Abstract

Return bends are frequently encountered in microfluidic systems. In this study, a three-dimensional spectral boundary element method for interfacial dynamics in Stokes flow has been adopted to investigate the dynamics of viscous droplets in rectangular return bends. The droplet trajectory, deformation, and migration velocity are investigated under the influence of various fluid properties and operational conditions, which are depicted by the Capillary number, viscosity ratio, and droplet size, as well as the dimensions of the return bend. While the computational results provide information for the design of return bends in microfluidic systems in general, the computational framework shows potential to guide the design and operation of a droplet-based microfluidic delivery system for cell seeding.

References

References
1.
Kelly
,
B. T.
,
Baret
,
J.-C.
,
Taly
,
V.
, and
Griffiths
,
A. D.
,
2007
, “
Miniaturizing Chemistry and Biology in Microdroplets
,”
Chem. Commun.
,
18
(
18
), pp.
1773
1788
.10.1039/b616252e
2.
Joensson
,
H. N.
, and
Andersson Svahn
,
H.
,
2012
, “
Droplet Microfluidics - A Tool for Single-Cell Analysis
,”
Angew. Chem. Int. Ed.
,
51
(
49
), pp.
12176
12192
.10.1002/anie.201200460
3.
Dittrich
,
P. S.
,
Jahnz
,
M.
, and
Schwille
,
P.
,
2005
, “
A New Embedded Process for Compartmentalized Cell-Free Protein Expression and On-Line Detection in Microfluidic Devices
,”
ChemBioChem
,
6
(
5
), pp.
811
814
.10.1002/cbic.200400321
4.
Huebner
,
A.
,
Srisa-Art
,
M.
,
Holt
,
D.
,
Abell
,
C.
,
Hollfelder
,
F.
,
deMello
,
A. J.
, and
Edel
,
J. B.
,
2007
, “
Quantitative Detection of Protein Expression in Single Cells Using Droplet Microfluidics
,”
Chem. Commun.
,
12
(
12
), pp.
1218
1220
.10.1039/b618570
5.
He
,
M.
,
Edgar
,
J. S.
,
Jeffries
,
G. D. M.
,
Lorenz
,
R. M.
,
Shelby
,
J. P.
, and
Chiu
,
D. T.
,
2005
, “
Selective Encapsulation of Single Cells and Subcellular Organelles Into Picoliter- and Femtoliter-Volume Droplets
,”
Anal. Chem.
,
77
(
6
), pp.
1539
1544
.10.1021/ac0480850
6.
Zheng
,
B.
, and
Ismagilov
,
R. F.
,
2005
, “
A Microfluidic Approach for Screening Submicroliter Volumes Against Multiple Reagents by Using Preformed Arrays of Nanoliter Plugs in a Three-Phase Liquid/Liquid/Gas Flow
,”
Angew. Chem. Int. Ed.
,
44
(
17
), pp.
2520
2523
.10.1002/anie.200462857
7.
Huh
,
D.
,
Gu
,
W.
,
Kamotani
,
Y.
,
Grotberg
,
J. B.
, and
Takayama
,
S.
,
2005
, “
Microfluidics for Flow Cytometric Analysis of Cells and Particles
,”
Physiol. Meas.
,
26
(
3
), pp.
R73
R98
.10.1088/0967-3334/26/3/R02
8.
Fair
,
R.
,
2007
, “
Digital Microfluicis: Is a True Lab-on-a-Chip Possible?
,”
Microfluid. Nanofluid.
,
3
(
3
), pp.
245
281
.10.1007/s10404-007-0161-8
9.
Link
,
D.
,
Anna
,
S.
,
Weitz
,
D.
, and
Stone
,
H.
,
2004
, “
Geometrically Mediated Breakup of Drops in Microfluidic Devices
,”
Phys. Rev. Lett.
,
92
(
5
), p.
054503
.10.1103/PhysRevLett.92.054503
10.
Tan
,
Y.
,
Fisher
,
J.
,
Lee
,
A.
,
Cristini
,
V.
, and
Lee
,
A.
,
2004
, “
Design of Microfluidic Channel Geometries for the Control of Droplet Volume, Chemical Concentration, and Sorting
,”
Lab Chip
,
4
(
4
), pp.
292
298
.10.1039/b403280m
11.
Singh
,
J. L.
,
Melbye
,
J.
,
Wang
,
Y.
,
Zhang
,
Y.
,
Brooks
,
A.
, and
Brooks
,
B.
,
2018
, “
Spectral Boundary Element Analysis on Droplet Based Microfluidics Used in Cell Seeding
,”
Biomed. Sci. Instrum.
,
54
(
1
), pp.
217
221
.https://iaexpress.ca/wp-content/uploads/2018/06/IAE-Biomed-Sci-Instrum-April-2018-Vol-54-1-1-2.pdf
12.
Singh
,
J. L.
,
Zhang
,
Y.
,
Wang
,
Y.
,
Gerber
,
B.
,
Stark
,
K.
,
Yon
,
K.
,
Brooks
,
A.
, and
Brooks
,
B.
,
2018
, “
Design of an Experimental Platform for Flow Visualization in a Microfluidic Chip
,”
Biomed. Sci. Instrum.
,
54
(
1
), pp.
184
188
.
13.
Ottino
,
J. M.
,
Wiggins
,
S. R.
,
Bringer
,
M. R.
,
Gerdts
,
C. J.
,
Song
,
H.
,
Tice
,
J. D.
, and
Ismagilov
,
R. F.
,
