The micromechanical measurement field has struggled to establish repeatable techniques because the deforming stresses can be difficult to model. A recent numerical study [Lu et al., J. Fluid Mech. 962, A26 (2023)] showed that viscoelastic capsules flowing through a cross-slot can achieve a quasi-steady strain near the extensional flow stagnation point that is equal to the equilibrium static strain, thereby implying that the capsule's elastic behavior can be captured in continuous device operation. However, no experimental microfluidic cross-slot studies have reported quasi-steady strains for suspended cells or particles to our knowledge. Here, we demonstrate experimentally the conditions necessary for the cross-slot microfluidic device to replicate a uniaxial creep test at the microscale and at relatively high throughput. By using large dimension cross-slots relative to the microparticle diameter, our cross-slot implementation creates an extensional flow region that is large enough for agarose hydrogel microparticles to achieve a strain plateau while dwelling near the stagnation point. This strain plateau will be key for accurately and precisely measuring viscoelastic properties of small microscale biological objects. We propose an analytical mechanical model to extract linear viscoelastic mechanical properties from observed particle strain histories. Particle image velocimetry measurements of the unperturbed velocity field is used to estimate where in the device particles experienced extensional flow and where the mechanical model might be applied to extract mechanical property measurements. Finally, we provide recommendations for applying the cross-slot microscale creep experiment to other biomaterials and criteria to identify particles that likely achieved a quasi-steady strain state.

1.
M.
Urbanska
,
H. E.
Muñoz
,
J.
Shaw Bagnall
,
O.
Otto
,
S. R.
Manalis
,
D.
Di Carlo
, and
J.
Guck
, “
A comparison of microfluidic methods for high-throughput cell deformability measurements
,”
Nat. Methods
17
(
6
),
587
593
(
2020
).
2.
M.
Urbanska
and
J.
Guck
, “
Single-cell mechanics: Structural determinants and functional relevance
,”
Annu. Rev. Biophys.
53
(
1
),
367
395
(
2024
).
3.
J.
Lin
,
D.
Kim
,
H. T.
Tse
,
P.
Tseng
,
L.
Peng
,
M.
Dhar
,
S.
Karumbayaram
, and
D.
Di Carlo
, “
High-throughput physical phenotyping of cell differentiation
,”
Microsyst. Nanoeng.
3
,
17013
17017
(
2017
).
4.
L. D.
Wittwer
,
F.
Reichel
,
P.
Müller
,
J.
Guck
, and
S.
Aland
, “
A new hyperelastic lookup table for RT-DC
,”
Soft Matter
19
,
2064
2073
(
2023
).
5.
F. J.
Armistead
,
J.
Gala De Pablo
,
H.
Gadêlha
,
S. A.
Peyman
, and
S. D.
Evans
, “
Cells under stress: An inertial-shear microfluidic determination of cell behavior
,”
Biophys. J.
116
(
6
),
1127
1135
(
2019
).
6.
K. D.
Nyberg
,
K. H.
Hu
,
S. H.
Kleinman
,
D. B.
Khismatullin
,
M. J.
Butte
, and
A. C.
Rowat
, “
Quantitative deformability cytometry: Rapid, calibrated measurements of cell mechanical properties
,”
Biophys. J.
113
(
7
),
1574
1584
(
2017
).
7.
J. R.
Lange
,
J.
Steinwachs
,
T.
Kolb
,
L. A.
Lautscham
,
I.
Harder
,
G.
Whyte
, and
B.
Fabry
, “
Microconstriction arrays for high-throughput quantitative measurements of cell mechanical properties
,”
Biophys. J.
109
(
1
),
26
34
(
2015
).
8.
L.
Guillou
,
J. B.
Dahl
,
J.-M. G.
Lin
,
A. I.
Barakat
,
J.
Husson
,
S. J.
Muller
, and
S.
Kumar
, “
Measuring cell viscoelastic properties using a microfluidic extensional flow device
,”
Biophys. J.
111
(
9
),
2039
2050
(
2016
).
9.
O.
Scrivener
,
C.
Berner
,
R.
Cressely
,
R.
Hocquart
,
R.
Sellin
, and
N. S.
Vlachos
, “
Dynamical behaviour of drag-reducing polymer solutions
,”
J. Non-Newton. Fluid Mech.
5
,
475
495
(
1979
).
10.
P. E.
Arratia
,
C. C.
Thomas
,
J.
Diorio
, and
J. P.
Gollub
, “
Elastic instabilities of polymer solutions in cross-channel flow
,”
Phys. Rev. Lett.
