Microfluidic systems have enormous potential for enabling point-of-care diagnostics due to a number of advantages, such as low sample volumes, small footprint, low energy requirements, uncomplicated setup, high surface-to-volume ratios, cost-effectiveness, etc. However, fluid mixing operations are constrained by molecular diffusion since the flow is usually in the laminar regime. The slow nature of molecular diffusion is a technological barrier to implementing fluid transformations in a reasonable time. In this context, magnetically actuated micro-mixers of different sizes, shapes, materials, and actuation techniques provide a way to enhance fluid mixing in microfluidic devices. In this paper, we review the currently existing micro-mixing technologies. From a fundamental perspective, the different magnetization models for permanent and induced dipoles are discussed. The single-particle dynamics in steady and oscillating magnetic fields is studied in order to determine the flow generated and the torque exerted on the fluid due to the magnetic particles. The effect of particle interactions, both magnetic and hydrodynamic, is examined.

1.
C. P.
Moerland
,
L. J.
van IJzendoorn
, and
M. W. J.
Prins
, “
Rotating magnetic particles for lab-on-chip applications—A comprehensive review
,”
Lab Chip
19
,
919
933
(
2019
).
2.
Z. M.
Saiyed
,
S. D.
Telang
, and
C. N.
Ramchand
, “
Application of magnetic techniques in the field of drug discovery and biomedicine
,”
BioMagn. Res. Technol.
1
,
2
(
2003
).
3.
M.
Shinkai
, “
Functional magnetic particles for medical application
,”
J. Biosci. Bioeng.
94
,
606
613
(
2002
).
4.
A.
deMello
, “
Control and detection of chemical reactions in microfluidic systems
,”
Nature
442
,
394
402
(
2006
).
5.
V.
Kumaran
and
P.
Bandaru
, “
Ultra-fast microfluidic mixing by soft-wall turbulence
,”
Chem. Eng. Sci.
149
,
156
168
(
2016
).
6.
F. G.
Bessoth
,
A. J.
DeMello
, and
A.
Manz
, “
Microstructure for efficient continuous flow mixing
,”
Anal. Commun.
36
,
213
215
(
1999
).
7.
S.
Lee
,
D. S.
Kim
,
S. S.
Lee
, and
T. H.
Kwon
, “
A split and recombination micromixer fabricated in a PDMS three-dimensional structure
,”
J. Micromech. Microeng.
16
,
1067
1072
(
2006
).
8.
A. D.
Stroock
,
S. K. W.
Dertinger
,
A.
Ajdari
,
I.
Mezić
,
H. A.
Stone
, and
G. M.
Whitesides
, “
Chaotic mixer for microchannels
,”
Science
295
,
647
651
(
2002
).
9.
K.
Ward
and
Z. H.
Fan
, “
Mixing in microfluidic devices and enhancement methods
,”
J. Micromech. Microeng.
25
,
094001
(
2015
).
10.
C.-Y.
Lee
,
C.-L.
Chang
,
Y.-N.
Wang
, and
L.-M.
Fu
, “
Microfluidic mixing: A review
,”
Int. J. Mol. Sci.
12
,
3263
3287
(
2011
).
11.
E.-S.
Shanko
,
Y.
van de Burgt
,
P. D.
Anderson
, and
J. M. J.
den Toonder
, “
Microfluidic magnetic mixing at low Reynolds numbers and in stagnant fluids
,”
Micromachines
10
,
731
(
2019
).
12.
V.
Hessel
,
L.
Holger
, and
F.
Schönfeld
, “
Micromixers—A review on passive and active mixing principles
,”
Chem. Eng. Sci.
60
,
2479
2501
(
2005
).
13.
N.-T.
Nguyen
and
Z.
Wu
, “
Micromixers—A review
,”
J. Micromech. Microeng.
15
,
R1
(
2004
).
14.
J. M.
Ottino
and
S.
Wiggins
, “
Introduction: Mixing in microfluidics
,”
Philos. Trans. A: Math. Phys. Eng. Sci.
362
,
923
935
(
2004
).
15.
H. E.
Meijer
,
M. K.
Singh
,
T. G.
Kang
,
J. M.
Den Toonder
, and
P. D.
Anderson
, “
Passive and active mixing in microfluidic devices
,”
Macromol. Symp.
279
,
201
209
(
2009
).
16.
D.
Ahmed
,
X.
