The functionality and performance of colloidal suspensions used in catalyst layer preparation and biomedical applications are largely dependent on the interaction between nanoparticles in colloidal suspension systems. Previous models (e.g., collision model) usually rely on an artificial repulsive force as the sole interaction between nanoparticles to prevent overlapping, but fail to capture the agglomeration or reveal the effect of solvents. In this study, the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory is implemented in conjunction with a lattice Boltzmann-smoothed profile method developed to simulate the dynamic solid–fluid and particle–particle interactions between nanoparticles in shear flow. Both aqueous and non-aqueous solvents are considered. The model consists of an attractive van der Waals force and repulsive electrostatic and Born forces in aqueous solvents and is modified for non-aqueous solvents by replacing the repulsive electrostatic force by Coulombic repulsion. The numerical model is validated against a benchmark analytic solution for the motion of one nanoparticle in shear flow. For two-particle systems, physically representative simulations are obtained with the DLVO models, resulting in nanoparticles that remain attached or eventually detach depending on a critical particle Reynolds number. Furthermore, the DLVO models properly resolve the effect of solvents on nanoparticle motion. The improved representation of inter-particle interactions achieved with the DLVO and modified-DLVO models provides a physically consistent approach to simulate and investigate agglomeration and dispersion in colloidal suspensions.

