Microfluid Nanofluid
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Supplementary material to “Microfluidic Centrifuge based on a
Counterflow Configuration”
N. Pertaya-Braun · T. Baier · S. Hardt
A1 Supplementary figures
Figure S1 For the epi-fluorescence measurements the inverted Nikon Ti-S microscope was equipped with a
fluorescence HG illuminator, an epi-fluorescence arm adapter, a tripleband filter, a 10x objective, an Optosplit-II
beamsplitter, and a Nikon DS-Qi1MC CCD camera. Two 10 ml syringes were used as solution reservoirs. The
solution was injected into two flow lines of the microfluidic device, operated in counterflow mode. The flow rate
was controlled by a KDS 210 syringe pump. The data were collected on the PC workstation and analyzed with
the Nikon NIS-Ar software. The pictures of a HG fiber illuminator, epi-fluorescence arm adapter, CCD camera,
and
workstation
are
adopted
from
the
Nikon
Eclipse
Ti
brochure
(http://www.nikoninstruments.eu/Products/Microscope-Systems/Inverted-Microscopes/Biological/Eclipse-Ti).
N. Pertaya-Braun · T. Baier · S. Hardt ()
Center of Smart Interfaces, TU Darmstadt, Petersenstrasse 32, 64287, Darmstadt, Germany. Fax: +49-06151-1672021; Tel:
+49-06151-162874; E-mail: hardt@csi.tu-darmstadt.de
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Figure S2 For the highspeed brightfield measurements the inverted Nikon Ti-S microscope was equipped with
a MotionPro-Y4 highspeed camera and a 10x objective. Again, two 10 ml syringes were used as solution
reservoirs. The solution was injected into two flow lines of the microfluidic device, operated in counterflow
mode. The flow rate was controlled by a KDS 210 syringe pump. The data were collected on the PC workstation
and analyzed with the MotionPro Software package.
A2 Separation efficiency
On the basis of the spatial distribution measurement done for 9.9 m, 4.8 m, and 0.52 m
microspheres, the separation efficiency was estimated. The averaged fluorescence intensity
distribution in the center of the centrifugation chamber was measured for all of the above mentioned
particle types, and recorded for average flow speeds between 0.99 and 1.95 m/s. For the entire range of
flow rates one can clearly see that the microparticles are separated according to their size. For
example, one can see that at low flow speed (0.99 – 1.31 m/s, see Fig. 5, lines a and b) the 9.9 m
microspheres are displaced away from the center of the centrifugation chamber, while the 0.52 m
microspheres are not. At higher flow speed (1.69 – 1.95 m/s, see Fig. 5, lines c and d), the 0.52 m
particles are starting to be displaced away from the center as well. The same effect is observed with
4.8 m and 0.52 m microspheres. This means that the best size separation performance of the
microcentrifuge is reached at flow velocities around 1 – 1.31 m/s. The centrifugation efficiencies of
the three different particles studied in the experiments are shown in Figure S4. Here two flow speeds
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are presented (0.99 and 1.69 m/s), and data was averaged over 15 measurements for each of the flow
speeds.
For a specific particle type with diameter x, the centrifugation efficiency is defined as
𝑛
(𝑥)
𝐸𝑐 (𝑥) = 1 − 𝑛 𝑐𝑒𝑛𝑡𝑒𝑟 (𝑥) ,
𝑐ℎ𝑎𝑛𝑛𝑒𝑙
where 𝑛𝑐𝑒𝑛𝑡𝑒𝑟 measures the number density of particles in the center of the centrifugation chamber
and 𝑛𝑐ℎ𝑎𝑛𝑛𝑒𝑙 the same quantity in the microchannel adjacent to the chamber. In the case considered
here (low particle concentration), to a good approximation the number densities are proportional to the
measured fluorescence intensities, i.e.
𝐼
(𝑥)
𝐸𝑐 (𝑥) = 1 − 𝐼 𝑐𝑒𝑛𝑡𝑒𝑟 (𝑥).
𝑐ℎ𝑎𝑛𝑛𝑒𝑙
A measure for the separation efficiency is
𝑑
𝐸 (𝑥).
