The behavior of a terminally anchored freely-jointed bead-rod chain, subjected to solvent shear flow, was investigated via Brownian dynamics simulations. Previous calculations have been improved by computing the segment density and fluid velocity profiles self-consistently. The segment density distributions, components of the radius of gyration, and chain attachment shear and normal stresses were found to be sensitive to low values of shear rate. Additionally, it was found that the thickness of a model polymer layer was a strong function of the shear rate, and that the functional dependence on shear rate changed dramatically as the chain length increased. For the longest chains studied, the thickness of the model polymer layer first increased as the shear rate increased, passed through a maximum, and then decreased at high shear rates, in accordance with experimental results in theta solvents. These results suggest that a dilute or semi-dilute layer model may explain hydrodynamic behavior previously thought to be due to the entanglements that occur in dense surface bound polymer layers.Nomenclature
a
i
acceleration of bead
i
-
b
radius of the beads
-
d
length of the rods connecting the chain beads
-
d
i
vector from bead
i to bead
i + 1
-
F
i
external force applied to bead
i
-
F
i
b
external force on bead
i due to Brownian motion of surrounding fluid
-
F
i
h
external force on bead
i due to viscous drag
-
F
i
s
external force on bead i due to surface interactions
-
f
Stokes drag coefficient
-
Boltzmann's constant
-
L
h
effective hydrodynamic thickness
-
m
i
mass of bead
i
-
N
number of beads on a model chain
-
n
number of chains anchored to the surface per unit surface area
-
P
segment density distribution
P pressure
-
Q
flow in a tube with no surface bound polymer layer
-
Q
a
flow in a tube with a surface bound polymer layer
-
R
g
vector representation of the radius of gyration
-
R
tube radius
-
r
radial coordinate in the tube geometry
-
S
ij
pair hydrodynamic interaction tensor for beads
i and
j
-
T
i
internal chain force in rod i connecting beads
i and
i + 1
-
T
X
component of the surface attachment force in the direction of the fluid flow
-
T
y
component of the surface attachment force perpendicular to the surface
-
T
temperature
-
v
i
velocity of the center of mass of bead
i
-
V
if
average fluid velocity at the location of bead
i
-
v
if
0
fluid velocity in the absence of a polymer chain
-
v
if
perturbation to the fluid velocity due to hydrodynamic interactions
-
V
b
bead volume = 4
b
3/3
-
scalar fluid speed in the axial direction down the tube
-
x
axial coordinate in the tube geometry
Greek symbols
w
apparent shear rate
-
fluid viscosity
-
polymer layer permeability
-
volume fraction of space occupied by chain beads
- (
w)
a
chain attachment stress perpendicular to the surface
- (
w)
a
chain attachment stress in the plane of the surface and in the direction of fluid flow
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