In a recent study, the resolution of a polymer chain model was shown to significantly affect rheological predictions from Brownian dynamics (BD) simulations [Kumar and Dalal, “Effects of chain resolution on the configurational and rheological predictions from Brownian dynamics simulations of an isolated polymer chain in flow,” J. Non-Newtonian Fluid Mech. 315, 105017 (2023)], even in the absence of hydrodynamic interactions (HI) and excluded volume. In this study, we investigate the effects of chain resolution in the presence of HI. Toward this, we perform BD simulations of a long polymer chain, with the discretization level varying from a single Kuhn step (bead–rod model) to several tens of Kuhn-steps (bead–spring model). The chain models were subjected to flow fields of uniaxial extension (purely stretching) and steady shear (equal rates of stretching and rotation). Broadly, our results indicate an amplification of the differences observed between the differently resolved bead–rod and bead–spring models, in the presence of HI. Interestingly, all rheological predictions qualitatively fall in two groups for extensional flow, with the predictions from the bead–spring model with HI being close to those of the bead–rod model without HI. This indicates significantly reduced sensitivity of coarser bead–spring models to HI, relative to the one resolved to a single Kuhn step. However, in shear flow, the bead–spring rheological predictions fall between those of the bead–rod model with and without HI, forming a third group. This is linked to the presence of stretched and coiled states in the ensemble for shear flow. HI effects are large for the coiled states and weak for the stretched states, thereby yielding predictions that are intermediate between those for no HI and dominant HI. Thus, quite surprisingly, the quality of predictions of the bead–spring models is strongly affected by the physics of the flow field, irrespective of the parameterization.

1.
P. E.
Rouse
, Jr.
, “
A theory of the linear viscoelastic properties of dilute solutions of coiling polymers
,”
J. Chem. Phys.
21
,
1272
1280
(
1953
).
2.
B. H.
Zimm
, “
Dynamics of polymer molecules in dilute solution: Viscoelasticity, flow birefringence and dielectric loss
,”
J. Chem. Phys.
24
,
269
278
(
1956
).
3.
C.-C.
Hsieh
,
L.
Li
, and
R. G.
Larson
, “
Modeling hydrodynamic interaction in Brownian dynamics: Simulations of extensional flows of dilute solutions of DNA and polystyrene
,”
J. Non-Newtonian Fluid Mech.
113
,
147
191
(
2003
).
4.
C.-C.
Hsieh
and
R. G.
Larson
, “
Modeling hydrodynamic interaction in Brownian dynamics: Simulations of extensional and shear flows of dilute solutions of high molecular weight polystyrene
,”
J. Rheol.
48
,
995
1021
(
2004
).
5.
C.-C.
Hsieh
,
S.
Jain
, and
R. G.
Larson
, “
Brownian dynamics simulations with stiff finitely extensible nonlinear elastic-fraenkel springs as approximations to rods in bead-rod models
,”
J. Chem. Phys.
124
,
044911
(
2006
).
6.
A.
Cohen
, “
A Padé approximant to the inverse Langevin function
,”
Rheol. Acta
30
,
270
273
(
1991
).
7.
P. T.
Underhill
and
P. S.
Doyle
, “
On the coarse-graining of polymers into bead-spring chains
,”
J. Non-Newtonian Fluid Mech.
122
,
3
31
(
2004
).
8.
I.
Saha Dalal
,
N.
Hoda
, and
R. G.
Larson
, “
Multiple regimes of deformation in shearing flow of isolated polymers
,”
J. Rheol.
56
,
305
332
(
2012
).
9.
I.
Saha Dalal
,
C.-C.
Hsieh
,
A.
Albaugh
, and
R. G.
Larson
, “
Effects of excluded volume and hydrodynamic interactions on the behavior of isolated bead-rod polymer chains in shearing flow
,”
AIChE J.
60
,
1400
1412
(
2014
).
10.
P.
Kumar
and
I.
Saha Dalal
, “
Fraenkel springs as an efficient approximation to rods for Brownian dynamics simulations and modeling of polymer chains
,”
Macromol. Theory Simul.
31
,
2200008
(
2022
).
11.
P.
Kumar
and
I. S.
Dalal
, “
Effects of chain resolution on the configurational and rheological predictions from Brownian dynamics simulations of an isolated polymer chain in flow
,”
J. Non-Newtonian Fluid Mech.
315
,
105017
(
2023
).
12.
J. R.
Prakash
, “
Universal dynamics of dilute and semidilute solutions of flexible linear polymers
,”
Curr. Opin. Colloid Interface Sci.
43
,
63
79
(
2019
).
13.
R.
Prabhakar
,
J. R.
Prakash
, and
T.
Sridhar
, “
A successive fine-graining scheme for predicting the rheological properties of dilute polymer solutions
,”
J. Rheol.
48
,
1251
1278
(
2004
).
14.
T. T.
Pham
,
P.
Sunthar
, and
J. R.
Prakash
, “
An alternative to the bead-rod model: Bead-spring chains with successive fine graining
,”
J. Non-Newtonian Fluid Mech.
149
,
9
19
(
2008
).