𝑑𝑥 𝑐
Considering particles consisting of the same
material (and neglecting the fact that the particles cannot be larger than the centrifugation chamber),
𝐸𝑐 (𝑥) is expected to take the limiting values lim 𝐸𝑐 (𝑥) = 0 and lim 𝐸𝑐 (𝑥) = 1. The transition
𝑥→0
𝑥→∞
between these limiting values will occur within a certain x range which depends, among others, on the
rotation speed of the centrifuge. Clearly, the separation efficiency will be large only within this
specific x range. With only three data points it is impossible to map the complete curve, however, the
expected s-shape is already indicated. To estimate the resolution of the separation process, the lower
limit of particles sizes than can still be separated can be defined as
∆𝑥 =
1
2
𝑑
𝐸
𝑑𝑥 𝑐
,
where the derivative should be evaluated in the x range close to where it assumes its maximum.
Approximating
𝑑
𝐸 (𝑥)
𝑑𝑥 𝑐
by the data points at 0.52 m and 4.8 m, one obtains ∆𝑥 ≈ 3.1 µm, which
serves as a rough estimate for the size interval that can be discriminated under the given conditions,
see Figure S4 (A). Figure S4 (B) shows the 0.52 m particles are starting to be displaced away from
the center as well, which means that the best size separation performance of the microcentrifuge is
reached at low flow velocities.
Figure S3 (A) Centrifugation efficiency for particles of different sizes at low flow speed, where the best size
separation is reached. Here the distribution of 9.9 m and 0.52 m microspheres at a flow velocity of 0.99 m/s is
shown. (B) The same for a flow velocity of 1.69 m/s.
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A3 Impact of additional outlet on the flow field inside the centrifuge
Using the centrifugation chamber in practical applications requires an additional outlet from the
chamber, from which specific particle fractions can be drawn. Depending on the flow rate at this
outlet, this will of course affect the vortex within the centrifugation chamber. In order to get an idea of
this impact, numerical simulations similar to the ones presented in the main text, but with an additional
outlet from the central chamber have been performed. The geometry is a cubic chamber with side
lengths of 200 µm. In the center of the chamber a circular outlet with diameter of 40 µm has been
added, c.f. figure S4. Again we assume a symmetric arrangement so that it suffices to consider half the
geometry. We choose an inlet flow velocity of 250 mm/s, corresponding to Re = 50. In this case the
flow velocity within the vortex is of the order of 20-30 mm/s. Accordingly, the outlet flow velocity
was chosen of the same order of magnitude and below. In practice, the outlet flow rate can be varied
over a wide range by tuning the hydrodynamic resistance of the duct behind the outlet hole.
Figure S4 shows three cases with outlet velocities between 2.5 mm/s and 10 mm/s. The largest
velocity corresponds to a flow rate of 0.013 mm³/s. In all cases streamlines (red) that are seeded on a
diagonal within the core of the vortex are shown. For comparison, corresponding streamlines (green)
are displayed for a flow field with vanishing flow at the outlet. As can be seen, mainly the flow in the
eye of the vortex is affected, while the impact is small in the high-velocity regions.
In addition to the streamlines we show in Figure S5 the flow field for the case of Uoutlet = 0 mm/s and
10 mm/s on planes parallel to and at different distances from the symmetry plane. Here, no marked
difference is noticeable between the two flow fields. In summary, we conclude that it should be
possible to add an outlet hole to the centrifugation chamber in such a way that the flow field is only
marginally affected. In particular, the conclusions drawn in the main text about centrifugal particle
separation inside the vortex should remain unchanged.
Uoutlet =
2.5 mm/s
5 mm/s
10 mm/s
Figure S4 Streamlines released on a line running diagonally through the centrifugation chamber (Re = 50) for
different values of the outlet velocity. The red lines correspond to a case with outlet flow, while the green lines
correspond to a closed outlet for comparison.
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Figure S5 Velocity field for outlet velocities of (top, green) 0 mm/s and (bottom, red) 10 mm/s at positions (from left to right) 20, 40, 60, 80 µm above the symmetry plane.
N. Pertaya-Braun · T. Baier · S. Hardt ()
Center of Smart Interfaces, TU Darmstadt, Petersenstrasse 32, 64287, Darmstadt, Germany. Fax: +49-06151-1672021; Tel: +49-06151-162874; E-mail: hardt@csi.tu-darmstadt.de