Rotational speed measurements of small spherical particles driven by acoustic viscous torques utilizing an optical trap

Abstract

Two orthogonal standing acoustic waves, generated by piezoelectric excitation, can form a two-dimensional pressure field in microfluidic devices. A phase difference of the excitation waves can be employed to rotate spherical µm-sized silica particles by a torque mediated through the viscous boundary δ around the particle. The measurement of the rotational rate is, so far, limited to high-speed cameras and their frame rate, and gets increasingly difficult when the sphere gets smaller. We report here a new method for measuring the rotational rate of µm sized spherical particles. We utilize an optical trap with high-speed position detection to overcome the frame rate limitation of wide field image recording. The power spectrum of an optically trapped, rotating particle reveals additional peaks corresponding to the rotational frequencies—compared to a non-rotating particle. We validate our method at low rotational rates against high-speed video observation. To demonstrate the potential of this method we addressed a recent controversy about the rotation of particles with a relatively large viscous boundary layer δ. We measured steady-state rotational rates up to 229 Hz (13.8\u2009×\u2009103 rpm) for a particle with a radius R\u2009≈\u2009δ. Recent numerical research suggests that in this regime the existing theoretical approach (valid for R≫δ ) overpredicts the steady-state rotational rate by a factor of 10. With our new method we also confirm the numerical results experimentally.