2004
, “
Microfluidic Systems for Chemical Kinetics That Rely on Chaotic Mixing in Droplets
,”
Philos. Trans. R. Soc. London. Ser. A: Math., Phys. Eng. Sci.
,
362
(
1818
), pp.
1087
1104
.10.1098/rsta.2003.1364
14.
Coulliette
,
C.
, and
Pozrikidis
,
C.
,
1998
, “
Motion of an Array of Drops Through a Cylindrical Tube
,”
J. Fluid Mech.
,
358
, pp.
1
28
.10.1017/S0022112097007957
15.
Ho
,
B.
, and
Leal
,
L.
,
1975
, “
The Creeping Motion of Liquid Drops Through a Circular Tube of Comparable Diameter
,”
J. Fluid Mech.
,
71
(
2
), pp.
361
383
.10.1017/S0022112075002625
16.
Martinez
,
M.
, and
Udell
,
K.
,
1990
, “
Axisymmetric Creeping Motion of Drops Through Circular Tubes
,”
J. Fluid Mech.
,
210
, pp.
565
591
.10.1017/S0022112090001409
17.
Olbricht
,
W.
, and
Kung
,
D.
,
1992
, “
The Deformation and Breakup of Liquid Drops in Low Reynolds Number Flow Through a Capillary
,”
Phys. Fluids A
,
4
(
7
), pp.
1347
1354
.10.1063/1.858412
18.
Kolb
,
W.
, and
Cerro
,
R.
,
1993
, “
The Motion of Long Bubbles in Tubes of Square Cross Section
,”
Phys. Fluids A
,
5
(
7
), pp.
1549
1557
.10.1063/1.858832
19.
Wong
,
H.
,
Radke
,
C.
, and
Morris
,
S.
,
1995
, “
The Motion of Long Bubbles in Polygonal Capillariers. Part 1. Thin Films
,”
J. Fluid Mech.
,
292
, pp.
71
94
.10.1017/S0022112095001443
20.
Wong
,
H.
,
Radke
,
C.
, and
Morris
,
S.
,
1995
, “
The Motion of Long Bubbles in Polygonal Capillariers. Part 2. Drag, Fluid Pressure and Fluid Flow
,”
J. Fluid Mech.
,
292
, pp.
95
110
.10.1017/S0022112095001455
21.
Wang
,
Y.
, and
Dimitrakopoulos
,
P.
,
2012
, “
Low-Reynolds-Number Droplet Motion in a Square Microfluidic Channel
,”
Theor. Comput. Fluid Dyn.
,
26
(
1–4
), pp.
361
379
.10.1007/s00162-011-0238-6
22.
Martinez
,
M.
, and
Udell
,
K.
,
1990
, “
Axisymmetric Creeping Motion of Drops Through a Periodically Constricted Tube
,”
AIP Conf. Proc.
,
197
, pp.
222
234
.10.1063/1.38959
23.
Olgac
,
U.
,
Kayaalp
,
A.
, and
Muradoglu
,
M.
,
2006
, “
Buoyancy-Driven Motion and Breakup of Viscous Drops in Constricted Capillaries
,”
Int. J. Multiphase Flow
,
32
(
9
), pp.
1055
1071
.10.1016/j.ijmultiphaseflow.2006.05.004
24.
Tsai
,
T.
, and
Miksis
,
M.
,
1994
, “
Dynamics of a Drop in a Constricted Capillary Tube
,”
J. Fluid Mech.
,
274
, pp.
197
217
.10.1017/S0022112094002090
25.
Pozrikidis
,
C.
,
1992
,
Boundary Integral and Singularity Methods for Linearized Viscous Flow
,
Cambridge University Press
,
New York
.
26.
Wang
,
Y.
, and
Dimitrakopoulos
,
P.
,
2006
, “
A Three-Dimensional Spectral Boundary Element Algorithm for Interfacial Dynamics in Stokes Flow
,”
Phys. Fluids
,
18
(
8
), p.
082106
.10.1063/1.2337572
27.
Khan
,
M.
, and
Wang
,
Y.
,
2010
, “
Droplet Motion in a Microconfined Shear Flow Via a Three-Dimensional Spectral Boundary Element Method
,”
Phys. Fluids
,
22
(
12
), p.
123301
.10.1063/1.3525357
28.
Qu
,
X.
, and
Wang
,
Y.
,
2012
, “
Dynamics of Concentric and Eccentric Compound Droplets Suspended in Extensional Flows
,”
Phys. Fluids
,
24
(
12
), p.
123302
.10.1063/1.4770294
29.
Yih
,
C.
,
Fluid Mechanics
,
West River Press
,
Ann Arbor, MI
.
30.
Muldowney
,
G. P.
, and
Higdon
,
J. J. L.
,
1995
, “
A Spectral Boundary Element Approach to Three-Dimensional Stokes Flow
,”
J. Fluid Mech.
,
298
, pp.
167
192
.10.1017/S0022112095003260
31.
Wang
,
Y.
,
Lutfurakhmanov
,
A.
, and
Akhatov
,
I. S.
,
2015
, “
Dynamics of Fluid Bridges Between a Rising Capillary Tube and a Substrate
,”
Microfluid. Nanofluid.
,
18
(
5–6
), pp.
807
818
.10.1007/s10404-014-1473-0
32.
Wang
,
Y.
, and
Dimitrakopoulos
,
P.
,
2006
, “
Normal Force Exerted on Vascular Endothelial Cells
,”
Phys. Rev. Lett.
,
96
(
2
), p.
028106
.10.1103/PhysRevLett.96.028106
33.
Wang
,
Y.
,
2007
, “
Flow and Interfacial Dynamics in Vascular Vessels and Microfluidics
,” Ph.D. thesis,
University of Maryland, College Park, MD.
You do not currently have access to this content.