Particle-wall interaction is important in various applications such as cell sorting, particle separation, the entire class of hydrodynamic filtration and its derivatives, etc. Yet, accurate implementation of interactions between the wall and finite-size particles is not trivial when working with the currently available particle tracking algorithms/packages as they typically work with point-wise particles. Herein, we report a particle tracking algorithm that takes into account interactions between particles of finite size and nearby solid objects. A particle is modeled as a set of circumferential points. While fluid–particle interactions are captured during the track of particle center, interactions between particles and nearby solid objects are modeled explicitly by examining circumferential points and applying a reflection scheme as needed to ensure impenetrability of solid objects. We also report a modified variant of auxiliary structured grid method to locate hosting cells, which in conjunction with a boundary condition scheme enables the capture of interactions between particles and solid objects. As a proof-of-concept, we numerically and experimentally study the particles’ motion within a deterministic lateral displacement microfluidic device. The results successfully demonstrate the zigzag and bump modes observed in our experiments. We also study a microfluidic device with pinched flow numerically and validate our results against experimental data from the literature. By demonstrating an almost 8 × speedup on a system with eight performance threads, our investigations suggest that the algorithm can benefit from parallel processing on multi-thread systems. We believe that the proposed framework can pave the way for designing related microfluidic chips precisely and conveniently.

1.
K.
Korotenko
,
R.
Mamedov
,
A.
Kontar
, and
L.
Korotenko
, “
Particle tracking method in the approach for prediction of oil slick transport in the sea: Modelling oil pollution resulting from river input
,”
J. Mar. Syst.
48
(
1–4
),
159
170
(
2004
).
2.
A.
Pilechi
,
A.
Mohammadian
, and
E.
Murphy
, “
A numerical framework for modeling fate and transport of microplastics in inland and coastal waters
,”
Mar. Pollut. Bull.
184
,
114119
(
2022
).
3.
Z.
Zhang
and
Q.
Chen
, “
Experimental measurements and numerical simulations of particle transport and distribution in ventilated rooms
,”
Atmos. Environ.
40
(
18
),
3396
3408
(
2006
).
4.
A.
Widiatmojo
,
K.
Sasaki
,
N. P.
Widodo
,
Y.
Sugai
,
A. Y.
Sahzabi
, and
R.
Nguele
, “
Predicting gas dispersion in large scale underground ventilation: A particle tracking approach
,”
Build. Env.
95
,
171
181
(
2016
).
5.
C.
Crawford
,
E.
Vanoli
,
B.
Decorde
,
M.
Lancelot
,
C.
Duprat
,
C.
Josserand
,
J.
Jilesen
,
L.
Bouadma
, and
J.-F.
Timsit
, “
Modeling of aerosol transmission of airborne pathogens in ICU rooms of COVID-19 patients with acute respiratory failure
,”
Sci. Rep.
11
(
1
),
11778
(
2021
).
6.
H.
Tan
,
K. Y.
Wong
,
M. H. D.
Othman
,
H. Y.
Kek
,
R. A.
Wahab
,
G. K. P.
Ern
,
W. T.
Chong
, and
K. Q.
Lee
, “
Current and potential approaches on assessing airflow and particle dispersion in healthcare facilities: A systematic review
,”
Environ. Sci. Pollut. Res.
29
(
53
),
80137
80160
(
2022
).
7.
C.-R.
Chu
and
K.-J.
Yang
, “
Transport process of outdoor particulate matter into naturally ventilated buildings
,”
Build. Sci.
207
,
108424
(
2022
).
8.
A.
Tsuda
,
F. S.
Henry
, and
J. P.
Butler
, “Particle transport and deposition: Basic physics of particle kinetics,” in Comprehensive Physiology (John Wiley & Sons, Ltd, 2013), pp. 1437–1471, see https://onlinelibrary.wiley.com/doi/abs/10.1002/cphy.c100085.
9.
K.
Inthavong
,
L.
Tian
, and
J.
Tu
, “
Lagrangian particle modelling of spherical nanoparticle dispersion and deposition in confined flows
,”
J. Aerosol. Sci.
96
,
56
68
(
2016
).