96
(
14
),
144502
(
2006
).
11.
S. J.
Haward
,
T. J.
Ober
,
M. S. N.
Oliveira
,
M. A.
Alves
, and
G. H.
McKinley
, “
Extensional rheology and elastic instabilities of a wormlike micellar solution in a microfluidic cross-slot device
,”
Soft Matter
8
(
2
),
536
555
(
2012
).
12.
C. M.
Schroeder
,
H. P.
Babcock
,
E. S. G.
Shaqfeh
, and
S.
Chu
, “
Observation of polymer conformation hysteresis in extensional flow
,”
Science
301
(
5639
),
1515
1519
(
2003
).
13.
C. M.
Schroeder
,
E. S. G.
Shaqfeh
, and
S.
Chu
, “
Effect of hydrodynamic interactions on DNA dynamics in extensional flow: Simulation and single molecule experiment
,”
Macromolecules
37
(
24
),
9242
9256
(
2004
).
14.
R.
Dylla-Spears
,
J. E.
Townsend
,
L. L.
Sohn
,
L.
Jen-Jacobson
, and
S. J.
Muller
, “
Fluorescent marker for direct detection of specific dsDNA sequences
,”
Anal. Chem.
81
(
24
),
10049
10054
(
2009
).
15.
T. T.
Perkins
,
D. E.
Smith
, and
S.
Chu
, “
Single polymer dynamics in an elongational flow
,”
Science
276
(
5321
),
2016
2021
(
1997
).
16.
V.
Kantsler
,
E.
Segre
, and
V.
Steinberg
, “
Critical dynamics of vesicle stretching transition in elongational flow
,”
Phys. Rev. Lett.
101
(
4
),
048101
(
2008
).
17.
J. B.
Dahl
,
V.
Narsimhan
,
B.
Gouveia
,
S.
Kumar
,
E. S. G.
Shaqfeh
, and
S. J.
Muller
, “
Experimental observation of the asymmetric instability of intermediate-reduced-volume vesicles in extensional flow
,”
Soft Matter
12
(
16
),
3787
3796
(
2016
).
18.
D.
Kumar
,
C. M.
Richter
, and
C. M.
Schroeder
, “
Double-mode relaxation of highly deformed anisotropic vesicles
,”
Phys. Rev. E
102
(
1
),
010605
(
2020
).
19.
D. R.
Gossett
,
H. T. K.
Tse
,
S. A.
Lee
,
Y.
Ying
,
A. G.
Lindgren
,
O. O.
Yang
,
J.
Rao
,
A. T.
Clark
, and
D.
Di Carlo
, “
Hydrodynamic stretching of single cells for large population mechanical phenotyping
,”
Proc. Natl. Acad. Sci. U. S. A.
109
(
20
),
7630
7635
(
2012
).
20.
H. T. K.
Tse
,
D. R.
Gossett
,
Y. S.
Moon
,
M.
Masaeli
,
M.
Sohsman
,
Y.
Ying
,
K.
Mislick
,
R. P.
Adams
,
J.
Rao
, and
D. D.
Carlo
, “
Quantitative diagnosis of malignant pleural effusions by single-cell mechanophenotyping
,”
Sci. Transl. Med.
5
(
212
),
212ra163
(
2013
).
21.
M. G.
Sorrells
,
Y.
Seo
,
M.
Magnen
,
B.
Broussard
,
R.
Sheybani
,
A. M.
Shah
,
H. R.
O’Neal
,
H. T. K.
Tse
,
M. R.
Looney
, and
D.
Di Carlo
, “
Biophysical changes of leukocyte activation (and NETosis) in the cellular host response to sepsis
,”
Diagnostics
13
(
8
),
1435
(
2023
).
22.
R. X.
Lu
,
Z. Y.
Guo
,
P.
Yu
, and
Y.
Sui
, “
Transient deformation of a viscoelastic capsule in a cross-slot microchannel: Effects of inertia and membrane viscosity
,”
J. Fluid Mech.
962
,
A26
(
2023
).
23.
S. J.
Hymel
,
H.
Lan
, and
D. B.
Khismatullin
, “
Elongation index as a sensitive measure of cell deformation in high-throughput microfluidic systems
,”
Biophys. J.
119
(
3
),
493
501
(
2020
).
24.
E. M.
Johnson-Chavarria
,
U.
Agrawal
,
M.
