Paper Lab on a Chip
Fig. 2 Acoustophoretic motion of 0.5 μm-diameter particles in the
nearly-square microchannel cross section. The rows (a–d) corresponds
to the four cases shown in Fig. 1. The actuation frequency was f1 in (a),
f2 in (b), and fm in (c–d). For each case, column 1 is a snapshot in time
of the amplitude of the oscillating first-order acoustic pressure (color
plot where red is positive, green is zero, and blue is negative). Column
2 is the acoustic radiation force (color plot and arrows where red is
positive and blue is zero) together with streamlines (black contour lines)
of the steady streaming velocity field. Column 3 is the acoustophoretic
trajectories (colors indicate the speed where red is positive and blue is
zero) of 0.5 μm-diameter particles released from a regular grid in the
channel cross section. To best illustrate the qualitative results, the
color scale is set by the maximum value in each plot individually. For
the color plots 1(a–c) the magenta arrow indicates that the pressure
has an almost static nodal line (green) while the amplitude oscillates.
For the color plot 1(d) the magenta arrows indicate that the nodal line
(green) of the pressure field rotates in time.
flow rolls at the top and bottom walls along with two smaller
flow rolls at the side walls. The small particles follow this
streaming flow and are not focused in the center. For ϕ = π/2
(d), the streaming flow consists of one large flow roll in the
center of the channel and two smaller flow rolls at the top
and bottom walls. The combined effect of the weak radiation
force towards the centre and the strong streaming-induced
drag force acts to focus the particles at the centre of the
channel cross section following a spiralling motion. This
allows for focusing of sub-micrometer particles, which is not
possible in the standard one-dimensional half-wavelength
resonance (a–b). By numerically tuning the phase shift ϕ a
solution was obtained where the large centred flow roll covered
the whole channel cross section without any smaller
bulk flow rolls, allowing all particles to be focused at the centre.
Changing the phase shift ϕ by π results in a counterrotating
streaming flow. The acoustic radiation force in
Fig. 2(c–d) is similar to that reported for acoustic focusing of
large particles in cylindrical channels.39 It should be stressed
that the steady streaming is a boundary driven second-order
flow, it is not driven by the rotation of the first-order pressure
in Fig. 2(d) first column.
This numerical analysis is a generic study not aimed at
direct simulation of the following experiments. Experimentally
it is very difficult to control, even to measure, the vibration
of the channel walls. Moreover, the wall oscillation
presumably varies along the length of the channel, by analogy
with what has already been verified experimentally for
the acoustic field of the half-wavelength resonance.40 However,
the numerical results indicate the existence of a streaming
flow that enables focusing of sub-micrometer particles,
which is impossible with the well-known quadrupolar
Rayleigh streaming. This new streaming flow strongly
depends on the relative phase of the vibrations of the walls,
i.e. the boundary conditions for the first-order acoustic field.
Moreover, the spatial variation of the actuation, which has
not been investigated, will presumably also influence the
streaming flow and thus the focusability. This calls for a
more in-depth numerical study of the dependency of the
acoustic streaming on the actuation boundary condition
which will be included in future work, as for the present
work the main emphasis is on the experimental results.
Materials and experimental methods
Design and fabrication of the device
The chips were fabricated from <110> oriented silicon using
photolithography and anisotropic wet etching in KOH (400 g L−1
H2O, 80 °C). Inlets and outlets were drilled through the silicon
using a diamond drill (Tools Sverige AB, Lund, Sweden) and
the chips were sealed by anodic bonding to a glass lid. The
two chips had one trifurcation inlet and outlet split each, of
which only a single inlet was used and the unused one was
sealed (Fig. 3). The square-cross-section channel had a width
Fig. 3 Photograph of the chip design. The main focusing channel is
35 mm long and 230 μm wide, while its height is either 230 μm (square
channel) or 150 μm (flat rectangular channel). After the trifurcation, the
side channels are connected to one outlet. The inlet marked with a blue
cross is not used.
2794 | Lab Chip, 2014, 14, 2791–2799 This journal is © The Royal Society of Chemistry 2014