High-speed microfluidic differential manometer
for cellular-scale hydrodynamics
Manouk Abkarian, Magalie Faivre, and Howard A. Stone*
Division of Engineering and Applied Sciences, Harvard University, Pierce Hall, Cambridge, MA 02138
Edited by Harden M. McConnell, Stanford University, Stanford, CA, and approved November 8, 2005 (received for review August 17, 2005)
We propose a broadly applicable high-speed microfluidic approach
for measuring dynamical pressure-drop variations along a micro-
meter-sized channel and illustrate the potential of the technique
by presenting measurements of the additional pressure drop
produced at the scale of individual flowing cells. The influence of
drug-modified mechanical properties of the cell membrane is
shown. Finally, single hemolysis events during flow are recorded
simultaneously with the critical pressure drop for the rupture of
be applied to any dynamical process or event that changes the
hydrodynamic resistance of micro- or nanochannels.
pressure measurement ? microcirculation ? hemolysis ? red blood cell ?
cesses (2), cellular-scale identifications (3), DNA sequencing (4),
protein crystallization (5) and many basic transport pathways in
plants (6), in the microcirculation (7), and specific to industrial
processes. The main characteristics of these advances lie in the
manipulation and understanding of the dynamics of ‘‘soft’’
objects such as polymers (8) (e.g., DNA), drops (9, 10), micro-
emulsions (11), microfoams (12), cells (13), vesicles and micro-
capsules (14). In fact, the interaction of the flow with these
deformable entities is a tool to further investigate the details of
their mechanical properties and their structural features (e.g.,
the entropic elasticity of a polymer, the viscoelastic properties of
a capsule, or the rheology of the liquid film between micro-
bubbles in a foam). For the case of strong confinement offered
by microchannels, the flow and shape of any close-fitting soft
object is controlled by a competition among the properties of the
objects, the fluid pressure, and the viscous stresses acting on the
boundaries that resist the motion. The hydrodynamic resistance
resulting from this fluid–structure interaction is reflected in a
dynamical variation of the pressure drop along the channel
during the flow and hence represents a crucial parameter to be
Nevertheless, rapid variations of pressure are very difficult to
measure at the micrometer scale and below. Indeed, the diffi-
culties do not originate from the lack of precision sensors
commercially available or those described in the research liter-
ature (15). The problem is a subtle mix of pragmatism and
technological limits. In addition to issues of dead volumes in
standard pressure-measurement techniques (16–18) and those
associated with interfacing microelectromechanical system de-
vices to standard pressure gauges (19), existing techniques are
simply difficult to implement [lasers, quadrant diodes, deform-
able membranes, multistep process of production (16–18)] and
are unable to measure at millisecond rates the pressure changes
in micrometer-scale flows. For instance, when a single red blood
cell (RBC) enters a channel of 5 ? 5 ?m, the volume variation
produced by a flow at physiological speeds of a few millimeters
per second is ?100 fL in a few milliseconds, which represents a
typical pressure-drop variation of tens to hundreds of pascals.
Such rapid pressure measurements at the cellular scale, crucial
to future device and microcirculatory advances, are not available
luid motions at the micrometer scale are at the heart of many
recent developments in microfabrication (1), separation pro-
at this time. Here we report a technique that overcomes these
limitations and demonstrate the ability to measure rapid varia-
tions of pressure drop between two points in a microfluidic
device. The technique needs no external elements and is easy to
implement with soft lithography. The basic principle should
naturally allow similar measurements of pressure variations in
We chose to illustrate the flexibility of our approach by focusing
on blood cells, which allows us to provide insights into outstanding
problems in hemodynamics. Indeed, there is a long history of the
study of cells at the micrometer scale for assessing mechanical
properties (20) and cell shape (21) and for applying these ideas for
understanding microcirculatory diseases (22, 23). In fact, the main
approach for characterizing the influence of possible diseases on a
suspension of cells is the filtration technique (23–25). Briefly, the
cells flow through a multipore polycarbonate membrane, and the
measured pressure-drop versus flow-rate relation (or the mean
passage time of the cells) serves as an index of the deformability
state in a population of healthy or sick cells (23, 26). Even if the
potential of this technique is for the analysis of large samples, the
resultant data reflect only the average properties: the technique is
not able to resolve information at the scale of a particular pore or
a single cell. Recent advances in microsystems technology allow
to the filtration geometry (27, 28); for example, area and volume
measurements for cell populations have been reported. However,
the fact remains that the most basic mechanical measurements that
are characteristic of the physical state of individual cells in physi-
ological flow conditions have not been accomplished.
