LINEAR VIBRATION ANALYSIS OF AN ULTRASONIC CLEANING PROBLEM

A micron-size spherical particle is bound to an elastic half-space by van der Waals forces. The particle and the surface of the half-space are immersed in an acoustic fluid and excited by harmonic plane waves propagating normally to the surface from either direction. The low-amplitude vibration of the particle is unidirectional and linear about an equilibrium position determined by van der Waals attraction and Hertz contact. An equation of motion is formulated for this problem that incorporates the effects of particle and fluid inertia, radiation and material damping, and surface and particle compliance. Numerical results are presented for a silicon particle adhering to a silicon half-space both in air and in water. Highly resonant response is found, the product of long-wavelength scattering in the resonance-frequency region. This result points to "resonance cleaning" as a promising method for efficient particle removal.