15.
I.
Saha Dalal
,
A.
Albaugh
,
N.
Hoda
, and
R. G.
Larson
, “
Tumbling and deformation of isolated polymer chains in shearing flow
,”
Macromolecules
45
,
9493
9499
(
2012
).
16.
R. G.
Larson
, “
The rheology of dilute solutions of flexible polymers: Progress and problems
,”
J. Rheol.
49
,
1
70
(
2005
).
17.
Z.
Saeed
and
B. R.
Elbing
, “
Polymer drag reduction: A review through the lens of coherent structures in wall-bounded turbulent flows
,”
Phys. Fluids
35
,
081304
(
2023
).
18.
H.
Massah
,
K.
Kontomaris
,
W. R.
Schowalter
, and
T. J.
Hanratty
, “
The configurations of a fene bead-spring chain in transient rheological flows and in a turbulent flow
,”
Phys. Fluids A
5
,
881
890
(
1993
).
19.
A.
Córdoba
and
J. D.
Schieber
, “
The effects of hydrodynamic interactions on the swimming velocity and stability of a swarm of microswimmers
,”
Phys. Fluids
35
,
111901
(
2023
).
20.
M.
Davoodi
,
K.
Zografos
,
P.
Oliveira
, and
R.
Poole
, “
On the similarities between the simplified Phan-Thien–Tanner model and the finitely extensible nonlinear elastic dumbbell (Peterlin closure) model in simple and complex flows
,”
Phys. Fluids
34
,
033110
(
2022
).
21.
B.
Hetland
,
E.
Jettestuen
, and
A.
Hiorth
, “
Solving the constitutive equation of dilute polymeric flows: A general Fokker–Planck approach for linear elastic dumbbell models
,”
Phys. Fluids
35
,
093117
(
2023
).
22.
D.
Shogin
and
P. A.
Amundsen
, “
A charged finitely extensible dumbbell model: Explaining rheology of dilute polyelectrolyte solutions
,”
Phys. Fluids
32
,
063101
(
2020
).
23.
T.
Sato
,
Y.
Kwon
,
Y.
Matsumiya
, and
H.
Watanabe
, “
A constitutive equation for rouse model modified for variations of spring stiffness, bead friction, and Brownian force intensity under flow
,”
Phys. Fluids
33
,
063106
(
2021
).
24.
A.
Giacomin
,
S.
Coombs
,
M. C.
Pak
, and
K.-I.
Kim
, “
General rigid bead-rod theory for steady-shear flow
,”
Phys. Fluids
35
,
083111
(
2023
).
25.
J.
Rotne
and
S.
Prager
, “
Variational treatment of hydrodynamic interaction in polymers
,”
J. Chem. Phys.
50
,
4831
4837
(
1969
).
26.
H.
Yamakawa
and
G.
Tanaka
, “
Translational diffusion coefficients of rodlike polymers: Application of the modified oseen tensor
,”
J. Chem. Phys.
57
,
1537
1542
(
1972
).
27.
D. L.
Ermak
and
J. A.
McCammon
, “
Brownian dynamics with hydrodynamic interactions
,”
J. Chem. Phys.
69
,
1352
1360
(
1978
).
28.
R. B.
Bird
,
C.
Curtiss
,
R.
Armstrong
, and
O.
Hassager
,
Dynamics of Polymer Liquids
, Vol.
2
: Kinetic Theory (
Wiley
,
1987
).
29.
R.
Larson
and
H.
Brenner
,
Constitutive Equations for Polymer Melts and Solutions
, Butterworths Series in Chemical Engineering (
Elsevier Science
, 1988).
30.
M.
Doi
and
S.
Edwards
,
The Theory of Polymer Dynamics
(
Oxford University Press
,
Oxford
,
1988
).
31.
R.
Larson
,
H.
Hu
,
D.
Smith
, and
S.
Chu
, “
Brownian dynamics simulations of a DNA molecule in an extensional flow field
,”
J. Rheol.
43
,
267
304
(
1999
).
32.
P.
De Gennes
, “
Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients
,”
J. Chem. Phys.
60
,
5030
5042
(
1974
).
33.
J. S.
Hur
,
E. S.
Shaqfeh
, and
R. G.
Larson
, “
Brownian dynamics simulations of single DNA molecules in shear flow
,”
J. Rheol.
44
,
713
742
(
2000
).
34.
D. E.
Smith
,
H. P.
Babcock
, and
S.
Chu
, “
Single-polymer dynamics in steady shear flow
,”
Science
283
,
1724
1727
(
1999
).
35.
E. C.
Lee
and
S. J.
Muller
, “
Flow light scattering studies of polymer coil conformation in solutions under shear: Effect of solvent quality
,”
Polymer
40
,
2501
2510
(
1999
).
36.
E. C.
Lee
and
S. J.
Muller
, “
Flow light scattering studies of polymer coil conformation in solutions in extensional flow
,”
Macromol.
32
,
3295
3305
(
1999
).
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