We propose several illustrations of our differential microma-
nometer that address these issues and indicate further avenues
for studies of dynamics and hemorheology. We measure (i) the
pressure-drop variation associated with the motion of single and
multiple RBCs and white blood cells (WBCs) in a microchannel,
(ii) the additional pressure drop associated with the flow of
drug-treated cells, and (iii) single hemolysis events.
To measure simultaneously the dynamical deformation of the cells
and the variation of the pressure drop produced by their motion in
the channel, we developed a device with twin channels: a test
channel (Fig. 1A Upper) and an identical control, or ‘‘comparator,’’
channel (Fig. 1A Lower), both of which produce downstream two
parallel and adjacent streams of fluid. To maintain a stable inter-
face, the two fluids are miscible, and the liquid flowing through the
control channel is dyed to visualize the interface downstream.
Hence, the principle of the measurement lies in the use of the
channel when a cell, or another object, is flowing through it. In
effect, for a given applied pressure difference across the device, the
Conflict of interest statement: No conflicts declared.
This paper was submitted directly (Track II) to the PNAS office.
Abbreviations: RBC, red blood cell; WBC, white blood cell; PDMS, poly(dimethylsiloxane).
*To whom correspondence should be addressed. E-mail: firstname.lastname@example.org.
© 2006 by The National Academy of Sciences of the USA
January 17, 2006 ?
vol. 103 ?
no. 3 www.pnas.org?cgi?doi?10.1073?pnas.0507171102
placement of an object in the channel decreases the flow rate and
consequently increases the pressure drop that occurs in the narrow
test section. A change in the pressure drop along the channel alters
the position of the interface downstream. The measurement of this
deflection allows the pressure to be determined after a basic
calibration procedure (see next paragraph), and consequently we
are able to monitor the time-dependent dynamical changes in the
pressure drop in the test channel. In the particular case of steady
channel flow, Groisman et al. (29) used a similar approach of
comparator channels for static measurements of pressure drop in a
microfluidic ‘‘diode’’ (i.e., a device in which the pressure varies
nonlinearly with flow rate and the direction of flow). We note that
for the experiment reported here by directly imaging the two-
of deformation of suspended particles and the dynamical variations
of the pressure drop. Finally, we emphasize that our measurement
technique is general and can be applied to any dynamical process
to the control channel (chemical reactions, changing viscosity, etc).
Device, Calibration, and Cells
The microfluidic device was manufactured by using principles of
soft lithography (30, †). The typical dimensions of the device are
shown in Fig. 1A. The dimensions are fixed by the size of the
object chosen for study. In the case of blood cells, we produced
the test and comparator channels at ?5 ? 5 ?m in cross section
device onto an inverted Leica (Deerfield, IL) DM IRB micro-
scope coupled with a Leica ?100 objective (NPlan) for bright-
field imaging (numerical aperture, 1.25) to observe the motion
of the cells. A high-speed camera (Phantom V5, Vision Re-
search, Inc., Wayne, NJ) is used to follow the motion and the
deformation of the cells through the capillaries; typically, we use
an imaging rate of a few thousands frame per second. The field
of view of the camera (1024 ? 1024) allows simultaneous
observation of the cells and the deflection of the interface.