10.
M. S.
Islam
,
S. C.
Saha
,
T.
Gemci
,
I. A.
Yang
,
E.
Sauret
,
Z.
Ristovski
, and
Y. T.
Gu
, “
Euler-Lagrange prediction of diesel-exhaust polydisperse particle transport and deposition in lung: Anatomy and turbulence effects
,”
Sci. Rep.
9
(
1
),
12423
(
2019
).
11.
C.
Atzeni
,
G.
Lesma
,
G.
Dubini
,
M.
Masi
,
F.
Rossi
, and
E.
Bianchi
, “
Computational fluid dynamic models as tools to predict aerosol distribution in tracheobronchial airways
,”
Sci. Rep.
11
(
1
),
1109
(
2021
).
12.
H.
Mortazavy Beni
,
H.
mortazavi
,
F.
Aghaei
, and
S.
Kamalipour
, “
Experimental tracking and numerical mapping of novel coronavirus micro-droplet deposition through nasal inhalation in the human respiratory system
,”
Biomech. Model. Mechanobiol.
20
(
3
),
1087
1100
(
2021
).
13.
M.
Kiasadegh
,
H.
Emdad
,
G.
Ahmadi
, and
O.
Abouali
, “
Transient numerical simulation of airflow and fibrous particles in a human upper airway model
,”
J. Aerosol. Sci.
140
,
105480
(
2020
).
14.
B. S.
Schuster
,
L. M.
Ensign
,
D. B.
Allan
,
J. S.
Suk
, and
J.
Hanes
, “
Particle tracking in drug and gene delivery research: State-of-the-art applications and methods
,”
Adv. Drug Delivery Rev.
91
,
70
91
(
2015
).
15.
I.
Rukshin
,
J.
Mohrenweiser
,
P.
Yue
, and
S.
Afkhami
, “
Modeling superparamagnetic particles in blood flow for applications in magnetic drug targeting
,”
Fluids
2
(
2
),
29
(
2017
).
16.
T.
Yuan
,
L.
Gao
,
W.
Zhan
, and
D.
Dini
, “
Effect of particle size and surface charge on nanoparticles diffusion in the brain white matter
,”
Pharm. Res.
39
(
4
),
767
781
(
2022
).
17.
N.-V.
Buchete
,
I.
Cicha
,
S.
Dutta
, and
P.
Neofytou
, “
Multiscale physics-based in silico modelling of nanocarrier-assisted intravascular drug delivery
,”
Front. Drug Deliv.
4
,
1362660
(
2024
).
18.
J.
Wu
,
Y.
Lv
,
Y.
He
,
X.
Du
,
J.
Liu
, and
W.
Zhang
, “
A numerical study on the erythrocyte flow path in I-shaped pillar DLD arrays
,”
Fluids
8
(
5
),
161
(
2023
).
19.
G.
de Timary
,
C. J.
Rousseau
,
L. V.
Melderen
, and
B.
Scheid
, “
Shear-enhanced sorting of ovoid and filamentous bacterial cells using pinch flow fractionation
,”
Lab Chip
23
(
4
),
659
670
(
2023
).
20.
Y.
Lv
,
J.
Wu
,
Y.
He
,
J.
Liu
,
W.
Zhang
, and
Z.
Yan
, “
Diseased erythrocyte enrichment based on I-shaped pillar DLD arrays
,”
Micromachines
15
(
2
),
214
(
2024
).
21.
M. S.
Saidi
,
M.
Rismanian
,
M.
Monjezi
,
M.
Zendehbad
, and
S.
Fatehiboroujeni
, “
Comparison between Lagrangian and Eulerian approaches in predicting motion of micron-sized particles in laminar flows
,”
Atmos. Environ.
89
,
199
206
(
2014
).
22.
Z.
Xu
,
Z.
Han
, and
H.
Qu
, “
Comparison between Lagrangian and Eulerian approaches for prediction of particle deposition in turbulent flows
,”
Powder Technol.
