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each particle size the flow rate was varied while keeping the
peak-to-peak voltage applied to the transducer constant.
In the experiments the relative focusability R of the
suspended particles, was measured. The relative focusability
is defined as the proportion of particles moved by the ultrasound
to the center outlet, particles which would otherwise
end up in the side outlets if the ultrasound was not turned
on. A relative focusability of R = 1 therefore corresponds to a
recovery of 100% of the particles at the center outlet while
a relative focusability of R = 0 corresponds to a recovery of
Qc/(Qc + Qs) = 40%, where Qc and Qs are the flow rates of the
center and side outlets, respectively. The 40% recovery corresponds
to the fraction of particles that would be obtained
at the center outlet when the ultrasound is turned off,
depending on the flow split ratio between the center and side
outlets.
The transverse focusing velocity urad due to the acoustic
radiation force is proportional to the square of the transducer
peak-to-peak voltage Upp and the square of the particle radius
a, i.e. urad ∝ Upp
2a2.29 To be able to acquire data for different
particle sizes while still maintaining a reasonable flow rate in
the system, the applied voltage Upp and therefore the acoustic
energy density, was set higher in experiments involving
smaller (weakly focusing) particles than in experiments with
larger (strongly focusing) particles. To compare the results,
the flow rates were normalized with respect to the transverse
focusing velocity urad. The 7 μm particle was used as a normalization
reference, as this was the largest particle used in
the experiments, and it shows an almost ideal radiation
force-dominated motion. The normalized flow rate Qnorm in a
particular experiments with nominal flow rates Q is thus
given by
Q Q
u
u
7
Q
. (2)
2 2
U a
rad m
pp m
norm U a
rad
pp
7
2 2
One-dimensional focusing in a channel of rectangular
cross-section
The small size of many bioparticles such as bacteria inherently
makes them less suitable for acoustic standing wave
focusing in microfluidic systems without experiencing severe
losses, a problem that is prominent when handling highly
dilute species in situations where recoveries of more than
90% are needed.
Fig. 4(a) shows the results of one-dimensional focusing
in a rectangular channel (230 μm × 150 μm in cross section)
where relatively large polystyrene particles with diameters
of 7 μm, 5 μm, and 3 μm (red, purple, and green) could
all be focused, with a relative focusability of more than 0.9
(R = 0.98 ± 0.10, 0.93 ± 0.003, and 0.98 ± 0.006, respectively).
Throughout the paper, the stated uncertainty in the value of
R is the standard deviation of three repeated measurements.
The smaller polystyrene particles with diameters of 1 μm and
0.6 μm (blue and turquoise) could not be focused under the
given conditions, and the focusability measured was only
R = 0.52 ± 0.17 and R = 0.48 ± 0.07, respectively. For these
particles, the relative focusability R will not approach unity
(i.e. improve) as the flow rate is decreased further because of
Fig. 4 (a) One-dimensional focusing in the rectangular channel. The relative focusability R plotted against the normalized flow rate Qnorm.
(b) Two-dimensional single-frequency focusing in the square channel. The relative focusability R plotted against Qnorm. All error bars are
standard deviations from three repeated measurements. The nominal flow rates for each data point are collected in Table 1.
2796 | Lab Chip, 2014, 14, 2791–2799 This journal is © The Royal Society of Chemistry 2014