a) b - École Polytechnique de Montréal

Reignier et al.(Reignier, et al., 2003) studied the effect of different factors on the composite
droplet formation. They showed the influence of elasticity on composite droplet formation by
introducing the dynamic interfacial tension term taken from VanOene(Vanoene, 1972) in the free
energy model developed by Guo et al.(Guo, Packirisamy, et al., 1997), and developed new
equations for the interfacial free energies in conditions of dynamic mixing:
Equation 2-35.
Equation 2-36.
Equation 2-37.
2 ⎡ Ri
⎤ 2 ⎡ Ri
( ∑ Aγ
) = 4πR
γ + ( N − N ) + 4πR
γ + ( N − N )
i
⎢
⎣
2 ⎡ Re
⎤ 2 ⎡ Ri
( ∑ Aγ
) = 4πR
γ + ( N − N ) + 4πR
γ + ( N − N )
i
ij B+
C
ij B
C
⎢
⎣
2 ⎡ Re
⎤ 2 ⎡ Ri
⎤
( ∑ Aiγ
ij ) C = 4πRe
⎢γ
CA + ( N1,
C − N1,
A ) ⎥
+ 4πRi
⎢γ
BC + ( N1,
B − N1,
C ) ⎥⎦
B
e
i
⎣
BA
BA
Normal stress differences for the phases A, B, and C are referred to by N1, γ ij is the interfacial
tension between the components i and j, and the internal and external radius of the core-shell
droplets are shown by Ri and Re, respectively. Reignier et al.(Reignier, et al., 2003) indicated that
the viscosity ratio estimated at a constant shear stress rather than at a constant shear rate is
accurate to study the effect of viscosity ratio on the morphology because shear stress is more
continuous at the interface between the dispersed phase and the matrix phase.
The effect of molecular weight of phases on the encapsulation process was
investigated(Reignier, et al., 2003). The equilibrium morphology for HDPE/low molecular
weight PS/low molecular weight PMMA illustrates that PS encapsulates PMMA (Figure 2-6a).
When components were replaced by high molecular weight PS and high molecular weight
PMMA, an inversion in encapsulation occurred and PMMA encapsulated PS (Figure 2-6b). They
related this discrepancy to the high viscosity of PS that does not allow PMMA to be
encapsulated. Finally, considering all the observations, they concluded that interfacial energy
reduction is the main driving force controlling encapsulation effects and that the viscosity ratio
and the absolute viscosity have little influence on encapsulation phenomena in composite
droplets.
6
6
6
1,
B
1,
B
1,
A
1,
A
⎥
⎦
⎥
⎦
⎦
i
i
⎢
⎣
⎢
⎣
⎣
CA
CB
6
6
6
1,
C
1,
C
1,
A
1,
B
28
⎤
⎥
⎦
⎤
⎥
⎦