Fig 1.
Schematic of the two acoustic focusing devices and their optical analysis points.
Within both of these systems, the one-dimensional focusing of particles was monitored downstream of the driving PZT. Both of these systems were driven at their fundamental half-wavelength mode, represented by the blue dashed lines in B top, which focused the particles into a single central node. The focusing performance of the capillary (A) was monitored through transparent tubing at the end of the device while the etched-through Si wafer (B) is monitored just downstream of the PZT.
Fig 2.
Close-up of capillary analysis technique.
Imaging was done through a simple, flexible tubing to continuously monitor the particle positions after they exit the steel capillary.
Fig 3.
For a model system of fluorescent 10- μm beads (Sky Blue FP-10070-2, Spherotech), an example of poorly focused (left) and well-focused image data (right). Each image shown here was constructed from a summed stack of 500 individual images taken over ~30s of data at a single frequency condition. The focusing width of each summed image was fit to a Gaussian curve using MATLAB and the width at half-maximum was used as a representative focusing width. Applying this process across an iterative frequency scan for a single temperature yields an experimental method of measuring the optimal resonance frequency condition. Repeating this process at a variety of temperatures allowed for the experimental characterisation the highest performing resonance frequencies as a function of temperature.
Fig 4.
Control logic used for the frequency scans at each discrete temperature point.
This automated scan allows for the collection and analysis of the system’s frequency-dependant focusing performance at any particular temperature point.
Fig 5.
Focusing width vs frequency for three input power levels within the cylindrical capillary system.
At the highest input power levels there was tight focusing across a wide frequency space, while at the lowest input power there was tight focusing (less than ~20 μm) across a small frequency bandwidth of a few kHz.
Fig 6.
Power dependence to focusing width in etched silica device.
For the Si etched device at low input power there was a single frequency bandwidth around 1.175 MHz that resulted in optimal focusing performance. At the high power level there were multiple local minima of high focusing performance.
Fig 7.
Capillary focusing and conductance spectra at two temperatures.
Focusing width (blue) and conductance information (red) for two representative temperature spectra. A) Frequency scan, conducted at 15°C ambient, demonstrates one clear focusing minimum with significantly better focusing than any other frequency range. Additionally, this focusing minimum corresponds to a local conductance maxima of similar frequency bandwidth. Circles on each plot mark the highest performing frequency. B) Frequency scan, conducted at 37°C, has one global minimum where focusing performance (blue) is maximized, but also has two additional minima with high focusing performance. Again, there is a local conductance maximum (red) coinciding with the best operating frequency.
Fig 8.
Capillary resonance frequency vs. temperature.
Experimental data and two models characterizing how the resonance frequency of the system changed with temperature (*note the black line is a model, not a fit to the data*). The experimental data (blue for absolute focusing width minima, red for secondary focusing width minima) was well characterized by both models, suggesting that for this system, the speed of sound within the liquid layer dominates the resonance frequency shift.
Fig 9.
Optimal focusing frequency over a range of media salinities within the capillary system.
The five blue scatter points were experimentally determined at each salinity while the red line plot represents a simple model that assumes that the speed of sound within the liquid media alone determines these resonance frequency shifts.
Fig 10.
Focusing width and conductance in Si system.
Calibrated impedance (A) and conductance (B) scans are shown overlaid with acoustic focusing width. A local conductance max (impedance minima) was correlated with the best performing driving frequency (1.179 MHz). The overlaid blue and red circles were selected from the focusing data alone, demonstrating near perfect correlation between the conductance maxima and focusing minima. Note that there were additional conductance peaks that could otherwise be indistinguishable from the optimal frequency if the search bandwidth was not limited.
Fig 11.
An environmental reference table for the capillary system’s resonance frequency (indicated by the color scale) modelled across a wide range of temperatures and salinities.