The so-called “raspberry” model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by Lobaskin and Dünweg [New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy this problem by adding internal coupling points. Finally, we examine a non-convex shape, namely, a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in de Graaf et al. [J. Chem. Phys. 143, 084108 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates.

1.
L.
Euler
,
Mem. Acad. Sci. Inst. Berlin
11
,
274
(
1757
).
2.
C.
Navier
,
Mem. Acad. Sci. Inst. France
6
,
389
(
1827
).
3.
G.
Stokes
,
Trans. Cambridge Philos. Soc.
8
,
287
(
1845
).
4.
J.
Hofman
,
H.
Clercx
, and
P.
Schram
,
Physica
268
,
353
(
1999
).
5.
J.
Giddings
,
Sep. Sci. Technol.
13
,
241
(
1978
).
6.
R.
Noel
,
K.
Gooding
,
F.
Regnier
,
C.
Orr
, and
M.
Mullins
,
J. Chromatogr. A
166
,
373
(
1978
).
7.
J.
de Graaf
,
T.
Peter
,
L.
Fischer
, and
C.
Holm
,
J. Chem. Phys.
143
,
084108
(
2015
).
8.
H.
Hasimoto
,
J. Fluid Mech.
5
,
317328
(
1959
).
9.
A.
Zick
and
G.
Homsy
,
J. Fluid Mech.
115
,
13
(
1982
).
10.
H.
Brenner
,
J. Colloid Interface Sci.
32
,
141
(
1970
).
11.
M.
Zuzovsky
,
P.
Adler
, and
H.
Brenner
,
Phys. Fluids
26
,
1714
(
1983
).
12.
B.
Dünweg
and
A.
Ladd
, “
Lattice Boltzmann simulations of soft matter systems
,” in
Advanced Computer Simulation Approaches for Soft Matter Sciences III
,
Advances in Polymer Science
Vol.
221
, edited by
C.
Holm
and
K.
Kremer
(
Springer
,
Berlin, Heidelberg
,
2009
), pp.
89
166
.
13.
P.
Ahlrichs
and
B.
Dünweg
,
J. Chem. Phys.
111
,
8225
(
1999
).
14.
V.
Lobaskin
and
B.
Dünweg
,
New J. Phys.
6
,
54
(
2004
).
15.
A.
Chatterji
and
J.
Horbach
,
J. Chem. Phys.
122
,
184903
(
2005
).
16.
17.
C.
Aidun
and
Y.
Lu
,
J. Stat. Phys.
81
,
49
(
1995
).
19.
J.
Wu
and
C.
Aidun
,
Int. J. Numer. Methods Fluids
62
,
765
(
2010
).
20.
U.
Schiller
,
Comput. Phys. Commun.
185
,
2586
(
2014
).
21.
P.
Hoogerbrugge
and
J.
Koelman
,
Europhys. Lett.
19
,
155
(
1992
).
22.
P.
Español
and
P.
Warren
,
Europhys. Lett.
30
,
191
(
1995
).
23.
A.
Malevanets
and
R.
Kapral
,
J. Chem. Phys.
110
,
8605
(
1999
).
24.
T.
Ihle
and
D.
Kroll
,
Phys. Rev. E
67
,
066705
(
2003
).
25.
J.
Brady
and
G.
Bossis
,
Annu. Rev. Fluid Mech.
20
,
111
(
1988
).
26.
V.
Lobaskin
,
B.
Dünweg
,
M.
Medebach
,
T.
Palberg
, and
C.
Holm
,
Phys. Rev. Lett.
98
,
176105
(
2007
).
27.
V.
Lobaskin
,
D.
Lobaskin
, and
I.
Kulić
,
Eur. Phys. J.: Spec. Top.
157
,
149
(
2008
).
28.
S.
Raafatnia
,
O.
Hickey
, and
C.
Holm
,
Phys. Rev. Lett.
113
,
238301
(
2014
).
29.
M.
Belushkin
,
R.
Winkler
, and
G.
Foffi
,
J. Phys. Chem. B
115
,
14263
(
2011
).
30.
S.
Poblete
,
A.
Wysocki
,
G.
Gompper
, and
R.
Winkler
,
Phys. Rev. E
90
,
033314
(
2014
).
31.
J.
Sané
,
J.
Padding
, and
A.
Louis
,
Phys. Rev. E
79
,
051402
(
2009
).
32.
F.
Lugli
,
E.
Brini
, and
F.
Zerbetto
,
J. Phys. Chem. C
116
,
592
(
2012
).
33.
J.
Zhou
and
F.
Schmid
,
Eur. Phys. J. E
36
,
33
(
2013
).
34.
S.
Ollila
,
T.
Ala-Nissila
, and
C.
Denniston
,
J. Fluid Mech.
709
,
123
(
2012
).
35.
S.
Ollila
,
C.
Smith
,
T.
Ala-Nissila
, and
C.
Denniston
,
Multiscale Model. Simul.
11
,
213
(
2013
).
36.
F.
Mackay
,
S.
Ollila
, and
C.
Denniston
,
Comput. Phys. Commun.
