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In the limit
the elastic force originated
from the thermal motion keeps the molecules coiled near their equilibrium
configuration, and the polymer solution is supposed to behave
like a Newtonian fluid.
Indeed, a perturbative expansion in
for the conformation tensor
 |
(3.26) |
plugged in the equation Eq. (3.20) gives for the zeroth and first
order terms:
 |
(3.27) |
We observe that at first order in
the elastic stress tensor
is proportional to the deformation tensor
 |
(3.28) |
which means that
the fluid is Newtonian up to higher order corrections
.
Anyway the presence of polymers
changes the properties of the fluid also in the Newtonian limit,
because the fluid is partially entrapped in the coiled polymers,
producing a change in the total viscosity of the solution
which is renormalized as:
 |
(3.29) |
Next: Energy balance
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Stefano Musacchio
2004-01-09