360
,
141
150
(
2020
).
23.
N.
Sato
,
J.
Yao
,
M.
Sugawara
, and
M.
Takei
, “
Numerical study of particle-fluid flow under AC electrokinetics in electrode-multilayered microfluidic device
,”
IEEE Trans. Biomed. Eng.
66
(
2
),
453
463
(
2019
).
24.
M.
Olfat
and
E.
Kadivar
, “
Particle separation based on dielectrophoresis force using boundary element method and point-particle approach in a microfluidic channel
,”
Microfluid. Nanofluid.
27
,
83
(
2023
).
25.
J. A. K.
Horwitz
and
A.
Mani
, “
Accurate calculation of Stokes drag for point–particle tracking in two-way coupled flows
,”
J. Comput. Phys.
318
,
85
109
(
2016
).
26.
S.
Trunk
,
A.
Brix
, and
H.
Freund
, “
Development and evaluation of a new particle tracking solver for hydrodynamic and mass transport characterization of porous media—A case study on periodic open cellular structures
,”
Chem. Eng. Sci.
244
,
116768
(
2021
).
27.
B.
Wang
,
I.
Wald
,
N.
Morrical
,
W.
Usher
,
L.
Mu
,
K.
Thompson
, and
R.
Hughes
, “
An GPU-accelerated particle tracking method for Eulerian–Lagrangian simulations using hardware ray tracing cores
,”
Comput. Phys. Commun.
271
,
108221
(
2022
).
28.
G.
Baldan
,
T.
Bellosta
, and
A.
Guardone
, “
Efficient Lagrangian particle tracking algorithms for distributed-memory architectures
,”
Comput. Fluids
256
,
105856
(
2023
).
29.
H.
Tang
,
J.
Niu
,
H.
Jin
,
S.
Lin
, and
D.
Cui
, “
Geometric structure design of passive label-free microfluidic systems for biological micro-object separation
,”
Microsyst. Nanoeng.
8
,
62
(
2022
).
30.
L. R.
Huang
,
E. C.
Cox
,
R. H.
Austin
, and
J. C.
Sturm
, “
Continuous particle separation through deterministic lateral displacement
,”
Science
304
(
5673
),
987
990
(
2004
).
31.
W.
Liang
,
R. H.
Austin
, and
J. C.
Sturm
, “
Scaling of deterministic lateral displacement devices to a single column of bumping obstacles
,”
Lab Chip
20
(
18
),
3461
3467
(
2020
).
32.
M.
Yamada
,
M.
Nakashima
, and
M.
Seki
, “
Pinched flow fractionation: Continuous size separation of particles utilizing a laminar flow profile in a pinched microchannel
,”
Anal. Chem.
76
(
18
),
5465
5471
(
2004
).
33.
J.
Takagi
,
M.
Yamada
,
M.
Yasuda
, and
M.
Seki
, “
Continuous particle separation in a microchannel having asymmetrically arranged multiple branches
,”
Lab Chip
5
(
7
),
778
784
(
2005
).
34.
M.
Yamada
and
M.
Seki
, “
Hydrodynamic filtration for on-chip particle concentration and classification utilizing microfluidics
,”
Lab Chip
5
(
11
),
1233
(
2005
).
35.
S.
Yang
,
A.
Ündar
, and
J. D.
Zahn
, “
A microfluidic device for continuous, real time blood plasma separation
,”
Lab Chip
6
(
7
),
871
880
(
2006
).
36.
H. M.
Ji
,
V.
Samper
,
Y.
Chen
,
C. K.
Heng
,
T. M.
Lim
, and
L.
Yobas
, “
Silicon-based microfilters for whole blood cell separation
,”
Biomed. Microdevices
10
(
2
),
251
257
(
2008
).
37.
B.
Çetin
,
S. D.
Öner
, and
B.
Baranoğlu
, “
Modeling of dielectrophoretic particle motion: Point particle versus finite-sized particle
,”
Electrophoresis
38
(
11
),
1407
1418
(
2017
).
38.
A.
Atay
,
A.