184
,
2021
(
2013
).
37.
F.
Mackay
and
C.
Denniston
,
J. Comput. Phys.
237
,
289
(
2013
).
38.
J.
Deutch
and
B.
Felderhof
,
J. Chem. Phys.
62
,
2398
(
1975
).
40.
P.
Debye
and
A.
Bueche
,
J. Chem. Phys.
16
,
573
(
1948
).
41.
B.
Felderhof
and
J.
Deutch
,
J. Chem. Phys.
62
,
2391
(
1975
).
42.
L.
Boltzmann
,
Lectures on Gas Theory
, 1st ed. (
University of California Press
,
Berkeley
,
1964
).
43.
S.
Chapman
and
T.
Cowling
,
The Mathematical Theory of Non-Uniform Gases
, 3rd ed. (
Cambridge University Press
,
Cambridge
,
1991
).
44.
U.
Frisch
,
B.
Hasslacher
, and
Y.
Pomeau
,
Phys. Rev. Lett.
56
,
1505
(
1986
).
45.
S.
Wolfram
,
J. Stat. Phys.
45
,
471
(
1986
).
46.
P.
Bhatnagar
,
E.
Gross
, and
M.
Krook
,
Phys. Rev.
94
,
511
(
1954
).
47.
H. J.
Limbach
,
A.
Arnold
,
B. A.
Mann
, and
C.
Holm
,
Comput. Phys. Commun.
174
,
704
(
2006
).
48.
A.
Arnold
 et al, “
ESPResSo 3.1—Molecular dynamics software for coarse-grained models
,” in
Meshfree Methods for Partial Differential Equations VI
,
Lecture Notes in Computational Science and Engineering
Vol.
89
, edited by
M.
Griebel
and
M. A.
Schweitzer
(
Springer
,
2013
), p.
1
.
49.
E.
Altschuler
 et al,
Phys. Rev. Lett.
78
,
2681
(
1997
).
50.
R.
Zwanzig
and
M.
Bixon
,
J. Fluid Mech.
69
,
21
(
1975
).
51.
D.
Roehm
and
A.
Arnold
,
Eur. Phys. J.: Spec. Top.
210
,
73
(
2012
).
52.
D.
d’Humières
,
I.
Ginzburg
,
M.
Krafczyk
,
P.
Lallemand
, and
L.-S.
Luo
,
Philos. Trans. R. Soc., A
360
,
437
(
2002
).
53.
R.
Adhikari
,
K.
Stratford
,
M. E.
Cates
, and
A. J.
Wagner
,
Europhys. Lett.
71
,
473
(
2005
).
54.
B.
Dünweg
,
U.
Schiller
, and
A.
Ladd
,
Phys. Rev. E
76
,
036704
(
2007
).
55.
B.
Dünweg
,
U.
Schiller
, and
A.
Ladd
,
Comput. Phys. Commun.
180
,
605
(
2009
).
56.
J.
Padding
and
A.
Louis
,
Phys. Rev. E
74
,
031402
(
2006
).
57.
A.
Louis
,
Faraday Discuss.
144
,
323
(
2010
).
58.
J.
Ramirez
,
S.
Sukumaran
,
B.
Vorselaars
, and
A.
Likhtman
,
J. Chem. Phys.
133
,
154103
(
2010
).
59.
E.
Hauge
and
A.
Martin-Löf
,
J. Stat. Phys.
7
,
259
(
1973
).
60.
B.
Felderhof
,
J. Chem. Phys.
140
,
134901
(
2014
).
61.
J.-P.
Hansen
and
I.
McDonald
,
Theory of Simple Liquids
, 2nd ed. (
Academic Press
,
London
,
1986
).
62.
63.
B.
Cichocki
and
R.
Jones
,
Physica A
258
,
273
(
1998
).
64.
65.
F. B.
Usabiaga
,
X.
Xie
,
R.
Delgado-Buscalioni
, and
A.
Donev
,
J. Chem. Phys.
139
,
214113
(
2013
).
66.
M.
Friese
,
T.
Nieminen
,
N.
Heckenberg
, and
H.
Rubinsztein-Dunlop
,
Nature
394
,
348
(
1998
).
67.
B.
Grzybowski
,
H.
Stone
, and
G.
Whitesides
,
Nature
405
,
1033
(
2000
).
68.
B.
Grzybowski
,
X.
Jiang
,
H.
Stone
, and
G.
Whitesides
,
Phys. Rev. E
64
,
011603
(
2001
).
69.
70.
H.
Brenner
,
J. Colloid Interface Sci.
23
,
407
(
1967
).
71.
J. G.
de la Torre
and
V.
Bloomfield
,
Q. Rev. Biophys.
14
,
81
(
1981
).
72.
J. G.
de la Torre
,
G.
del Rio
, and
A.
Ortega
,
J. Phys. Chem. B
111
,
955
(
2007
).
73.
D.
Kraft
 et al,
Phys. Rev. E
88
,
050301
(
2013
).
74.
D.
Roehm
,
S.
Kesselheim
, and
A.
Arnold
,
Soft Matter
10
,
5503
(
2014
).
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