Tanyeri
,
T. E.
Kuhlman
, and
C. M.
Schroeder
, “
Automated single cell microbioreactor for monitoring intracellular dynamics and cell growth in free solution
,”
Lab Chip
14
(
15
),
2688
2697
(
2014
).
25.
Y.
Xia
and
G. M.
Whitesides
, “
Soft lithography
,”
Annu. Rev. Mater. Sci.
28
(
1
),
153
184
(
1998
).
26.
F.
Khalkhal
,
K. H.
Chaney
, and
S. J.
Muller
, “
Optimization and application of dry film photoresist for rapid fabrication of high-aspect-ratio microfluidic devices
,”
Microfluid Nanofluid
20
(
11
),
1
10
(
2016
).
27.
O.
Otto
,
P.
Rosendahl
,
A.
Mietke
,
S.
Golfier
,
C.
Herold
,
D.
Klaue
,
S.
Girardo
,
S.
Pagliara
,
A.
Ekpenyong
,
A.
Jacobi
,
M.
Wobus
,
N.
Töpfner
,
U. F.
Keyser
,
J.
Mansfeld
,
E.
Fischer-Friedrich
, and
J.
Guck
, “
Real-time deformability cytometry: On-the-fly cell mechanical phenotyping
,”
Nat. Methods
12
,
199
202
(
2015
).
28.
B.
Fregin
,
F.
Czerwinski
,
D.
Biedenweg
,
S.
Girardo
,
S.
Gross
,
K.
Aurich
, and
O.
Otto
, “
High-throughput single-cell rheology in complex samples by dynamic real-time deformability cytometry
,”
Nat. Commun.
10
(
1
),
415
(
2019
).
29.
F.
Reichel
,
R.
Goswami
,
S.
Girardo
, and
J.
Guck
, “
High-throughput viscoelastic characterization of cells in hyperbolic microchannels
,”
Lab Chip
24
(
9
),
2440
2453
(
2024
).
30.
S.
Goldblum
,
Y.
Bae
,
W. F.
Hink
, and
J.
Chalmers
, “
Protective effect of methylcellulose and other polymers on insect cells subjected to laminar shear stress
,”
Biotechnol. Prog.
6
(
5
),
383
390
(
1990
).
31.
M.
Raffel
,
C. E.
Willert
,
S. T.
Wereley
, and
J.
Kompenhans
,
Particle Image Velocimetry: A Practical Guide
, 2nd ed. (Springer Berlin Heidelberg,
2007
).
32.
J. G.
Santiago
,
S. T.
Wereley
,
C. D.
Meinhart
,
D. J.
Beebe
, and
R. J.
Adrian
, “
A particle image velocimetry system for microfluidics
,”
Exp. Fluids
25
(
4
),
316
319
(
1998
).
33.
A. D.
Edelstein
,
M. A.
Tsuchida
,
N.
Amodaj
,
H.
Pinkard
,
R. D.
Vale
, and
N.
Stuurman
, “
Advanced methods of microscope control using μManager software
,”
J. Biol. Methods
1
(
2
),
1
10
(
2014
).
34.
W.
Thielicke
and
E. J.
Stamhuis
, “
PIVlab—Towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB
,”
J. Open Res. Software
2
(
1
),
e30
(
2014
).
35.
S. M.
Pizer
,
E. P.
Amburn
,
J. D.
Austin
,
R.
Cromartie
,
A.
Geselowitz
,
T.
Greer
,
B.
ter Haar Romeny
,
J. B.
Zimmerman
, and
K.
Zuiderveld
, “
Adaptive histogram equalization and its variations
,”
Comput. Vis. Graph. Image Process.
39
(
3
),
355
368
(
1987
).
36.
J.
Westerweel
and
F.
Scarano
, “
Universal outlier detection for PIV data
,”
Exp. Fluids
39
(
6
),
1096
1100
(
2005
).
37.
H. A.
Stone
, “
Introduction to fluid dynamics for microfluidic flows
,” in
CMOS Biotechnology
, edited by
H.
Lee
,
R. M.
Westervelt
, and
D.
Ham
(
Springer
,
Boston
,
MA
,
2007
), pp.
5
30
.
38.
D.
Blair
and
E.
Dufresne
, “The Matlab particle tracking code repository,” https://site.physics.georgetown.edu/matlab/ (last accessed January 2019).
39.
J. C.
Crocker
and
D. G.
Grier
, “
Methods of digital video microscopy for colloidal studies
,”
J. Colloid Interface Sci.
179
(
1
),
298
310
(
1996
).