It first is necessary to calibrate the deflection of the interface
as a function of the pressure drop. The flow is produced by
pressurizing the fluids in the syringes connected to the two inlets
of the microfluidic device. With no RBCs in the solution, the
pressure P1applied in the test channel and the pressure P2in the
control channel are fixed so that the fluid–fluid interface
downstream is centered in the main exit channel (Fig. 1A). We
change the pressure P1in small increments ?P without changing
the pressure P2in the control channel and follow the displace-
ment of the interface in the Y direction by performing image
analysis with MATLAB software (Fig. 1B). The variation ?Y is
linear in ?P for the two initial working pressures applied: P1?
5 psi, and P1? 10 psi (Fig. 1C). Also, the slope of ?Y(?P) at
P1? 5 psi is twice as large as the slope at P1? 10 psi (in absolute
value); both responses are expected for small variations of this
viscously driven flow.
The RBCs used during the experiment are extracted from a
droplet of blood obtained by pricking a finger of a healthy donor.
The blood sample is diluted and washed twice with a solution of
PBS at an osmolarity of 300 mOs (physiological value). All of the
solutions are made with dextran of molecular weight 2 ? 106at
a concentration of 9% (wt?wt). The viscosity of the solutions is
†Briefly, a negative mask is placed on a silicon wafer that is spin-coated with a 5-?m-thick
layer of photoresist polymer (SU-8) and exposed to UV light. The cross-linked design then
is developed to obtain a positive mold, and liquid poly(dimethylsiloxane) (PDMS) (Dow-
Corning) is poured over the mold. The PDMS is cured and peeled from the mold, and two
inlet holes are punched with custom-prepared 20-gauge needles. The PDMS negative
mold is bonded irreversibly to a glass slide to produce the device. The suspension of cells
inlet hole of the control channel of the device. A similar setup is used with the dyed
solution without the suspension and is connected to the inlet hole of the control channel
of the device. Pressure applied to the needles is independently controlled by a regulator
(Bellofram, St. Louis, MO) with a precision of 0.001 psi (1 psi ? 6.89 kPa).
drop in the upper channel. The pressures P1and P2are fixed when no RBCs are flowing so that the fluid–fluid interface is centered in the exit channel. (B) Image
analysis determines the variation ?Y of the position of the co-flowing line that marks the interface. (C) Variation of ?Y as a function of the change in pressure,
?P, in the upper channel for two different upstream pressures P1at 5 psi (F) and 10 psi (■). The slope ?Y??P at 5 psi is twice the slope at 10 psi in absolute value.
(D) Variation of the relative position ?Y of the interface as a function of time when cells enter the channel (Inset). The dashed vertical line separates the plot
into two regions. (Left) Valid points for the pressure-drop measurement. (Right) Points caused by the exiting cells passing close to, and thus disturbing, the
co-flowing line that marks the interface.
The height of the channels measured by a profilometer is the same in all of the devices and is equal to 4.7 ?m. (A) Calibration of the excess pressure
Abkarian et al.PNAS ?
January 17, 2006 ?
vol. 103 ?
no. 3 ?
of the ink solution has been measured to be 1.07 centipoise, i.e.,
approximately the viscosity of water.
To obtain rigidified RBCs, which allows characterization of
the changes in pressure drop caused by mechanical changes in
the cell membrane, an extra step is added in the process of
dilution. The RBCs are maintained in PBS solution containing
a given concentration of glutaraldehyde [0.001–0.01% (vol?vol)]
at 25°C for 4 min. The rigidified cells then are dispersed in the
PBS solution with the same osmolarity, pH, and viscosity as
described previously. In the process of blood separation, a few
WBCs are separated with the RBCs, which allows the study of
their motion in the microchannels as well.