1.
A.
Zadick
,
L.
Dubau
,
N.
Sergent
,
G.
Berthomé
, and
M.
Chatenet
, “
Huge instability of Pt/C catalysts in alkaline medium
,”
ACS Catal.
5
,
4819
4824
(
2015
).
2.
M.
Doyen
,
J.
Goole
,
K.
Bartik
, and
G.
Bruylants
, “
Amino acid induced fractal aggregation of gold nanoparticles: Why and how
,”
J. Colloid Interface Sci.
464
,
160
166
(
2016
).
3.
S.
Dutta
,
S.
Parida
,
C.
Maiti
,
R.
Banerjee
,
M.
Mandal
, and
D.
Dhara
, “
Polymer grafted magnetic nanoparticles for delivery of anticancer drug at lower pH and elevated temperature
,”
J. Colloid Interface Sci.
467
,
70
80
(
2016
).
4.
P. C.
Sui
,
X.
Zhu
, and
N.
Djilali
, “
Modeling of PEM fuel cell catalyst layers: Status and outlook
,”
Electrochem. Energy Rev.
2
,
428
(
2019
).
5.
A.
Halder
,
S.
Patra
,
B.
Viswanath
,
N.
Munichandraiah
, and
N.
Ravishankar
, “
Porous, catalytically active palladium nanostructures by tuning nanoparticle interactions in an organic medium
,”
Nanoscale
3
,
725
730
(
2011
).
6.
K. J.
Lange
,
P.-C.
Sui
, and
N.
Djilali
, “
Determination of effective transport properties in a PEMFC catalyst layer using different reconstruction algorithms
,”
J. Power Sources
208
,
354
365
(
2012
).
7.
D. H.
Schwarz
and
N.
Djilali
, “
3D modeling of catalyst layers in PEM fuel cells
,”
J. Electrochem. Soc.
154
,
B1167
B1178
(
2007
).
8.
H.
Huang
,
Y.
Xin
, and
X. Y.
Lu
, “
Sedimentation of an ellipsoidal particle in narrow tubes
,”
Phys. Fluids
26
,
053302
(
2014
).
9.
Z.-G.
Feng
and
E. E.
Michaelides
, “
The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems
,”
J. Comput. Phys.
195
,
602
628
(
2004
).
10.
A. J. C.
Ladd
and
R.
Verberg
, “
Lattice-Boltzmann simulations of particle-fluid suspensions
,”
J. Stat. Phys.
104
,
1191
1251
(
2001
).
11.
S.
Shukla
,
S.
Bhattacharjee
, and
M.
Secanell
, “
Rationalizing catalyst inks for PEMFC electrodes based on colloidal interactions
,”
ECS Trans.
58
,
1409
1428
(
2013
).
12.
S.
Shukla
,
S.
Bhattacharjee
,
A. Z.
Weber
, and
M.
Secanell
, “
Experimental and theoretical analysis of ink dispersion stability for polymer electrolyte fuel cell applications
,”
J. Electrochem. Soc.
164
,
F600
F609
(
2017
).
13.
J. C.
Berg
,
An Introduction to Interfaces & Colloids: The Bridge to Nanoscience
(
World Scientific Publishing
,
Singapore
,
2010
), ISBN: 9789814293075.
15.
Z. L.
Guo
and
C.
Zheng
,
Theory and Applications of Lattice Boltzmann Method
(
Science Press
,
Beijing
,
2009
).
16.
S.
Jafari
,
R.
Yamamoto
, and
M.
Rahnama
, “
Lattice-Boltzmann method combined with smoothed-profile method for particulate suspensions
,”
Phys. Rev. E
83
,
026702
(
2011
).
17.
Y.
Nakayama
and
R.
Yamamoto
, “
Simulation method to resolve hydrodynamic interactions in colloidal dispersions
,”
Phys. Rev. E
71
,
036707
(
2005
).
18.
T.
Shi
,
H.
Zhang
,
Z.
Guo
, and
L. P.
Wang
, “
A combined immersed boundary and discrete unified gas kinetic scheme for particle-fluid flows
,”
J. Comput. Phys.
375
,
498
518
(
2018
).
19.
Z.-G.
Feng
and
E. E.
Michaelides
, “
Proteus: A direct forcing method in the simulations of particulate flows
,”
J. Comput. Phys.
202
,
20
51
(
2005
).
20.
R.
Glowinski
,
T. W.
Pan
,
T. I.
Hesla
,
D. D.
Joseph
, and
J.
Périaux
, “
A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow
,”
J. Comput. Phys.
169
,
363
426
(
2001
).
21.
B. V.
Derjaguin
and
L. D.
Landau
, “
Stability theory of strongly charged lyophobic sols and of the adhesion of strongly charged particles in electrolyte solutions
,”
Acta Physicochim. URSS
14
,
633
662
(
1941
).
22.
E. J. W.
Verwey
, “
Theory of the stability of lyophobic colloids
,”
J. Phys. Chem.
51
,
631
636
(
1947
).
23.
G. R.
Zeichner
and
W. R.
Schowalter
, “
Use of trajectory analysis to study stability of colloidal dispersions in flow fields
,”
AIChE J.
23
,
243
254
(
1977
).
24.
D. A.
Haydon
, “
The electrical double layer and electrokinetic phenomena
,” in
Recent Progress in Surface Science
(
Elsevier
,
1964
), Vol. 1, pp.
94
158
.
25.
H. C.
Hamaker
, “
The London-van der Waals attraction between spherical particles
,”
Physica
4
,
1058
1072
(
1937
).
26.
J.
Gregory
, “
Interaction of unequal double layers at constant charge
,”
J. Colloid Interface Sci.
51
,
44
51
(
1975
).
27.
Y. T.
Zhang
and
T.
Lv
,
Colloid and Interface Chemistry
(
China Textile and Apparel Press
,
Beijing
,
2008
), ISBN: 9787506453097.
28.
D. L.
Feke
,
N. D.
Prabhu
,
J. A.
Mann
, Jr.
, and
J. A.
Mann
 III
, “
A formulation of the short-range repulsion between spherical colloidal particles
,”
J. Phys. Chem.
88
,
5735
5739
(
1984
).
29.
M.
Elimelech
,
J.
Gregory
, and
X.
Jia
,
Particle Deposition and Aggregation: Measurement, Modelling and Simulation
(
Butterworth-Heinemann
,
Oxford
,
2013
), ISBN: 1483161374.
30.
Y. J.
Choi
and
N.
Djilali
, “
Direct numerical simulations of agglomeration of circular colloidal particles in two-dimensional shear flow
,”
Phys. Fluids
28
,
013304
(
2016
).
31.
J.
Kromkamp
,
D.
van den Ende
,
D.
Kandhai
,
R.
van der Sman
, and
R.
Boom
, “
Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow
,”
Chem. Eng. Sci.
61
,
858
873
(
2006
).
32.
T.
Kempe
and
J.
Fröhlich
, “
Collision modelling for the interface-resolved simulation of spherical particles in viscous fluids
,”
J. Fluid Mech.
709
,
445
489
(
2012
).

Supplementary Material

You do not currently have access to this content.