Mao
,
J.
Shi
,
B. K.
Juluri
, and
T. J.
Huang
, “
A millisecond micromixer via single-bubble-based acoustic streaming
,”
Lab Chip
9
,
2738
2741
(
2009
).
17.
J. D.
Posner
and
J. G.
Santiago
, “
Convective instability of electrokinetic flows in a cross-shaped microchannel
,”
J. Fluid Mech.
555
,
1
42
(
2006
).
18.
M. Z.
Bazant
and
T. M.
Squires
, “
Induced-charge electrokinetic phenomena: Theory and microfluidic applications
,”
Phys. Rev. Lett.
92
,
066101
(
2004
).
19.
A.
Rida
and
M. A. M.
Gijs
, “
Manipulation of self-assembled structures of magnetic beads for microfluidic mixing and assaying
,”
Anal. Chem.
76
,
6239
6246
(
2004
).
20.
H.
Suzuki
, “A magnetic force driven chaotic micro-mixer,” IEEE Proceedings of the International Conference on Micro Electro Mechanical Systems 2002 (MEMS’02) (IEEE, 2002), pp. 40–43.
21.
T. G.
Kang
,
M. A.
Hulsen
,
P. D.
Anderson
,
J. M. J.
den Toonder
, and
H. E. H.
Meijer
, “
Chaotic mixing induced by a magnetic chain in a rotating magnetic field
,”
Phys. Rev. E
76
,
066303
(
2007
).
22.
L.-H.
Lu
,
K. S.
Ryu
, and
C.
Liu
, “
A magnetic microstirrer and array for microfluidic mixing
,”
J. Microelectromech. Syst.
11
,
462
469
(
2002
).
23.
C.-Y.
Chen
,
C.-C.
Hsu
,
K.
Mani
, and
B.
Panigrahi
, “
Hydrodynamic influences of artificial cilia beating behaviors on micromixing
,”
Chem. Eng. Process.: Process Intensif.
99
,
33
40
(
2016
).
24.
S.
Khaderi
,
J.
Hussong
,
J.
Westerweel
,
J. D.
Toonder
, and
P.
Onck
, “
Fluid propulsion using magnetically-actuated artificial cilia—Experiments and simulations
,”
RSC Adv.
3
,
12735
12742
(
2013
).
25.
C.-Y.
Chen
,
C.-Y.
Chen
,
C.-Y.
Lin
, and
Y.-T.
Hu
, “
Magnetically actuated artificial cilia for optimum mixing performance in microfluidics
,”
Lab Chip
13
,
2834
2839
(
2013
).
26.
Y.-A.
Wu
,
B.
Panigrahi
,
Y.-H.
Lu
, and
C.-Y.
Chen
, “
An integrated artificial cilia based microfluidic device for micropumping and micromixing applications
,”
Micromachines
8
,
260
(
2017
).
27.
S. N.
Khaderi
,
M. G. H. M.
Baltussen
,
P. D.
Anderson
,
J. M. J.
den Toonder
, and
P. R.
Onck
, “
Breaking of symmetry in microfluidic propulsion driven by artificial cilia
,”
Phys. Rev. E
82
,
027302
(
2010
).
28.
A.
Bhattacharjee
,
M.
Jabbarzadeh
,
G.
Kararsiz
,
H. C.
Fu
, and
M. J.
Kim
, “
Bacteria-inspired magnetically actuated rod-like soft robot in viscous fluids
,”
Bioinspir. Biomim.
17
,
065001
(
2022
).
29.
A.
Cebers
and
K.
Erglis
, “
Flexible magnetic filaments and their applications
,”
Adv. Funct. Mater.
26
,
3783
3795
(
2016
).
30.
B. A.
Evans
,
A. R.
Shields
,
R. L.
Carroll
,
S.
Washburn
,
M. R.
Falvo
, and
R.
Superfine
, “
Magnetically actuated nanorod arrays as biomimetic cilia
,”
Nano Lett.
7
,
1428
1434
(
2007
), pMID: 17419660.
31.
A.
Cēbers
, “
Flexible magnetic filaments
,”
Curr. Opin. Colloid Interface Sci.
10
,
167
175
(
2005
).
32.
D.
Vella
,
E.
du Pontavice
,
C. L.
Hall
, and
A.
Goriely
, “
The magneto-elastica: From self-buckling to self-assembly
,”
Proc. R. Soc. A
470
,
20130609
(
2014
).
