84
4
The three parameters are η 0 ,
γ 0 , and n.
5 Bird–Carreau Model—This model overcomes the limitations of
independence of both temperature and molecular weight
distribution of the power law and the truncated power law. The
Bird–Carreau model is dependent on temperature and
molecular weight distribution. This model has four parameters
and may be written as
η η
η η
λ γ
0
0
2
1 2
1
−
−
= +( )
∞
∞
−
( )
n /
(4.6)
where
5 λ = Time constant
5 η = Viscosity
5 η 0 = Initial viscosity
5 η ∞ = Infinite viscosity
The time constant, λ, is the time after which shear thinning starts
and any change in molecular configuration becomes effective. The
melt flow index is the indication for molecular weight.
5 Ellis Model—This model has three parameters and may be
written as
η
η
τ τ
τ τ
α
0
1 2
1 2
1 2
1
1
1
= +(
)
= +(
)
−
( )
−
( )
/
/
/
/
/
n
(4.7)
where
5 α = 1/n
5 τ = Shear stress
5 τ 1/2 = Shear stress at η = η 0 /2
5 λ = Time constant
5 η = Viscosity
5 η 0 = Initial viscosity
4.1.1.4 Factors Affecting Viscosity
The factors which affect the viscosity of composite medium are as
follows:
5 Temperature—Temperature causes the separation of polymeric
chains when thermal energy surpasses the bond (secondary
bonds) energy among the polymeric chains. Therefore, the
viscosity of the composite mix at high temperatures is reduced.
5 Molecular Weight—Higher molecular weight signifies longer
polymeric chains; hence, more sites are available for intermolecular attraction on the polymeric chain of a polymer. This
causes high-melt viscosities or high temperatures to overcome
the intermolecular attraction among the polymeric chains of
the polymer.
5 Pressure—High pressures lead to high viscosities of polymer
melt or liquid resin because the pressure puts polymeric chains
under a physical constraint to move freely. This leads to an
increase in the viscosity of liquid resin and polymeric melt
under pressure.
Chapter 4 · Rheology in Processing of Polymeric Composites
4
The three parameters are η 0 ,
γ 0 , and n.
5 Bird–Carreau Model—This model overcomes the limitations of
independence of both temperature and molecular weight
distribution of the power law and the truncated power law. The
Bird–Carreau model is dependent on temperature and
molecular weight distribution. This model has four parameters
and may be written as
η η
η η
λ γ
0
0
2
1 2
1
−
−
= +( )
∞
∞
−
( )
n /
(4.6)
where
5 λ = Time constant
5 η = Viscosity
5 η 0 = Initial viscosity
5 η ∞ = Infinite viscosity
The time constant, λ, is the time after which shear thinning starts
and any change in molecular configuration becomes effective. The
melt flow index is the indication for molecular weight.
5 Ellis Model—This model has three parameters and may be
written as
η
η
τ τ
τ τ
α
0
1 2
1 2
1 2
1
1
1
= +(
)
= +(
)
−
( )
−
( )
/
/
/
/
/
n
(4.7)
where
5 α = 1/n
5 τ = Shear stress
5 τ 1/2 = Shear stress at η = η 0 /2
5 λ = Time constant
5 η = Viscosity
5 η 0 = Initial viscosity
4.1.1.4 Factors Affecting Viscosity
The factors which affect the viscosity of composite medium are as
follows:
5 Temperature—Temperature causes the separation of polymeric
chains when thermal energy surpasses the bond (secondary
bonds) energy among the polymeric chains. Therefore, the
viscosity of the composite mix at high temperatures is reduced.
5 Molecular Weight—Higher molecular weight signifies longer
polymeric chains; hence, more sites are available for intermolecular attraction on the polymeric chain of a polymer. This
causes high-melt viscosities or high temperatures to overcome
the intermolecular attraction among the polymeric chains of
the polymer.
5 Pressure—High pressures lead to high viscosities of polymer
melt or liquid resin because the pressure puts polymeric chains
under a physical constraint to move freely. This leads to an
increase in the viscosity of liquid resin and polymeric melt
under pressure.
Chapter 4 · Rheology in Processing of Polymeric Composites