40.
J. C.
Crocker
,
D.
Grier
, and
E. R.
Weeks
, “Particle tracking using IDL,” http://www.physics.emory.edu/faculty/weeks//idl/ (last accessed January 2019).
41.
O.
Gal
,
Fit_ellipse
(
MATLAB Central File Exchange
,
2003
).
42.
B.
Bechtold
, “
Violin plots for MATLAB
” (
GitHub
,
2016
).
43.
R. M.
Christensen
,
Theory of Viscoelasticity
, 2nd ed. (Academic Press, Inc.,
1982
).
44.
T.
Murata
, “
Deformation of an elastic particle suspended in an arbitrary flow field
,”
J. Phys. Soc. Jpn.
50
(
3
),
1009
1016
(
1981
).
45.
Z.
Xue
,
J. J.
Charonko
, and
P. P.
Vlachos
, “
Particle image velocimetry correlation signal-to-noise ratio metrics and measurement uncertainty quantification
,”
Meas. Sci. Technol.
25
(
11
),
115301
(
2014
).
46.
B.
Büyükurgancı
,
S. K.
Basu
,
M.
Neuner
,
J.
Guck
,
A.
Wierschem
, and
F.
Reichel
, “
Shear rheology of methyl cellulose based solutions for cell mechanical measurements at high shear rates
,”
Soft Matter
19
(
9
),
1739
1748
(
2023
).
47.
J. T.
Cabral
and
S. D.
Hudson
, “
Microfluidic approach for rapid multicomponent interfacial tensiometry
,”
Lab Chip
6
(
3
),
427
436
(
2006
).
48.
C.
Trégouët
,
T.
Salez
,
C.
Monteux
, and
M.
Reyssat
, “
Transient deformation of a droplet near a microfluidic constriction: A quantitative analysis
,”
Phys. Rev. Fluids
3
(
5
),
053603
(
2018
).
49.
M.
Masaeli
,
D.
Gupta
,
S.
O’Byrne
,
H. T. K.
Tse
,
D. R.
Gossett
,
P.
Tseng
,
A. S.
Utada
,
H.-J.
Jung
,
S.
Young
,
A. T.
Clark
, and
D.
Di Carlo
, “
Multiparameter mechanical and morphometric screening of cells
,”
Sci. Rep.
6
(
1
),
37863
(
2016
).
50.
A.
Mietke
,
O.
Otto
,
S.
Girardo
,
P.
Rosendahl
,
A.
Taubenberger
,
S.
Golfier
,
E.
Ulbricht
,
S.
Aland
,
J.
Guck
, and
E.
Fischer-Friedrich
, “
Extracting cell stiffness from real-time deformability cytometry: Theory and experiment
,”
Biophys. J.
109
(
10
),
2023
2036
(
2015
).
51.
N.
Gundogan
,
O.
Okay
, and
W.
Oppermann
, “
Swelling, elasticity and spatial inhomogeneity of poly(N,N-dimethylacrylamide) hydrogels formed at various polymer concentrations
,”
Macromol. Chem. Phys.
205
(
6
),
814
823
(
2004
).
52.
A. K.
Denisin
and
B. L.
Pruitt
, “
Tuning the range of polyacrylamide gel stiffness for mechanobiology applications
,”
ACS Appl. Mater. Interfaces
8
(
34
),
21893
21902
(
2016
).
53.
S.
Girardo
,
N.
Träber
,
K.
Wagner
,
G.
Cojoc
,
C.
Herold
,
R.
Goswami
,
R.
Schlüßler
,
S.
Abuhattum
,
A.
Taubenberger
,
F.
Reichel
,
D.
Mokbel
,
M.
Herbig
,
M.
Schürmann
,
P.
Müller
,
T.
Heida
,
A.
Jacobi
,
E.
Ulbricht
,
J.
Thiele
,
C.
Werner
, and
J.
Guck
, “
Standardized microgel beads as elastic cell mechanical probes
,”
J. Mater. Chem. B
6
(
39
),
6245
6261
(
2018
).
54.
M. S. C. A.
Brito
, “
Design of model fluids for flow characterization experiments involving mixing of dissimilar fluids—Refractive index matching and physical properties
,”
Processes
10
(
7
),
1260
(
2022
).
55.
E. M.
Darling
and
D.
Di Carlo
, “
High-throughput assessment of cellular mechanical properties
,”
Annu. Rev. Biomed. Eng.
17
(
1
),
35
62
(
2015
).
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