33.
J.
Yan
,
K.
Chaudhary
,
S.
Chul Bae
,
J. A.
Lewis
, and
S.
Granick
, “
Colloidal ribbons and rings from Janus magnetic rods
,”
Nat. Commun.
4
,
1516
(
2013
).
34.
S. L.
Biswal
and
A. P.
Gast
, “
Rotational dynamics of semiflexible paramagnetic particle chains
,”
Phys. Rev. E
69
,
041406
(
2004
).
35.
A.
Spatafora-Salazar
,
S.
Kuei
,
L. H. P.
Cunha
, and
S. L.
Biswal
, “
Coiling of semiflexible paramagnetic colloidal chains
,”
Soft Matter
19
,
2385
2396
(
2023
).
36.
A.
Spatafora-Salazar
,
D. M.
Lobmeyer
,
L. H. P.
Cunha
,
K.
Joshi
, and
S. L.
Biswal
, “
Hierarchical assemblies of superparamagnetic colloids in time-varying magnetic fields
,”
Soft Matter
17
,
1120
1155
(
2021
).
37.
V.
Kumaran
, “
The effect of inter-particle hydrodynamic and magnetic interactions in a magnetorheological fluid
,”
J. Fluid Mech.
944
,
A49
(
2022
).
38.
See https://www.doitpoms.ac.uk/tlplib/ferromagnetic/printall.php for K. Sandeman, C. Hopwood, D. Brook, and L. Sallows, “Ferromagnetic materials” (all conent).
39.
R. S. M.
Rikken
,
R. J. M.
Nolte
,
J. C.
Maan
,
J. C. M.
van Hest
,
D. A.
Wilson
, and
P. C. M.
Christianen
, “
Manipulation of micro- and nanostructure motion with magnetic fields
,”
Soft Matter
10
,
1295
1308
(
2014
).
40.
C.
Tannous
and
J.
Gieraltowski
, “
The Stoner-Wohlfarth model of ferromagnetism
,”
Eur. J. Phys.
29
(
3
),
475
(
2008
).
41.
V.
Kumaran
, “
Dynamics of polarizable spheroid in a shear flow subjected to a parallel magnetic field
,”
Phys. Rev. Fluids
6
,
043702
(
2021
).
42.
V.
Kumaran
, “
Steady and rotating states of a polarizable spheroid subjected to a magnetic field and a shear flow
,”
Phys. Rev. Fluids
6
,
063701
(
2021
).
43.
J.
Connolly
and
T. G.
St Pierre
, “
Proposed biosensors based on time-dependent properties of magnetic fluids
,”
J. Magn. Magn. Mater.
225
,
156
160
(
2001
), Proceedings of the Third International Conference on Scientific and Clinical Applications of Magnetic Carriers.
44.
S. H.
Chung
,
A.
Hoffmann
,
S. D.
Bader
,
C.
Liu
,
B.
Kay
,
L.
Makowski
, and
L.
Chen
, “
Biological sensors based on Brownian relaxation of magnetic nanoparticles
,”
Appl. Phys. Lett.
85
,
2971
2973
(
2004
).
45.
G.
Bossis
,
O.
Volkova
,
S.
Lacis
, and
A.
Meunier
, “Magnetorheology: Fluids, structures and rheology,” in Ferrofluids: Magnetically Controllable Fluids and Their Applications, edited by S. Odenbach (Springer, Berlin, 2002), pp. 202–230.
46.
G.
Bossis
,
S.
Lacis
,
A.
Meunier
, and
O.
Volkova
, “
Magnetorheological fluids
,”
J. Magn. Magn. Mater.
252
,
224
228
(
2002
).
47.
G. K.
Batchelor
, “
The stress system in a suspension of force-free particles
,”
J. Fluid Mech.
41
,
545
570
(
1970
).
48.
G. B.
Jeffery
and
L. N. G.
Filon
, “
The motion of ellipsoidal particles immersed in a viscous fluid
,”
Proc. Royal Soc. Lond. Ser. A
102
,
161
179
(
1922
).
49.
H.
Brenner
, “
Rheology of a dilute suspension of axisymmetric Brownian particles
,”
Int. J. Multiph. Flow
1
,
195
341
(
1974
).
50.
E. J.
Hinch
and
L. G.
Leal
, “
Rotation of small non-axisymmetric particles in a simple shear flow
,”
J. Fluid Mech.
92
,
591
607
(
1979
).