Pressure-Drop Change due to Blood Cells. After calibration of the
interface deflection as a function of the change in pressure drop,
the dilute suspension of RBCs is introduced in the device. Each
time a cell enters the test channel (Fig. 1D Inset), we record a
movie of the whole field of view, which allows us to follow the
position of the interface (Fig. 1B) and the deformation of the
cell. Each event is analyzed with MATLAB software to measure
the dynamical variations of the interface position (i.e., the
pressure drop) as a function of time and the deformation of the
cell. An example of the measured pressure-drop variations after
the entry of a cell into a channel and continuing until after the
cell has exited the channel is shown in Fig. 1D. The second bump
which directly disturbs the position of the interface, but does not
have any physical significance in terms of the global pressure-
Two comments about details of the measurement approach
are in order. First, PDMS channels are known to be deformable
under pressure-driven flow. Thus, it is necessary to estimate the
maximum deformation produced by the passage of a cell, which
causes a pressure drop ?P. The additional strain in the walls of
the PDMS channel is estimated by the ratio of ?P (of the order
700 Pa) to the Young modulus of PDMS (?5 ? 105Pa), which
is ?10?3. Hence, any such deformation is negligible. Second, the
characteristics. There are three different time scales relevant to
describe the time resolution of the device: (i) the time scale
related to the propagation of sound waves (speed c) along the
channel (length L and height H), which controls the axial
development of the velocity profile and is estimated to be
?L?c ? 10?6to 10-7s; (ii) the time scale associated with the
diffusion of vorticity across the channel, which controls the
evolution of the nearly parabolic velocity profile and is estimated
to be ?H2?? ? 10?6, where ? is the kinematic viscosity of the
fluid); and (iii) the time scale associated with the fluid rear-
rangement because of the pressure changes, which is the longest
time scale in the problem. This last time scale is of the order of
??U, where ? is the length on which the velocity of the fluid is
disturbed (typically the cell size). With the estimates ? ? 10 ?m
and the mean velocity of the fluid passing in the channels U ?
1 cm?s, this time scale is of the order of a few milliseconds. This
time can be even shorter for higher mean speeds U, which
suggests a way to reduce and tune the time response of the device
by working at higher injection pressures (i.e., higher flow mean
speeds). Finally, we note that experimentally we visually observe
on the high-speed movie the link between the motion (and
instantaneous position) of the cell and the deformation of the
The next illustration of our technique consists in the mea-
surement of the complete sequence of the deformation and the
time evolution of the excess pressure drop when the cells flow in
the channel as shown in Fig. 2. An RBC enters the channel,
followed shortly thereafter by a larger (and stiffer) WBC. The
time trace of the pressure-drop variations can be compared with
the images of the sequence of deformations represented in the
figure. The time evolution of the pressure drop while the same
cell is in the channel, and away from either the entrance or exit,
is a consequence of the deformation of the cell. This example
illustrates the ability to monitor dynamically pressure drop and
mechanical processes comparable to in vivo conditions that
occur in the microcirculation.
entry and translation in cylindrical geometries with models for
the mechanical response of the cell. In one study (14), the RBC
is treated as a viscous droplet surrounded by a thin elastic
which pass successively through the upper channel. A plot of the variation of
the pressure drop is shown as a function of time (in milliseconds). The corre-
sponding position and shape of the cells are represented on the plot by the
numbering of the sequence.
Sequence showing the deformation first of an RBC and then a WBC,
state of the RBCs; the driving pressure is 5 psi. ?, healthy RBC; open symbols,
RBCstreatedwith0.001%glutaraldehyde; ‚,oneRBC; ?,atrainoftwoRBCs;
E, a train of five RBCs.
Pressure drop versus time for different conditions characterizing the
www.pnas.org?cgi?doi?10.1073?pnas.0507171102Abkarian et al.
