Microfluidic acoustic trapping force and stiffness measurement using viscous drag effect

It has recently been demonstrated that it was possible to individually trap 70 μm droplets flowing within a 500 μm wide microfluidic channel by a 24 MHz single element piezo-composite focused transducer. In order to further develop this non-invasive approach as a microfluidic particle manipulation tool of high precision, the trapping force needs to be calibrated to a known force, i.e., viscous drag force arising from the fluid flow in the channel. However, few calibration studies based on fluid viscosity have been carried out with focused acoustic beams for moving objects in microfluidic environments. In this paper, the acoustic trapping force (F _trapping) and the trap stiffness (or compliance k) are experimentally determined for a streaming droplet in a microfluidic channel. F _trapping is calibrated to viscous drag force produced from syringe pumps. Chebyshev-windowed chirp coded excitation sequences sweeping the frequency range from 18 MHz to 30 MHz is utilized to drive the transducer, enabling the beam transmission through the channel/fluid interface for interrogating the droplets inside the channel. The minimum force (F _min,trapping) required for initially immobilizing drifting droplets is determined as a function of pulse repetition frequency (PRF), duty factor (DTF), and input voltage amplitude (V _in) to the transducer. At PRF = 0.1 kHz and DTF = 30%, F _{min ,trapping} is increased from 2.2 nN for V _in = 22 V _pp to 3.8 nN for V _in = 54 V _pp. With a fixed V _in = 54 V _pp and DTF = 30%, F _{min ,trapping} can be varied from 3.8 nN at PRF = 0.1 kHz to 6.7 nN at PRF = 0.5 kHz. These findings indicate that both higher driving voltage and more frequent beam transmission yield stronger traps for holding droplets in motion. The stiffness k can be estimated through linear regression by measuring the trapping force (F _trapping) corresponding to the displacement (x) of a droplet from the trap center. By plotting F _trapping - x curves for certain values of V _in (22/38/54 V _pp) at DTF = 10% and PRF = 0.1 kHz, k is 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 _in = 54 V _pp, k is increased from 0.20 to 0.42 nN/μm. It is shown that a higher PRF leads to a more compliant trap formation (or a stronger F _trapping) for a given displacement x. Hence the results suggest that this acoustic trapping method has the potential as a noninvasive manipulation tool for individual moving targets in microfluidics by adjusting the transducer's excitation parameters.