51.
L. G.
Leal
and
E. J.
Hinch
, “
The effect of weak Brownian rotations on particles in shear flow
,”
J. Fluid Mech.
46
,
685
703
(
1971
).
52.
K.
Asokan
,
T. R.
Ramamohan
, and
V.
Kumaran
, “
A novel approach to computing the orientation moments of spheroids in simple shear flow at arbitrary Péclet number
,”
Phys. Fluids
14
,
75
84
(
2002
).
53.
G.
Almondo
,
J.
Einarsson
,
J. R.
Angilella
, and
B.
Mehlig
, “
Intrinsic viscosity of a suspension of weakly Brownian ellipsoids in shear
,”
Phys. Rev. Fluids
3
,
064307
(
2018
).
54.
Y.
Almog
and
I.
Frankel
, “
The motion of axisymmetric dipolar particles in homogeneous shear flow
,”
J. Fluid Mech.
289
,
243
261
(
1995
).
55.
C. A.
Sobecki
,
J.
Zhang
,
Y.
Zhang
, and
C.
Wang
, “
Dynamics of paramagnetic and ferromagnetic ellipsoidal particles in shear flow under a uniform magnetic field
,”
Phys. Rev. Fluids
3
,
084201
(
2018
).
56.
V.
Kumaran
, “
Bifurcations in the dynamics of a dipolar spheroid in a shear flow subjected to an external field
,”
Phys. Rev. Fluids
5
,
033701
(
2020
).
57.
I.
Puyesky
and
I.
Frankel
, “
The motion of a dipolar spherical particle in homogeneous shear and time-periodic fields
,”
J. Fluid Mech.
369
,
191
216
(
1998
).
58.
P.
Dhar
,
C. D.
Swayne
,
T. M.
Fischer
,
T.
Kline
, and
A.
Sen
, “
Orientations of overdamped magnetic nanorod-gyroscopes
,”
Nano Lett.
7
,
1010
1012
(
2007
).
59.
X.
Janssen
,
A.
Schellekens
,
K.
van Ommering
,
L.
van IJzendoorn
, and
M.
Prins
, “
Controlled torque on superparamagnetic beads for functional biosensors
,”
Biosens. Bioelectron.
24
,
1937
1941
(
2009
).
60.
A.
Ghosh
,
P.
Mandal
,
S.
Karmakar
, and
A.
Ghosh
, “
Analytical theory and stability analysis of an elongated nanoscale object under external torque
,”
Phys. Chem. Chem. Phys.
15
,
10817
10823
(
2013
).
61.
M. N.
Romodina
,
E. V.
Lyubin
, and
A. A.
Fedyanin
, “
Detection of Brownian torque in a magnetically-driven rotating microsystem
,”
Sci. Rep.
6
,
21212
(
2016
).
62.
K. S.
Kumar
and
T. R.
Ramamohan
, “
Chaotic rheological parameters of periodically forced suspensions of slender rods in simple shear flow
,”
J. Rheol.
39
,
1229
1241
(
1995
).
63.
I.
Misra
and
V.
Kumaran
, “
Dynamics of a magnetic particle in an oscillating magnetic field
,”
Phys. Rev. Fluids
9
,
074303
(
2024
).
64.
“Small denominators. I. Mapping of the circumference onto itself,” in Collected Works: Representations of Functions, Celestial Mechanics and KAM Theory, 1957–1965, edited by A. B. Givental, B. A. Khesin, J. E. Marsden, A. N. Varchenko, V. A. Vassiliev, O. Y. Viro, and V. M. Zakalyukin (Springer, Berlin, 2009), pp. 152–223.
65.
L.
Glass
and
R.
Perez
, “
Fine structure of phase locking
,”
Phys. Rev. Lett.
48
,
1772
1775
(
1982
).
66.
N.
Narinder
,
J.
Behera
, and
A.
Ghosh
, “Dynamics of colloidal rods rotating in viscoelastic media,” arXiv:2406.14505 (2024).
67.
L.
Chevry
,
N. K.
Sampathkumar
,
A.
Cebers
, and
J.-F.
Berret
, “
Magnetic wire-based sensors for the microrheology of complex fluids
,”
Phys. Rev. E
88
,
062306
(
2013
).
68.
F.
Loosli
,
M.
Najm
, and
J.-F.