Beşkök
, and
B.
Çetin
, “
DC-electrokinetic motion of colloidal cylinder(s) in the vicinity of a conducting wall
,”
Electrophoresis
43
(
12
),
1263
1274
(
2022
).
39.
M. M.
Villone
,
M. A.
Hulsen
,
P. D.
Anderson
, and
P. L.
Maffettone
, “
Simulations of deformable systems in fluids under shear flow using an arbitrary Lagrangian Eulerian technique
,”
Comput. Fluids
90
,
88
100
(
2014
).
40.
N.
Balcázar
,
O.
Lehmkuhl
,
J.
Rigola
, and
A.
Oliva
, “
A multiple marker level-set method for simulation of deformable fluid particles
,”
Int. J. Multiphase Flow
74
,
125
142
(
2015
).
41.
N.
Balcázar
,
J.
Rigola
,
J.
Castro
, and
A.
Oliva
, “
A level-set model for thermocapillary motion of deformable fluid particles
,”
Int. J. Heat Fluid Flow
62
,
324
343
(
2016
).
42.
C. W.
Hirt
,
A. A.
Amsden
, and
J. L.
Cook
, “
An arbitrary Lagrangian-Eulerian computing method for all flow speeds
,”
J. Comput. Phys.
14
(
3
),
227
253
(
1974
).
43.
T.
Gao
and
H. H.
Hu
, “
Deformation of elastic particles in viscous shear flow
,”
J. Comput. Phys.
228
(
6
),
2132
2151
(
2009
).
44.
G.
Kabacaoğlu
and
G.
Biros
, “
Sorting same-size red blood cells in deep deterministic lateral displacement devices
,”
J. Fluid Mech.
859
,
433
475
(
2019
).
45.
R.
Mittal
and
G.
Iaccarino
, “
Immersed boundary methods
,”
Annu. Rev. Fluid Mech.
37
(
37
),
239
261
(
2005
).
46.
H. T.
Kazerooni
,
W.
Fornari
,
J.
Hussong
, and
L.
Brandt
, “
Inertial migration in dilute and semidilute suspensions of rigid particles in laminar square duct flow
,”
Phys. Rev. Fluids
2
(
8
),
084301
(
2017
).
47.
M. S.
Wullenweber
,
J.
Kottmeier
,
I.
Kampen
,
A.
Dietzel
, and
A.
Kwade
, “
Simulative investigation of different DLD microsystem designs with increased Reynolds numbers using a two-way coupled IBM-CFD/6-DOF approach
,”
Processes
10
(
2
),
403
(
2022
).
48.
G. B.
Macpherson
,
N.
Nordin
, and
H. G.
Weller
, “
Particle tracking in unstructured, arbitrary polyhedral meshes for use in CFD and molecular dynamics
,”
Commun. Numer. Methods Eng.
25
(
3
),
263
273
(
2009
).
49.
F.
Greifzu
,
C.
Kratzsch
,
T.
Forgber
,
F.
Lindner
, and
R.
Schwarze
, “
Assessment of particle-tracking models for dispersed particle-laden flows implemented in OpenFOAM and ANSYS FLUENT
,”
Eng. Appl. Comput. Fluid Mech.
10
(
1
),
30
43
(
2016
).
50.
T.
Weinhart
,
L.
Orefice
,
M.
Post
,
M. P.
van Schrojenstein Lantman
,
I. F. C.
Denissen
,
D. R.
Tunuguntla
,
J. M. F.
Tsang
,
H.
Cheng
,
M. Y.
Shaheen
,
H.
Shi
,
P.
Rapino
,
E.
Grannonio
,
N.
Losacco
,
J.
Barbosa
,
L.
Jing
,
J. E.
Alvarez Naranjo
,
S.
Roy
,
W. K.
den Otter
, and
A. R.
Thornton
, “
Fast, flexible particle simulations—An introduction to MercuryDPM
,”
Comput. Phys. Commun.
249
,
107129
(
2020
).
51.
L.
Fries
,
S.
Antonyuk
,
S.
Heinrich
, and
S.
