concentration in bulk aqueous solution remains constant. In presence of an adsorbing
phase, it happens at a higher value. Through the monomer adsorption at the NAPL–
water interface, their interfacial tension is decreased which favors NAPL mobilization. Moreover, some other solution properties change, like the solubility of HOCs
which may be significantly increased for C S > CMC (Fig. 1.9b). Indeed, the
apparent solubility at the chemical equilibrium S i,app,eq for any sparingly soluble
component as a function of C S is given by:
S i,app,eq ¼ S i,w,eq þ SC C S À CMC
ð
Þ
ð 1:18Þ
where S i,w,eq is the apparent solubility in aqueous solution of the given compound
(mol l
À1 ) in absence of surfactant, SC is the solubilization capacity (mole mole
À1 ),
which is specific of the system (surfactant, HOC) and is often constant over a large
range of C S (Rosen and Kunjappu 2012). SC is defined as the average number of
host molecules solubilized in micelles per surfactant monomer that are under the
micellar form. Typical solubilization capacities for PAHs are lower than 0.4, showing that swollen micelles contain more surfactants than HOCs (Zhu and Feng 2003;
Liang et al. 2014). Expressed as the partition coefficient, K m,i , for any component
i between the micellar and the aqueous phases, it gives:
K m,i ¼
X i,m
X i,w
ð1:19Þ
with X i,m ¼
C i,m
C i,m þ C S,m
¼
SC
1 þ SC
and X i,w ¼
S i,w,eq
C w
¼ S i,w,eq V w
where X i,m and X i,w are the mole fraction for any solute i in the micellar and in the
aqueous phases, respectively, C i,m and C S,m are the concentrations (mol l
À1 ) of the
solute i and of the surfactant in the micellar phase, respectively, C w and V w are the
concentration and the molar volume of water, respectively (55.5 mol l
À1 and
1.8 Â 10
À2 l mol
À1 at 20
C). Valsaraj and Thibodeaux (1989) have shown that
K m,i is related to the partition constant for the solute i between octanol and water,
K ow,i , according to the following relationship:
log K m,i ¼ α log K ow,i þ β
ð1:20Þ
where α and β are positive values, which depend only on the solubilizing medium.
The SC and solubility values of HOCs in micellar solutions decrease as their K ow
value. However, low mobilization efficiencies for heavy PAHs larger than four rings
are generally observed, because of their very low solubility in pure water, the
difficulty to solubilize large molecules in micelles and the longer desorption kinetics.
24
N. Fatin-Rouge
phase, it happens at a higher value. Through the monomer adsorption at the NAPL–
water interface, their interfacial tension is decreased which favors NAPL mobilization. Moreover, some other solution properties change, like the solubility of HOCs
which may be significantly increased for C S > CMC (Fig. 1.9b). Indeed, the
apparent solubility at the chemical equilibrium S i,app,eq for any sparingly soluble
component as a function of C S is given by:
S i,app,eq ¼ S i,w,eq þ SC C S À CMC
ð
Þ
ð 1:18Þ
where S i,w,eq is the apparent solubility in aqueous solution of the given compound
(mol l
À1 ) in absence of surfactant, SC is the solubilization capacity (mole mole
À1 ),
which is specific of the system (surfactant, HOC) and is often constant over a large
range of C S (Rosen and Kunjappu 2012). SC is defined as the average number of
host molecules solubilized in micelles per surfactant monomer that are under the
micellar form. Typical solubilization capacities for PAHs are lower than 0.4, showing that swollen micelles contain more surfactants than HOCs (Zhu and Feng 2003;
Liang et al. 2014). Expressed as the partition coefficient, K m,i , for any component
i between the micellar and the aqueous phases, it gives:
K m,i ¼
X i,m
X i,w
ð1:19Þ
with X i,m ¼
C i,m
C i,m þ C S,m
¼
SC
1 þ SC
and X i,w ¼
S i,w,eq
C w
¼ S i,w,eq V w
where X i,m and X i,w are the mole fraction for any solute i in the micellar and in the
aqueous phases, respectively, C i,m and C S,m are the concentrations (mol l
À1 ) of the
solute i and of the surfactant in the micellar phase, respectively, C w and V w are the
concentration and the molar volume of water, respectively (55.5 mol l
À1 and
1.8 Â 10
À2 l mol
À1 at 20
C). Valsaraj and Thibodeaux (1989) have shown that
K m,i is related to the partition constant for the solute i between octanol and water,
K ow,i , according to the following relationship:
log K m,i ¼ α log K ow,i þ β
ð1:20Þ
where α and β are positive values, which depend only on the solubilizing medium.
The SC and solubility values of HOCs in micellar solutions decrease as their K ow
value. However, low mobilization efficiencies for heavy PAHs larger than four rings
are generally observed, because of their very low solubility in pure water, the
difficulty to solubilize large molecules in micelles and the longer desorption kinetics.
24
N. Fatin-Rouge