**Greek letters**

200 Mass Transfer in Chemical Engineering Processes

Cs Concentration of target species in the stripping solution

Cs\* Concentration of target species at membrane-stripping interface

C(0,t) Concentration of target species at liquid membrane thickness = 0

C(x0,t) Concentration of target species at liquid membrane thickness of x0

ki Feed- or aqueous-phase mass transfer coefficient or mass transfer

km Organic-phase mass transfer coefficient or mass transfer coefficient in

ks Stripping-phase mass transfer coefficient or mass transfer coefficient

(moles per unit volume)

(moles per unit volume)

ELM Emulsion liquid membrane

ILM Immobilized liquid membrane

Kex Extraction equilibrium constant

L Length of the hollow fiber (cm)

lif Feed interfacial film thickness lis Stripping interfacial film thickness

MRn Complex species in the membrane phase N Number of hollow fibers in the module

Qf, Qfeed Volumetric flow rate of feed solution (cm3/s) Qs, Qstripping solution Volumetric flow rate of stripping solution (cm3/s)

<rA> Average value of the reaction rate of copper ions

Pm Membrane permeability coefficient Q Volumetric flow rate (cm3/min)

RH General form of the extractant ri Inside radius of the hollow fiber (cm) rlm Log-mean radius of the hollow ber ro Outside radius of the hollow ber (cm)

SLMs Supported liquid membranes

Vf Volume of the feed phase (cm3) VOCs Volatile organic compounds

x Spatial coordinate, direction of fiber axis

coefficient in feed phase

liquid membrane phase

in stripping phase

LMs Liquid membranes

n Order of the reaction P Permeability coefficient

M Target species

rA Reaction rate

t Time (min)

D Distribution ratio

J Flux (mol/cm2 s)

and any time (moles per unit volume)

and any time (moles per unit volume)

H+ Hydrogen ion representing pH gradient HFSLM Hollow fiber supported liquid membrane

kf Forward reaction rate constant (cm3/mgmin)