Berret
, “
Viscoelasticity of model surfactant solutions determined by magnetic rotation spectroscopy
,”
Colloids Surf. A
510
,
143
149
(
2016
).
69.
M.
Radiom
,
R.
Hénault
,
S.
Mani
,
A. G.
Iankovski
,
X.
Norel
, and
J.-F.
Berret
, “
Magnetic wire active microrheology of human respiratory mucus
,”
Soft Matter
17
,
7585
7595
(
2021
).
70.
F.
Meshkati
and
H. C.
Fu
, “
Modeling rigid magnetically rotated microswimmers: Rotation axes, bistability, and controllability
,”
Phys. Rev. E
90
,
063006
(
2014
).
71.
A.
Codutti
,
F.
Bachmann
,
D.
Faivre
, and
S.
Klumpp
, “
Bead-based hydrodynamic simulations of rigid magnetic micropropellers
,”
Front. Robot. AI
5
,
109
(
2018
).
72.
A.
Tokarev
,
B.
Kaufman
,
Y.
Gu
,
T.
Andrukh
,
P. H.
Adler
, and
K. G.
Kornev
, “
Probing viscosity of nanoliter droplets of butterfly saliva by magnetic rotational spectroscopy
,”
Appl. Phys. Lett.
102
,
033701
(
2013
).
73.
A.
Tokarev
,
I.
Luzinov
,
J. R.
Owens
, and
K. G.
Kornev
, “
Magnetic rotational spectroscopy with nanorods to probe time-dependent rheology of microdroplets
,”
Langmuir
28
,
10064
10071
(
2012
).
74.
M.
Allione
,
B.
Torre
,
A.
Casu
,
A.
Falqui
,
P.
Piacenza
,
R.
Di Corato
,
T.
Pellegrino
, and
A.
Diaspro
, “
Rod-shaped nanostructures based on superparamagnetic nanocrystals as viscosity sensors in liquid
,”
J. Appl. Phys.
110
,
064907
(
2011
).
75.
V.
Kumaran
, “
A suspension of conducting particles in a magnetic field—The particle stress
,”
J. Fluid Mech.
901
,
A36
(
2020
).
76.
A. V.
Anupama
,
V.
Kumaran
, and
B.
Sahoo
, “
Magnetorheological fluids containing rod-shaped lithium–zinc ferrite particles: The steady-state shear response
,”
Soft Matter
14
,
5407
5419
(
2018
).
77.
D.
Vågberg
and
B. P.
Tighe
, “
On the apparent yield stress in non-Brownian magnetorheological fluids
,”
Soft Matter
13
,
7207
7221
(
2017
).
78.
D. J.
Klingenberg
, “
Magnetorheology: Applications and challenges
,”
AIChE J.
47
,
246
249
(
2001
).
79.
S.
Melle
,
O. G.
Calderón
,
M. A.
Rubio
, and
G. G.
Fuller
, “
Microstructure evolution in magnetorheological suspensions governed by Mason number
,”
Phys. Rev. E
68
,
041503
(
2003
).
80.
Z.
Sun
,
S.
Liu
,
D.
Zhao
,
L.
Dong
,
J.
Qi
, and
C.
Guo
, “
Study on the motion of single particle chain in the magnetorheological fluid under the action of traveling magnetic field
,”
Smart Mater. Struct.
32
,
115027
(
2023
).
81.
V.
Kumaran
, “
Rheology of a suspension of conducting particles in a magnetic field
,”
J. Fluid Mech.
871
,
139
185
(
2019
).
82.
A. C. H.
Coughlan
and
M. A.
Bevan
, “
Rotating colloids in rotating magnetic fields: Dipolar relaxation and hydrodynamic coupling
,”
Phys. Rev. E
94
,
042613
(
2016
).
83.
C.
Pease
,
H.
Wijesinghe
,
J.
Etheridge
,
C.
Pierce
, and
R.
Sooryakumar
, “
Magnetic and hydrodynamic torques: Dynamics of superparamagnetic bead doublets
,”
J. Magn. Magn. Mater.
466
,
323
332
(
2018
).
84.
J.
Zhang
,
R.
Zhou
, and
C.
Wang
, “
Dynamics of a pair of ellipsoidal microparticles under a uniform magnetic field
,”
J. Micromech. Microeng.
29
,
104002
(
2019
).
85.
Y.
