Spatial distribution of acoustic forces on particles : implications for particle separation and resonator design
Creators: name: Woodside, Steven Murray
Publisher: name: University of British Columbia
Year: 2009

description: A major challenge for large-scale mammalian cell perfusion reactor design and operation is the reliability of the device used to separate cells from the effluent stream and retain them in the bioreactor. Analysis of the relative merits of different cell retention systems indicates that ultrasonic separation overcomes many of the inherent disadvantages of more conventional systems, such as fouling, long hold-up times and mechanical complexity. To assist in the design, scale-up and optimization of ultrasonic separation technology, this work aims to provide a fundamental understanding of the relationship between the 3-dimensional ultrasonic resonator design, the ultrasonic force distribution and the separation efficiency. The magnitude and direction of the ultrasonic forces that act on individual particles in a standing wave field were determined using a microscope-based imaging system. The forces were calculated from measured particle velocities assuming that the drag force, given by Stokes' law, was exactly counterbalanced by the imposed ultrasonic forces. The axial primary radiation force was found to vary sinusoidally with axial position and to be proportional to the local acoustic energy density (E[sub ac]), as predicted by theory. The magnitude of the transverse primary force, a function of the E[sub ac] gradient, was determined by two independent methods to be about 100-fold weaker than the axial force. However, cell separation systems have successfully exploited the transverse force to aid in cell retention because of the reduced hydrodynamic forces on aggregates aligned in the pressure node planes parallel to the transverse flow. Measurements of the E[sub ac] distribution in the liquid using the imaging system were compared to laser interferometer measurements of the velocity amplitude distribution on the transducer and reflector surfaces of the ultrasonic separator. The E[sub ac] followed the same trend as the surface oscillation velocity, being highest near the resonator centre and approaching zero near the walls. The E[sub ac] maxima in the liquid and the grid-like distribution of amplitude maxima on the reflector had characteristic lengths of 1.4 mm. Based on these results, the E[sub ac] distribution in the liquid was modelled as the sum of contributions from a plane axial compression wave with a maximum amplitude at the transverse centre of the resonator, and two orthogonal surface shear waves. The compression wave contribution term was based on a solution of the 2-dimensional wave equation, with the parameters determined from the power input, resonator quality factor and transverse dimensions. The amplitude of the shear wave contribution was calculated from measured E[sub ac] gradients. The model agreed well with the measured liquid amplitude distribution. Cell and polystyrene particle retention efficiencies for different resonators were simulated by combining the E[sub ac] model and a model for the drag on aggregates. The simulation results agreed qualitatively with measured retention efficiencies under a number of experimental conditions. Simulations may thus be useful for examining the relative performance of resonators under different conditions and in assessing the feasibility of novel applications. The simulations also suggest that resonators could be designed specifically to generate the appropriate force distribution for given applications.