Reduced Order Modeling and Experimental Investigation of Acoustic Particle Manipulation in Complex 3D Geometries

Abstract

A reduced order computational model and imaging experiments are presented as a combined method to investigate migration and trapping of microscale particles within an ultrasonic droplet generator. Use of two-dimensional (2D) cross-sectional representations of the three-dimensional (3D) device enables observation of acoustic focusing phenomena that are otherwise visually inaccessible. Our approach establishes relationships between system operating parameters and particle retention due to acoustic radiation forces that arise during atomization of heterogeneous particle suspensions. The droplet generator consists of a piezoelectric transducer for ultrasonic actuation, a resonant fluid-filled chamber, and an array of microscopic pyramidal nozzles. 2D visualization chips were produced through anodic bonding of glass to microfluidic reservoirs deep reactive ion etched in silicon. Open nozzle orifices of the 3D microarray were sealed in its 2D representation to facilitate filling and testing. Finite element analysis was used to model the harmonic response of the 2D assembly from 500 kHz to 2 MHz. The average nozzle tip pressure amplitude across the 2D array was then used to identify operating frequencies that correspond to optimal droplet ejection from the 3D device (ejection modes). The pressure field at these resonant frequencies predicts the equilibrium distribution of polymeric beads suspended in the reservoirs of the 2D chips. To qualitatively assess the accuracy of the model results, visualization experiments were performed at the first three ejection modes of the system (fn1 ≈ 620–680 kHz, fn2 ≈ 1.14 MHz, and fn3 ≈ 1.63 MHz) using 10 μm polystyrene beads. The model demonstrates a remarkable ability to capture the overall shape, as well as specific details of the terminal particle distributions, defined as the state with no further movement toward a pressure node or antinode. Finally, time course trials of acoustic focusing of heterogeneous particle suspensions were used to observe the influence of particle volume on the magnitude of the acoustic radiation force. A mixture of 5 μm and 20 μm diameter polystyrene beads was subjected to a standing acoustic field in the 2D chips. Particle position was recorded at 5 ms intervals until an equilibrium distribution was achieved. As expected, the larger beads focused much more rapidly than smaller beads, acquiring their final positions in seconds (versus 10s of seconds for the 5 μm particles). The method and results reported here serve as building blocks toward translation of an existing ultrasonic droplet generator into a high-throughput particle separation and isolation platform.