In:
Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 334 ( 1997-03-10), p. 251-291
Abstract:
We present a study of the rheological and optical behaviour of
Kramers bead–rod
chains in dilute solution using stochastic computer simulations. We consider two
model linear flows, steady shear and uniaxial extensional flow, in which we calculate
the non-Newtonian Brownian and viscous stress contribution of the polymers, their
birefringence and a stress-optic coefficient. We have developed a computer algorithm
to differentiate the Brownian from the viscous stress contributions which also
avoids the order (δ t ) −1/2 noise associated
with the Brownian forces. The strain or shear rate is made dimensionless with
a molecular relaxation time determined by simulated
relaxation of the birefringence and stress after a strong flow is applied. The characteristic long relaxation time obtained from the birefringence
and stress are equivalent
and shown to scale with N 2 where N is the
number of beads in the chain.
For small shear or extension rates the viscous contribution to the effective viscosity is constant and scales as N . We obtain an analytic
expression which explains the scaling and magnitude of this viscous contribution. In uniaxial extensional
flow we find an increase in the extensional viscosity with the dimensionless flow
strength up to a plateau value. Moreover, the Brownian stress also reaches a plateau
and we develop an analytic expression which shows that the Brownian stress in
an aligned bead–rod chain scales as N 3 . Using scaling arguments
we show that the Brownian stress dominates in steady uniaxial extensional
flow until large Wi , Wi ≈ 0.06 N 2 ,
where Wi is the chain Weissenberg number. In shear flow the viscosity decays as Wi −1/2 and the first normal stress
as Wi −4/3 at moderate Wi . We demonstrate
that these scalings can be understood through a quasi-steady balance of shear
forces with Brownian forces. For small Wi (in shear and uniaxial extensional
flow) and for long times (in stress relaxation) the stress-optic law is found
to be valid. We show that the rheology of the bead–rod chain can be qualitatively described by an equivalent FENE dumbbell for small Wi .
Type of Medium:
Online Resource
ISSN:
0022-1120
,
1469-7645
DOI:
10.1017/S0022112096004302
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1997
detail.hit.zdb_id:
1472346-3
detail.hit.zdb_id:
218334-1
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