Resonator frequency shift due to ultrasonically induced microparticle migration in an aqueous suspension: Observations and model for the maximum frequency shift

Abstract

Aqueous suspensions of plastic and hollow-glass microspheres are subjected to the radiation pressure of an ultrasonic standing wave. It is well known that the particles are attracted to the pressure nodes of the standing wave for the particle and host properties considered. We demonstrated that the radiation pressure induced migration of particles leads to a significant shift in the resonant frequency of a suitably designed chamber. This shift is easily resolved with a phase-locked loop even if the particle volume fraction is as small as 0.001. For sufficient ultrasonic amplitudes, the shift is found to saturate at a limiting value. To approximate the limiting frequency shift, the principle of adiabatic invariance is first applied to the case of a single compressible sphere in a standing wave and then superposition is used to give the collective shift for the suspension. The measured limiting shifts are typically within 25% of the calculated value and this method may have application to the characterization of dilute suspensions since the shift is proportional to the volume fraction and to a material contrast factor. The applicability of adiabatic invariance is confirmed by comparing frequency shifts for certain cases of idealized particle spatial distributions with results based on transfer matrix eigenvalues combined with an effective-medium approximation.