Palzer
, “
DEM–CFD modeling of a fluidized bed spray granulator
,”
Chem. Eng. Sci.
66
(
11
),
2340
2355
(
2011
).
52.
D.
Jajcevic
,
E.
Siegmann
,
C.
Radeke
, and
J. G.
Khinast
, “
Large-scale CFD–DEM simulations of fluidized granular systems
,”
Chem. Eng. Sci.
98
,
298
310
(
2013
).
53.
S.
Deb
and
D. K.
Tafti
, “
A novel two-grid formulation for fluid–particle systems using the discrete element method
,”
Powder Technol.
246
,
601
616
(
2013
).
54.
J.
Capecelatro
and
O.
Desjardins
, “
An Euler–Lagrange strategy for simulating particle-laden flows
,”
J. Comput. Phys.
238
,
1
31
(
2013
).
55.
R.
Garg
,
J.
Galvin
,
T.
Li
, and
S.
Pannala
, “
Open-source MFIX-DEM software for gas–solids flows: Part I—Verification studies
,”
Powder Technol.
220
,
122
137
(
2012
).
56.
R.
Sun
and
H.
Xiao
, “
SediFoam: A general-purpose, open-source CFD–DEM solver for particle-laden flow with emphasis on sediment transport
,”
Comput. Geosci.
89
,
207
219
(
2016
).
57.
J.
Rojek
, “
Contact modeling in the discrete element method
,” in
Contact Modeling for Solids and Particles
, edited by A. Popp and P. Wriggers (
Springer International Publishing
,
Cham
,
2018
), pp.
177
228
.
58.
C.
Liu
,
H.
Liu
, and
H.
Zhang
, “
MatDEM—Fast matrix computing of the discrete element method
,”
Earthq. Res. Adv.
1
(
3
),
100010
(
2021
).
59.
M.
Singh
,
S.
Shirazian
,
V.
Ranade
,
G. M.
Walker
, and
A.
Kumar
, “
Challenges and opportunities in modelling wet granulation in pharmaceutical industry—A critical review
,”
Powder Technol.
403
,
117380
(
2022
).
60.
H.
Zhou
,
Y.
Chen
, and
M. A.
Sadek
, “
Modelling of soil–seed contact using the Discrete Element Method (DEM)
,”
Biosyst. Eng.
121
,
56
66
(
2014
).
61.
H.
Cheng
,
A. R.
Thornton
,
S.
Luding
,
A. L.
Hazel
, and
T.
Weinhart
, “
Concurrent multi-scale modeling of granular materials: Role of coarse-graining in FEM-DEM coupling
,”
Comput. Methods Appl. Mech. Eng.
403
,
115651
(
2023
).
62.
F.
Ye
,
C.
Wheeler
,
B.
Chen
,
J.
Hu
,
K.
Chen
, and
W.
Chen
, “
Calibration and verification of DEM parameters for dynamic particle flow conditions using a backpropagation neural network
,”
Adv. Powder Technol.
30
(
2
),
292
301
(
2019
).
63.
C.
Coetzee
, “
Calibration of the discrete element method: Strategies for spherical and non-spherical particles
,”
Powder Technol.
364
,
851
878
(
2020
).
64.
T.
Roessler
,
C.
Richter
,
A.
Katterfeld
, and
F.
Will
, “
Development of a standard calibration procedure for the DEM parameters of cohesionless bulk materials—Part I: Solving the problem of ambiguous parameter combinations
,”
Powder Technol.
343
,
803
812
(
2019
).
65.
C.
Richter
,
T.
Rößler
,
G.
Kunze
,
A.
Katterfeld
, and
F.
Will
, “
Development of a standard calibration procedure for the DEM parameters of cohesionless bulk materials—Part II: Efficient optimization-based calibration
,”
Powder Technol.
360
,
967
976
(
2020
).
66.
J.
Wang
,
V. G. J.
Rodgers
,
P.
Brisk
, and
W. H.
Grover
, “
MOPSA: A microfluidics-optimized particle simulation algorithm
,”
Biomicrofluidics
11
(
3
),
034121
(
2017
).