membrane of two-dimensional modulus ES. The dynamical
response of these systems depends on the capillary number,
which is a dimensionless parameter ? ? ?V0?ES, where ? is the
in the channel. For example, the maximum additional pressure
drop ?Paddduring the flow is calculated to be ?Padd? O(10–
100)?V0?Rtfor 10?3? ? ? 0.05, where Rtis the radius of the
circular capillary (see figure 14 in ref. 14). Using the measure-
ments shown in Fig. 3, our results give ?Padd? 16 ?V0?Rt, which
is in good agreement with the order of magnitude from the
computational model. Finally, we note that the computational
models provide ?Paddas a function of the position along the
channel, and our results are in qualitative agreement. A detailed
comparison of simulation and experiment would require the
same geometry and should, in principle, allow extraction of the
The interactions of cells, and their number density, in the
microcirculation impact the overall pressure drop in a tissue
and is still not well understood (31). Next, we report in Fig. 3
results that suggest a way to study these hydrodynamic inter-
actions of cells through the measurement of the pressure drop
for the flow of one, two, and five cells translating through a
microchannel (cells are closely spaced, similar to a rouleaux).
The pressure drop systematically increases as the number of
cells increases, but the results are not simply proportional to
the number of cells. This qualitative response is typical of
confined geometries with suspended particles spaced closer
than the microchannel width.
Pressure-Drop Change due to Membrane-Modified Cells. Next, we
consider the change in the hydrodynamic resistance that occurs
when the mechanical properties of the cells are modified. In Fig.
3, we compare a single healthy cell with a glutaraldehyde-treated
cell, which is known to be stiffer (25): the pressure drop is
enhanced after treatment with glutaraldehyde, and the station-
ary shape of the cell is obtained at later times. Thus, we conclude
that our approach allows differentiation of cells with different
mechanical properties or geometrical features, which may pro-
vide a simple biomedical tool for clinical hemorheology and
Hemolysis. As a final example that illustrates the insights that can
be obtained with our microfluidic differential manometer in Fig.
4, we visualize a cell blocking the entrance to a channel (Fig.
4A2) and the subsequent hemolysis event (the cell membrane
ruptures) (Fig. 4 A4–A6). When the blockage event begins, the
pressure drop increases linearly over ?10 ms and reaches a
maximum value of ?1.1 psi when hemolysis happens. We then
see the ghost of the RBC (Fig. 4 A4–A6) as well as the
hemoglobin solution, which follows the parabolic velocity dis-
tribution. This critical value of stress that is necessary for
hemolysis is in good agreement with the approximate value of
4,000 Pa ? 0.6 psi found with static micropipette experiment on
preswollen RBCs (32). It is interesting to note also that malaria-
infected RBCs have increased rigidity, which is associated with
organ failure. Microfluidic approaches have been used recently
to examine qualitatively the flow-induced hemolysis (or ‘‘pit-
ting’’) of malaria-infected cells (7), and our methodology pro-
vides a quantitative approach for more in-depth studies of these
In summary, we have provided an approach for time-
dependent pressure-drop measurements at the micrometer scale
with millisecond resolution. We have shown how insights into
mechanical processes can be obtained at the scale of individual
cells. These ideas naturally apply to other soft objects and to
We acknowledge V. Studer for inspiring discussions on the device and
G. Cristobal-Azkarate for sharing his experience with the soft-
lithography technique. We thank G.M. Whitesides for helpful feedback.
We acknowledge L. Courbin for his help measuring viscosities. We also
thank the Harvard Nanoscale Science and Engineering Center for
support of this research.
1. Quake, S. R. & Scherer, A. (2000) Science 290, 1536–1540.
2. Huang, L. R., Cox, E. C., Austin, R. H. & Sturm, J. C. (2004) Science 304,
3. Fu, A. Y., Spence, C., Scherer, A., Arnold, F. H. & Quake, S.R. (1999) Nat.
Biotechnol. 17, 1109–1111.
4. Meller, A., Nivon, L., Brandin, E., Golovchenko, J. & Branton, D. (2000) Proc.
Natl. Acad. Sci. USA 97, 1079–1084.
5. Zheng, B., Tice, J. D. & Ismagilov, R. F. (2004) Adv. Mater. 16, 1365–1368.
6. Zwieniecki, M. A., Melcher, P. J. & Holbrook, N. M. (2001) Science 291,
7. Shelby, J. P., White, J., Ganesan, K., Rathod, P. K. & Chiu, D. T. (2003) Proc.
Natl. Acad. Sci. USA 100, 14618–14622.
