation performance. Additionally, it was shown that the effect of the column diameter on axial mixing does not influence sublation performance.

Acknowledgment

This work was supported in part by the National

Science Foundation/EPSCOR program {NSF/LaSER (1992-96) ADP-03}.

Nomenclature

a ) bubble radius, cm

A ) dimensionless air concentration, A CA/HCw°

CA ) effective concentration of pollutant in air, mol/cm3 Co ) concentration of pollutant in solvent, mol/cm3

Cv ) concentration of pollutant in air, mol/cm3 Cw ) concentration of pollutant in water, mol/cm3 CP ) chlorinated phenol

di ) bubble-wake thickness, cm D ) dispersion coefficient, cm2/s

Eo ) solvent-side entrainment number, Eo 3QAdi/QoKowa Ew ) water-side entrainment number, Ew 3(QAdi/Qwa) FR ) fractional removal, FR 1 - Cw/Cw°

H ) effective Henry's law constant, Hc + 3KA/a Hc ) Henry's law constant, cm3/cm3

i ) number of stages comprising the SCM

k ) overall mass-transfer coefficient (air-water), cm/s kl ) overall water-side mass-transfer coefficient (solvent-

water), cm/s

KA ) surface adsorption constant, cm

Kow ) solvent-water partition coefficient, cm3/cm3 Kow′′ ) octanol-water partition coefficient, cm3/cm3 L ) length of bubble column, cm

L/Dc ) column length to diameter ratio

m ) mass of pollutant carried by an air bubble, g

n ) number of stages comprising the water column, n ) i - 1

PA ) air-solvent capacity factor, PA QAHc/QoKow

Pw ) water-solvent capacity factor, Pw Eo/Ew Qw/QoKow PAH ) polynuclear aromatic hydrocarbon

Pe1 ) air-phase Peclet number, Pe1 QAL/ðrc2 D

Pe2 ) water-phase Peclet number, Pe2 QwL/ðrc2(1 - )D QA ) air flow rate, cm3/s (cm3/min)

Qo ) solvent flow rate, cm3/s (cm3/min) Qw ) water flow rate, cm3/s (cm3/min) rc ) radius of bubble column, cm

S ) dimensionless solvent concentration, S Co/KowCw° Sh1 ) air-phase Sherwood number, Sh1 3kL2/aDH Sh2 ) water-phase Sherwood number, Sh2 (3kL2/aD)( /

(1 - ))

StA ) air-side Stanton number (air-water), StA 3kðrc2L /

aQAH

Sto ) solvent-side Stanton number (solvent-water), Sto

kðrc2(1 - )/QoKow

Stw ) water-side Stanton number (solvent-water), Stw

klðrc2(1 - )/Qw

Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996 1697

StwA ) water-side Stanton number (air-water), StwA

3kðrc2L /aQw

te ) exposure time

ug ) superficial gas velocity, cm/s Vb ) bubble volume, cm3

Vo ) volume of solvent, cm3 Vw ) wake volume, cm3

W ) dimensionless water concentration, W Cw/Cw°

Greek Letters

) gas holdup, cm3/cm3

H ) Henry's enhancement factor, H 1 + 3KA/aHc) scale factor, QoL2/DVo

¡ ) surface concentration, mol/cm2

ì) dispersivity, cm

í) fluid viscosity, g/cm s F ) fluid density, g/cm3

ó ) surface tension, dyn/cm

ª ) separation factor, ª Co/KowCw ô ) dimensionless time, ô tD/L2 ê ) dimensionless distance, ê x/L ¾ ) kinetic factor

Appendix

The analytic solution to the SCM with i ) 2 (n ) 1)

is

W ) [(1 + StA)(1 + Sto + Eo + PA)]/

[(1 + StA){(1 + PA)(1 + Ew + Stw) + Eo + Sto} +

StwA(1 + Eo + Sto + PA) - StAPA H(Ew + Stw)]

A ) [StA(1 + Sto + Eo + PA)]/

[(1 + StA){(1 + PA)(1 + Ew + Stw) + Eo + Sto} +

StwA(1 + Eo + Sto + PA) - StAPA H(Ew + Stw)]

S ) [(1 + StA)(Sto + Eo) + PAStA H]/

[(1 + StA){(1 + PA)(1 + Ew + Stw) + Eo + Sto} +

StwA(1 + Eo + Sto + PA) - StAPA H(Ew + Stw)]

By manipulating eq 15, one can express the fractional removal and the separation factor in simple terms of the water and solvent concentrations,

When the analytic solution is substituted for W and S, the exact solutions for the fractional removal and the separation factor result.

1698 Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996

1 - ª ) ( StA )

1 + PA 1 - H1 + StA

The appropriate boundary conditions for the ADM2 are

ddAêjê)0 ) 0 ddWê jê)1 ) 0

ddAêjê)1 ) -Pe1Aê)1

ddWê jê)0 ) Pe2(Ew + Stw)(Wjê)0 - S) - Pe2(1 - Wjê)0)

where it has been assumed that the solvent and air enter the column free of pollutant. The analytic solution is given in terms of the following variables:

a1 ) Pe1 - Pe2

a2 ) -(Pe1Pe2 + Sh1 + Sh2)

a3 ) Sh1Pe2 - Sh2Pe1

cos õ ) R/x-Q3

PA H

ç2 ) Pe2(Ew + Stw)1 + PA + Eo + Sto

and

S ) HPAAjê)0 + (Eo + Sto)Wjê)0

1 + PA + Eo + Sto

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Received for review June 16, 1995

Accepted February 13, 1996X

IE9503656

X Abstract published in Advance ACS Abstracts, April 1, 1996.