Gao
,
A.
van Reenen
,
M. A.
Hulsen
,
A. M.
de Jong
,
M. W. J.
Prins
, and
J. M. J.
den Toonder
, “
Chaotic fluid mixing by alternating microparticle topologies to enhance biochemical reactions
,”
Microfluid. Nanofluidics
16
,
265
274
(
2014
).
86.
A. K.
Vuppu
,
A. A.
Garcia
, and
M. A.
Hayes
, “
Video microscopy of dynamically aggregated paramagnetic particle chains in an applied rotating magnetic field
,”
Langmuir
19
,
8646
8653
(
2003
).
87.
S.
Melle
,
O. G.
Calderón
,
M. A.
Rubio
, and
G. G.
Fuller
, “
Rotational dynamics in dipolar colloidal suspensions: Video microscopy experiments and simulations results
,”
J. Non-Newtonian Fluid Mech.
102
,
135
148
(
2002
).
88.
R.
Calhoun
,
A.
Yadav
,
P.
Phelan
,
A.
Vuppu
,
A.
Garcia
, and
M.
Hayes
, “
Paramagnetic particles and mixing in micro-scale flows
,”
Lab Chip
6
,
247
257
(
2006
).
89.
T. G.
Kang
,
M. A.
Hulsen
,
J. M.
den Toonder
,
P. D.
Anderson
, and
H. E.
Meijer
, “
A direct simulation method for flows with suspended paramagnetic particles
,”
J. Comput. Phys.
227
,
4441
4458
(
2008
).
90.
S.
Melle
and
J. E.
Martin
, “
Chain model of a magnetorheological suspension in a rotating field
,”
J. Chem. Phys.
118
,
9875
9881
(
2003
).
91.
T.
Lund-Olesen
,
B. B.
Buus
,
J. G.
Howalt
, and
M. F.
Hansen
, “
Magnetic bead micromixer: Influence of magnetic element geometry and field amplitude
,”
J. Appl. Phys.
103
,
07E902
(
2008
).
92.
Y.
Seong
,
T. G.
Kang
,
M. A.
Hulsen
,
J. M. J.
den Toonder
, and
P. D.
Anderson
, “
Magnetic interaction of Janus magnetic particles suspended in a viscous fluid
,”
Phys. Rev. E
93
,
022607
(
2016
).
93.
H. E.
Kim
,
K.
Kim
,
T. Y.
Ma
, and
T. G.
Kang
, “
Numerical investigation of the dynamics of Janus magnetic particles in a rotating magnetic field
,”
Korea Aust. Rheol. J.
29
,
17
27
(
2017
).
94.
C.
Sobecki
,
J.
Zhang
, and
C.
Wang
, “
Dynamics of a pair of paramagnetic Janus particles under a uniform magnetic field and simple shear flow
,”
Magnetochemistry
7
,
16
(
2021
).
95.
K. P.
Yuet
,
D. K.
Hwang
,
R.
Haghgooie
, and
P. S.
Doyle
, “
Multifunctional superparamagnetic Janus particles
,”
Langmuir
26
,
4281
4287
(
2010
).
96.
R. V.
Ramachandran
,
A.
Barman
,
P.
Modak
,
R.
Bhat
,
A.
Ghosh
, and
D. K.
Saini
, “
How safe are magnetic nanomotors: From cells to animals
,”
Biomater. Adv.
140
,
213048
(
2022
).
97.
D.
Nouri
,
A.
Zabihi-Hesari
, and
M.
Passandideh-Fard
, “
Rapid mixing in micromixers using magnetic field
,”
Sens. Actuators A: Phys.
255
,
79
86
(
2017
).
98.
G.
Kitenbergs
,
K.
Erglis
,
R.
Perzynski
, and
A.
Cēbers
, “
Magnetic particle mixing with magnetic micro-convection for microfluidics
,”
J. Magn. Magn. Mater.
380
,
227
230
(
2015
).
99.
R.
Zhou
and
A. N.
Surendran
, “
Study on micromagnets induced local wavy mixing in a microfluidic channel
,”
Appl. Phys. Lett.
117
,
132408
(
2020
).
100.
H.
Suzuki
and
C.-M.
Ho
, “A magnetic force driven chaotic micro-mixer,” in Technical Digest. MEMS 2002 IEEE International Conference. Fifteenth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.02CH37266) (IEEE, 2002), pp. 40–43.
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