Calibration of microfluidic acoustic trapping force on single microdroplet (2012)

It was recently demonstrated that it was possible to individually trap micron-sized droplets flowing within a microfluidic channel by a focused ultrasound beam. The sound beam emitted from a 24 MHz single element piezo-composite transducer created a restoring force on 50 μm droplets that act like an elastic spring. In order to further develop this noninvasive approach as a microfluidic separation tool of high precision, the trapping mechanism must be quantitatively characterized by calibrating the applied body forces to known forces, i.e., viscous drag forces arising from the fluid flow in the channel. In order to do so, the trapping force (F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">trapping</sub> ) and its trap stiffness (or compliance k) were experimentally measured under various conditions. The Chebyshev-windowed chirp coded excitation signal drove the transducer, transmitting sufficient beam energy through the channel wall before the incident beam interrogated the droplets inside the channel. The minimum force (F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min,trapping</sub> ) needed for initially immobilizing drifting droplets was determined as a function of pulse repetition frequency (PRF), duty factor (DTF), and input voltage amplitude (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</sub> ) to the transducer. For example, Fmin,trapping was increased to 3.8 nN at PRF = 0.1 kHz. With variable PRF, Fmin,trapping was found to be as high as 6.7 nN at Vin = 54 V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pp</sub> and PRF = 0.5 kHz. These findings indicate that both higher driving voltage and more frequent beam transmission enable stronger traps for holding droplets in motion. For estimating k through linear regression, the drag force displaced a trapped droplet by a certain distance x parallel to the flow direction while the trap was activated. By plotting the measured F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">trapping</sub> – x curves for different values of V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</sub> (22/38/54 V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pp</sub> ) at DTF = 10 % and PRF = 0.1 kHz, k was measured to be 0.09, 0.14, and 0.20 nN/μm, respectively. With variable PRF from 0.1 to 0.5 kHz at V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</sub> = 54 V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pp</sub> , k was increased from 0.20 to 0.42 nN/μm. The results show that a higher PRF produces a more compliant trap formation, in turn, a stronger F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">trapping</sub> . They suggest that this acoustic trapping method has the potential as a noninvasive tool for manipulating individual targeted particles in microfluidic channels by adjusting the applied force associated with the transducer’s excitation parameters.