3. The average rate constants μ 0E and μ 0a for dynamic disentanglement and
disadsorption for polymeric chains.
4. The average recreation rate constants μ rE and μ ra for the two kinds of polymer
chains dynamically and reversely reentangled and readsorbed after the disentanglement and disadsorption.
5. With the above multiple dynamic and reversible reorganization (disentanglement and disadsorption, reentanglement and readsorption) of E and
A-constituent chains on two kinds of polymer chains, the reputation mechanism
leads to the displacement of mass center of polymeric chains and flow of fluids,
and demonstrates relaxation spectrum and mechanical behaviors of polymeric
suspensions. The corresponding rate constants are expressed as [8]:
μ tE ¼
G
0
NE
η 0E
1=m E
μ ta ¼
G
0
Na e
τ γ _
γ
η 0a
1=m a
ð5Þ
μ 1E ¼
G
0
NE
η 0E_ γ
! a E
μ 1a ¼
G
0
Na e
τ γ _
γ
η 0a
m a
ð6Þ
μ 0E ¼
η 0E
G
0
NE
! 1=m E
1 þ
η 0E_ γ
G
0
NE
! a E
"
#
ð7Þ
μ 0a ¼
η 0a
G
0
Na
! 1=m a
1 þ
η 0E e
τ γ _
γ
_
γ
G
0
Na
! a a
"
#
ð8Þ
where, μ 0E and μ 0a are average rate constants of the disentanglement and
disadsorption, respectively; η 0E , η 0a , G
0
NE and G
0
Na are viscosity and elastic
modulus of entangled and adsorbed chains at zero shear rate, respectively.
2.2.2 Destructibi1ity of Particle in Flowing System [8]
Generally, the hard filler is rigid particle which is hardly deformed. At low
deformation rates, the non-hydrodynamic interactions of the particles will dominate
the stress of polymeric suspensions. When the stress is larger than the forces of the
non-hydrodynamic interactions of the particles, the deformation rates have a strong
effect on the non-hydrodynamic interactions of the particles. In this time, the
primary particles may be destructed into secondary particles. However, the rate
of change in the number of secondary particles n ia (t) is depended both on the
number of destructible particles and their coefficient of diffusion. As a result, the
number of particles with increasing rate ( _
γ ), the corresponding increase in the
number of secondary A-constituent chains n ia (t) and modulus G
0
Na (t) will be
increased while the average constrained dimensional number of A-constituent
chains (-ma) with increasing rate ( _
γ ) is decreased. When the stress of fluids is
equal to the force of non-hydrodynamic interactions of particles,
166
Y. Chen and C. Xu
disadsorption for polymeric chains.
4. The average recreation rate constants μ rE and μ ra for the two kinds of polymer
chains dynamically and reversely reentangled and readsorbed after the disentanglement and disadsorption.
5. With the above multiple dynamic and reversible reorganization (disentanglement and disadsorption, reentanglement and readsorption) of E and
A-constituent chains on two kinds of polymer chains, the reputation mechanism
leads to the displacement of mass center of polymeric chains and flow of fluids,
and demonstrates relaxation spectrum and mechanical behaviors of polymeric
suspensions. The corresponding rate constants are expressed as [8]:
μ tE ¼
G
0
NE
η 0E
1=m E
μ ta ¼
G
0
Na e
τ γ _
γ
η 0a
1=m a
ð5Þ
μ 1E ¼
G
0
NE
η 0E_ γ
! a E
μ 1a ¼
G
0
Na e
τ γ _
γ
η 0a
m a
ð6Þ
μ 0E ¼
η 0E
G
0
NE
! 1=m E
1 þ
η 0E_ γ
G
0
NE
! a E
"
#
ð7Þ
μ 0a ¼
η 0a
G
0
Na
! 1=m a
1 þ
η 0E e
τ γ _
γ
_
γ
G
0
Na
! a a
"
#
ð8Þ
where, μ 0E and μ 0a are average rate constants of the disentanglement and
disadsorption, respectively; η 0E , η 0a , G
0
NE and G
0
Na are viscosity and elastic
modulus of entangled and adsorbed chains at zero shear rate, respectively.
2.2.2 Destructibi1ity of Particle in Flowing System [8]
Generally, the hard filler is rigid particle which is hardly deformed. At low
deformation rates, the non-hydrodynamic interactions of the particles will dominate
the stress of polymeric suspensions. When the stress is larger than the forces of the
non-hydrodynamic interactions of the particles, the deformation rates have a strong
effect on the non-hydrodynamic interactions of the particles. In this time, the
primary particles may be destructed into secondary particles. However, the rate
of change in the number of secondary particles n ia (t) is depended both on the
number of destructible particles and their coefficient of diffusion. As a result, the
number of particles with increasing rate ( _
γ ), the corresponding increase in the
number of secondary A-constituent chains n ia (t) and modulus G
0
Na (t) will be
increased while the average constrained dimensional number of A-constituent
chains (-ma) with increasing rate ( _
γ ) is decreased. When the stress of fluids is
equal to the force of non-hydrodynamic interactions of particles,
166
Y. Chen and C. Xu