The motion and concentration distribution of particles and cells in flow are important factors which affect the fluid properties, flow structure, and mass transfer of biological and chemical species in blood vessels and channels. In this study, number density distributions of particles and rigidized red blood cells (RBCs) in a microchannel whose size is comparable to the sizes of the particle and RBCs are measured. Measurements were conducted at several streamwise locations for suspensions of particles and RBCs with hematocrits of the order of 10% and particle sizes of 5 and 8 µm. Analysis of the migration and resulting concentration distribution of the particles and RBCs was conducted using a model that considers the particle–particle collision and fluid dynamic force. As the size of the microchannel is small, the wall effect on the collision and migration of the particles and RBCs was significant. The wall reduced the overlapping area of the particles in collision and their displacement after collision (mobility), which varied the number, location, and magnitude of the maximum peaks observed in the number density distribution. Furthermore, the rotational motion of the rigidized RBCs in the channel flow reduced the effective lengths of the overlapping area and displacement, whereas it produced additional migration at the wall. With these terms added in the model, the number density distributions of the particles and RBCs showed reasonable agreement with those of the measurement. Especially, the number of peaks and their location for the maximum values in the model and measurement matched well.

1.
N.
Tateishi
,
Y.
Suzuki
,
I.
Cicha
, and
N.
Maeda
, “
O2 release from erythrocytes flowing in a narrow O2-permeable tube: Effects of erythrocyte aggregation
,”
Am. J. Physiol.: Heart Circ. Physiol.
281
,
H448
(
2001
).
2.
D. A.
Fedosov
,
W.
Pan
,
B.
Caswell
,
G.
Gompper
, and
G. E.
Karniadakis
, “
Predicting human blood viscosity in silico
,”
Proc. Natl. Acad. Sci. U. S. A.
108
,
11772
(
2011
).
3.
H.
Lei
,
D. A.
Fedosov
,
B.
Caswell
, and
G.
Em Karniadakis
, “
Blood flow in small tubes: Quantifying the transition to the non-continuum regime
,”
J. Fluid Mech.
722
,
214
(
2013
).
4.
D.
Alizadehrad
,
Y.
Imai
,
K.
Nakaaki
,
T.
Ishikawa
, and
T.
Yamaguchi
, “
Quantification of red blood cell deformation at high-hematocrit blood flow in microvessels
,”
J. Biomech.
45
,
2684
(
2012
).
5.
H.
Zhao
,
E. S. G.
Shaqfeh
, and
V.
Narsimhan
, “
Shear-induced particle migration and margination in a cellular suspension
,”
Phys. Fluids
24
,
011902
(
2012
).
6.
J. M.
Sherwood
,
E.
Kaliviotis
,
J.
Dusting
, and
S.
Balabani
, “
Hematocrit, viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel
,”
Biomech. Model. Mechanobiol.
13
,
259
(
2014
).
7.
Q. M.
Qi
and
E. S. G.
Shaqfeh
, “
Theory to predict migration and margination in the pressure-driven channel flow of blood
,”
Phys. Rev. Fluids
2
,
093102
(
2017
).
8.
Q. M.
Qui
and
E. S. G.
Shaqfeh
, “
Time-dependent particle migration and margination in the pressure-driven channel flow of blood
,”
Phys. Rev. Fluids
3
,
034302
(
2018
).
9.
J. L.
McWhirter
,
H.
Noguchi
, and
G.
Gompper
, “
Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries
,”
Proc. Natl. Acad. Sci. U. S. A.
106
,
6039
(
2009
).
10.
J. B.
Freund
and
M. M.
Orescanin
, “
Cellular flow in a small blood vessel
,”
J. Fluid Mech.
671
,
466
(
2011
).
11.
A.
Kumar
and
M. D.
Graham
, “
Margination and segregation in confined flows of blood and other multicomponent suspensions
,”
Soft Matter
8
,
10536
(
2012
).
12.
D. A.
Reasor
, Jr.
,
M.
Mehrabadi
,
D. N.
Ku
, and
C. K.
Aidun
, “
Determination of critical parameters in platelet margination
,”
Ann. Biomed. Eng.
41
,
238
(
2013
).
13.
N.
Takeishi
,
Y.
Imai
,
T.
Yamaguchi
, and
T.
Ishikawa
, “
Flow of a circulating tumor cell and red blood cells in microvessels
,”
Phys. Rev. E
92
,
063011
(
2015
).
14.
M.
Faivre
,
M.
Abkarian
,
K.