67.
A.
Ebadi
,
R.
Toutouni
,
M. J.
Farshchi Heydari
,
M.
Fathipour
, and
M.
Soltani
, “
A novel numerical modeling paradigm for bio particle tracing in non-inertial microfluidics devices
,”
Microsyst. Technol.
25
,
3703
3711
(
2019
).
68.
R.
Lubbe
,
W.-J.
Xu
,
D. N.
Wilke
,
P.
Pizette
, and
N.
Govender
, “
Analysis of parallel spatial partitioning algorithms for GPU based DEM
,”
Comput. Geotech.
125
,
103708
(
2020
).
69.
R.
Löhner
and
J.
Ambrosiano
, “
A vectorized particle tracer for unstructured grids
,”
J. Comput. Phys.
91
(
1
),
22
31
(
1990
).
70.
A.
Haselbacher
,
F.
Najjar
, and
J.
Ferry
, “
An efficient and robust particle-localization algorithm for unstructured grids
,”
J. Comput. Phys.
225
(
2
),
2198
2213
(
2007
).
71.
S.
Zhao
,
Z.
Lai
, and
J.
Zhao
, “
Leveraging ray tracing cores for particle-based simulations on GPUs
,”
Int. J. Numer. Methods Eng.
124
(
3
),
696
713
(
2023
).
72.
O.
Mahian
,
L.
Kolsi
,
M.
Amani
,
P.
Estellé
,
G.
Ahmadi
,
C.
Kleinstreuer
,
J. S.
Marshall
,
M.
Siavashi
,
R. A.
Taylor
,
H.
Niazmand
,
S.
Wongwises
,
T.
Hayat
,
A.
Kolanjiyil
,
A.
Kasaeian
, and
I.
Pop
, “
Recent advances in modeling and simulation of nanofluid flows—Part I: Fundamentals and theory
,”
Phys. Rep.
790
,
1
48
(
2019
).
73.
G.
Ahmadi
and
J. B.
McLaughlin
, “
Transport, deposition and removal of fine particles—Biomedical applications
,” in
Medical Applications of Colloids
, edited by E. Matijevic (
Springer
,
New York
,
2008
), pp.
92
173
. .
74.
T.
Salafi
,
Y.
Zhang
, and
Y.
Zhang
, “
A review on deterministic lateral displacement for particle separation and detection
,”
Nano-Micro. Lett.
11
(
1
),
77
(
2019
).
75.
A.
Mehboudi
,
S.
Singhal
, and
S. V.
Sreenivasan
, “
Investigation of pressure balance in proximity of sidewalls in deterministic lateral displacement
,”
Biomicrofluidics
19
,
034102
(
2025
).
76.
S.-C.
Kim
,
B. H.
Wunsch
,
H.
Hu
,
J. T.
Smith
,
R. H.
Austin
, and
G.
Stolovitzky
, “
Broken flow symmetry explains the dynamics of small particles in deterministic lateral displacement arrays
,”
Proc. Natl. Acad. Sci. U.S.A.
114
(
26
),
E5034
E5041
(
2017
).
77.
A.
Mehboudi
,
S.
Singhal
, and
S. V.
Sreenivasan
, “
A universal framework for design and manufacture of deterministic lateral displacement chips
,”
Lab Chip
25
(
6
),
1521
1536
(
2025
).
78.
A.
Mehboudi
, see https://zenodo.org/doi/10.5281/zenodo.14357811 for “mnFlow: A package for micro/nanoflow” (2024).
79.
J. A.
Davis
, “Microfluidic separation of blood components through deterministic lateral displacement,” Ph.D. thesis (Princeton University, 2008), see https://swh.princeton.edu/∼sturmlab/theses/Davis-Thesis.pdf.
80.
A.
Mehboudi
, See https://github.com/am-0code1/fspt for fspt: a package for finite-size particle tracking.
81.
A.
Mehboudi
, See https://utexas.app.box.com/v/am-fspt-docs for “fspt documentation.”
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