8. Schroeder, C. M., Babcock, H. P., Shaqfeh, E. S. G. & Chu, S. (2003) Science
9. Anna, S. L., Bontoux, N. & Stone, H. A. (2003) Appl. Phys. Lett. 82,
by some particulate matter that clogs the entry of the upper channel. The
equivalent size of the entry pore is 2 ?m.
Hemolysis of an RBC passing through a narrow constriction formed
Abkarian et al. PNAS ?
January 17, 2006 ?
vol. 103 ?
no. 3 ?
10. Link, D. R., Anna, S. L., Weitz, D. A. & Stone, H. A. (2004) Phys. Rev. Lett. Download full-text
11. Lewis, P. C., Graham, R. R., Nie, Z. H., Xu, S. Q., Seo, M. & Kumacheva, E.
(2005) Macromolecules 38, 4536–4538.
12. Garstecki, P., Gitlin, I., DiLuzio, W., Whitesides, G. M., Kumacheva, E. &
Stone, H. A. (2004) Appl. Phys. Lett. 85, 2649–2651.
13. Faivre, M., Abkarian, M., Bickraj, K. & Stone, H. A. Biorheology, in press.
14. Queguiner, C. & Barthe `s-Biesel, D. (1997) J. Fluid Mech. 348, 349–376.
15. Voldman, J., Gray, M. L. & Schmidt, M. A. (1999) Annu. Rev. Biomed. Eng. 1,
16. Hosokawa, K., Hanada, K. & Maeda, R. (2002) J. Micromech. Microeng. 12, 1–6.
17. Blom, M. T., Chmela, E., van der Heyden, F. H. J., Oosterbroek, R. E., Tijssen,
R., Elwenspoek, M. & van den Berg, A. (2005) J. Micromech. Microeng. 14,
18. van der Heyden, F. H. J., Blom, M. T., Gardeniers, J. G. E., Chmela, E.,
Elwenspoek, M., Tijssen, R. & van den Berg, A. (2003) Sens. Actuators B Chem
19. Kohl, M. J., Abdel-Khalik, S. I., Jeter, S. M. & Sadowski, D. L. (2005) Sens.
Actuators A Phys. 118, 212–221.
20. Evans, E. A. (1989) Methods Enzymol. 173, 3–33.
21. Gaehtgens, P., Du ¨hrssen, C. & Albrecht, K. H. (1980) Blood Cells 6,
22. Chien, S., Luse, S. A. & Bryant, C. A. (1971) Microvasc. Res. 3, 183–203.
23. Nash, G.B. (1990) Biorheology 27, 873–882.
24. Skalak, R., Impelluso, T., Schmalzer, E. A. & Chien, S. (1983) Biorheology 20,
26. Drochon, A., Barthes-Biesel, D., Bucherer, C., Lacombe, C. & Lelievre, J. C.
(1993) Biorheology 30, 1–8.
27. Gifford, S. C., Frank, M. G., Derganc, J., Gabel, C., Austin, R. H., Yoshida,
T. & Bitensky, M. W. (2003) Biophys. J. 84, 623–633.
(1997) Microvasc. Res. 53, 272–281.
29. Groisman, A., Enzelberger, M. & Quake, S. R. (2003) Science 300, 955–958.
30. Duffy, D. C., McDonald, J. C., Schueller, O. J. A. & Whitesides, G. M. (1998)
Anal. Chem. 70, 4974–4984.
31. Helmke, B. P., Bremner, S. N., Zweifach, B. W., Skalak, R. & Schmid-
Scho ¨nbein, G. W. (1997) Am. J. Physiol. 273, H2884–H2890.
32. Mohandas, N. & Evans, E. A. (1994) Annu. Rev. Biophys. Biomol. Struct. 23,
www.pnas.org?cgi?doi?10.1073?pnas.0507171102Abkarian et al.