Bickraj
, and
H. A.
Stone
, “
Geometrical focusing of cells in a microfluidic device: An approach to separate blood plasma
,”
Biorheology
43
,
147
(
2006
), https://content.iospress.com/articles/biorheology/bir384.
15.
D.
Di Carlo
,
J. F.
Edd
,
K. J.
Humphry
,
H. A.
Stone
, and
M.
Toner
, “
Particle segregation and dynamics in confined flows
,”
Phys. Rev. Lett.
102
,
094503
(
2009
).
16.
T.
Kulrattanarak
,
R. G. M.
van der Sman
,
C. G. P. H.
Schroën
, and
R. M.
Boom
, “
Classification and evaluation of microfluidic devices for continuous suspension fractionation
,”
Adv. Colloid Interface Sci.
142
,
53
(
2008
).
17.
A. A. S.
Bhagat
,
S. S.
Kuntaegowdanahalli
, and
I.
Papautsky
, “
Enhanced particle filtration in straight microchannels using shear-modulated inertial migration
,”
Phys. Fluids
20
,
101702
(
2014
).
18.
K.
Tatsumi
,
K.
Kawano
,
H.
Shintani
, and
K.
Nakabe
, “
Analysis and measurement of dielectrophoretic manipulation of particles and lymphocytes using rail-type electrodes
,”
Med. Eng. Phys.
38
,
24
(
2016
).
19.
G.
Segre
and
A.
Silberberg
, “
Behaviour of macroscopic rigid spheres in Poiseuille flow: Part 2. Experimental results and interpretation
,”
J. Fluid Mech.
14
,
136
(
1962
).
20.
B. P.
Ho
and
L. G.
Leal
, “
Inertial migration of rigid spheres in two-dimensional unidirectional flows
,”
J. Fluid Mech.
65
,
365
(
1974
).
21.
M. R.
Maxey
, “
Equation of motion for a small rigid sphere in a nonuniform flow
,”
Phys. Fluids
26
,
883
(
1983
).
22.
J.
Schonberg
and
E. J.
Hinch
, “
Inertial migration of a sphere in Poiseuille flow
,”
J. Fluid Mech.
203
,
517
(
1989
).
23.
R. E.
Hampton
,
A. A.
Mammoli
,
A. L.
Graham
, and
N.
Tetlow
, “
Migration of particles undergoing pressure-driven flow in a circular conduit
,”
J. Rheol.
41
,
612
(
1997
).
24.
M.
Han
and
C.
Kim
, “
Particle migration in tube flow of suspensions
,”
J. Rheol.
43
,
1157
(
1999
).
25.
E. S.
Asmolov
, “
The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number
,”
J. Fluid Mech.
381
,
63
(
1999
).
26.
J.-P.
Matas
,
J. F.
Morris
, and
E.
Guazzelli
, “
Inertial migration of rigid spherical particles in Poiseuille flow
,”
J. Fluid Mech.
515
,
171
(
2004
).
27.
K. J.
Humphry
,
P. M.
Kulkarni
,
D. A.
Weitz
,
J. F.
Morris
, and
H. A.
Stone
, “
Axial and lateral particle ordering in finite Reynolds number channel flows
,”
Phys. Fluids
22
,
081703
(
2010
).
28.
M.
Abbas
,
P.
Magaud
,
Y.
Gao
, and
S.
Geoffroy
, “
Migration of finite sized particles in a laminar square channel flow from low to high Reynolds number
,”
Phys. Fluids
26
,
123301
(
2014
).
29.
T.
Fukuda
,
S.
Takeuchi
, and
T.
Kajishima
, “
Effects of curvature and vorticity in rotating flows on hydrodynamic forces acting on a sphere
,”
Int. J. Multiphase Flow
58
,
292
(
2014
).
30.
T.
Roth
,
L.
Sprenger
,
S.
Odenbach
, and
U. O.
Häfeli
, “
Continuous form-dependent focusing of non-spherical microparticles in a highly diluted suspension with the help of microfluidic spirals
,”
Phys. Fluids
30
,
045102
(
2018
).
31.
A.
Shamloo
and
A.
Mashhadian
, “
Inertial particle focusing in serpentine channels on a centrifugal platform
,”
Phys. Fluids
30
,
012002
(
2018
).
32.
M. M.
Reddy
and
A.
Singh
, “
Shear-induced particle migration and size segregation in bidisperse suspension flowing through symmetric T-shaped channel
,”
Phys. Fluids
31
,
053305
(
2019
).
33.
M.
Abkarian
,
C.
Lartigue
, and
A.
Viallat
, “
Tank treading and unbinding deformable vesicles in shear flow: Determination of the lift force
,”
Phys. Rev. Lett.
