a) b - École Polytechnique de Montréal

where the parameter z is dependent on the blend system and is evaluated experimentally for each
system.
Some other researchers focused on the elasticity or used it along with viscosity to predict the
phase inversion composition. The first approach based on the elasticity ratio was described by
Van Oene(Vanoene, 1972). He defined an equation to describe interfacial tension under dynamic
conditions adding an elastic properties term to interfacial tension under static conditions:
Equation 2-26. γ = γ + [ ( N ) − ( N ) ]
where γ eff is the effective interfacial tension under dynamic conditions, d represents droplet
diameter, γ is the static interfacial tension and (N2)d , (N2)m are the second normal stress
functions of the dispersed and matrix phases, respectively.
Considering that the storage modulus G′ and tan δ represent the elasticity of phase i, Bourry and
i
Favis(Bourry & Favis, 1998a) introduced elasticity into the understanding of phase inversion.
eff
d
12
Equation 2-27. φ G′
( ω)
I 1 2 =
φ G′
( ω)
Equation 2-28. φ tanδ
( ω)
I 1
1 =
φ tanδ
( ω)
G ′′ i
whereδ
= . It was reported(Bourry & Favis, 1998a) that these formulas are in much better
′
i
Gi
agreement with experimental data than other equations based only on viscous effects,
particularly at high shear rates. Steinmann et al.(Steinmann, et al., 2001) compared some of the
mentioned approaches and found that the factors are still inadequate to predict the phase
inversion point. Consequently, they developed a semi-empirical equation based on elasticity ratio
Ψ eff . G′′
:
Equation 2-29. φ
− . 34log(
Ψ ) + 0.
67
I 2
I 2
= 0 I 1
eff . G′
′
1
2
2
d
2
m
19