Frequency shift of a quartz crystal oscillator bounded by a self-affine fractal rough surface in contact with a liquid.

Abstract

An investigation of the coupling of shear oscillations of a quartz crystal resonator bounded by a self-affine rough surface with dumped waves in a liquid is performed. Calculation of the roughness effect is achieved in terms of a correlation model for self-affine fractal rough surfaces with analytic form of the associated roughness spectrum G(k)\ensuremath{\propto}(1+${\mathit{ak}}^{2}$${\ensuremath{\xi}}^{2}$${)}^{\mathrm{\ensuremath{-}}1\mathrm{\ensuremath{-}}\mathit{H}}$.