88
,
068103-1
(
2002
).
34.
T. M.
Geislinger
and
T.
Franke
, “
Hydrodynamic lift of vesicles and red blood cells in flow—From Fåhræus and Lindqvist to microfluidic cell sorting
,”
Adv. Colloid Interface Sci.
208
,
161
(
2014
).
35.
D.
Abreu
,
M.
Levant
,
V.
Steinberg
, and
U.
Seifert
, “
Fluid vesicles in flow
,”
Adv. Colloid Interface Sci.
208
,
129
(
2014
).
36.
A. H.
Karnis
,
L.
Goldsmith
, and
S. G.
Mason
, “
The kinetics of flowing dispersions: I. Concentrated suspensions of rigid particles
,”
J. Colloid Interface Sci.
22
,
531
(
1966
).
37.
I. M.
Krieger
, “
Rheology of monodisperse latices
,”
Adv. Colloid Interface Sci.
3
,
111
(
1972
).
38.
C. J.
Koh
,
P.
Hookham
, and
L. G.
Leal
, “
An experimental investigation of concentrated suspension flows in a rectangular channel
,”
J. Fluid Mech.
266
,
1
(
1994
).
39.
H.
Iddir
and
H.
Arastoopour
, “
Modeling of multitype particle flow using the kinetic theory approach
,”
AIChE J.
51
,
1620
(
2005
).
40.
D.
Leighton
and
A.
Acrivos
, “
The shear-induced migration of particles in concentrated suspensions
,”
J. Fluid Mech.
181
,
415
(
1987
).
41.
R. J.
Phillips
,
R. C.
Armstrong
, and
R. A.
Brown
, “
A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration
,”
Phys. Fluids A
4
,
30
(
1992
).
42.
S. R.
Subia
,
M. S.
Ingber
,
L. A.
Mondy
,
S. A.
Altobelli
, and
A. L.
Graham
, “
Modelling of concentrated suspensions using a continuum constitutive equation
,”
J. Fluid Mech.
373
,
193
(
1998
).
43.
A. S.
Sangani
,
A.
Acrivos
, and
P.
Peyla
, “
Roles of particle-wall and particle-particle interactions in highly confined suspensions of spherical particles being sheared at low Reynolds numbers
,”
Phys. Fluids
23
,
083302
(
2011
).
44.
J. R.
Agudo
,
S.
Dasilva
, and
A.
Wierschem
, “
How do neighbors affect incipient particle motion in laminar shear flow?
,”
Phys. Fluids
26
,
053303
(
2014
).
45.
P.
Pham
,
B.
Metzger
, and
J. E.
Butler
, “
Particle dispersion in sheared suspensions: Crucial role of solid-solid contacts
,”
Phys. Fluids
27
,
051701
(
2015
).
46.
J.
Hu
and
Z.
Guo
, “
Effect of interaction between a particle cluster and a single particle on particle motion and distribution during sedimentation: A numerical study
,”
Phys. Fluids
31
,
033301
(
2019
).
47.
R. B.
Reboucas
,
I. R.
Siqueira
,
P. R.
de Souza Mendes
, and
M. S.
Carvalho
, “
On the pressure-driven flow of suspensions: Particle migration in shear sensitive liquids
,”
J. Non-Newtonian Fluid Mech.
243
,
178
(
2016
).
48.
X.
Grandchamp
,
G.
Coupier
,
A.
Srivastav
,
C.
Minetti
, and
T.
Podgorski
, “
Lift and down-gradient shear-induced diffusion in red blood cell suspensions
,”
Phys. Rev. Lett.
110
,
108101
(
2013
).
49.
S.
Inoue
and
K. R.
Spring
,
Video Microscopy: The Fundamentals
, 2nd ed. (
Plenum Press
,
New York
,
1997
).
50.
J.
Schindelin
,
I.
Arganda-Carreras
,
E.
Frise
,
V.
Kaynig
,
M.
Longair
,
T.
Pietzsch
,
S.
Preibisch
,
C.
Rueden
,
S.
Saalfeld
,
B.
Schmid
,
J. Y.
Tinevez
,
D. J.
White
,
V.
Hartenstein
,
K.
Eliceiri
,
P.
Tomancak
, and
A.
Cardona
, “
Fiji: An open-source platform for biological-image analysis
,”
Nat. Methods
9
,
676
(
2012
).
51.
G. B.
Jeffery
, “
The motion of ellipsoidal particles immersed in a viscous fluid
,”
Proc. R. Soc. A
125
,
161
(
1922
).
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