Viscoelastic Film in Liquid

As usual, we start the calculation from the small-load approximation. Equation 68 still applies, but the coefficient of reflection at the outer interface of the film now is not imity but (Zf - Z]jq)/(Zf + Ziiq) instead. The amplitude Uf is given by  

At the pole of the tangent one again has a film resonance [91]. The Chalmers group (E Hook and B. Kasemo, 2006, in this volirme) have derived an equivalent equation, which they term Voigt model [92]. Expanding Eq. 75 to first order in df, one finds  

The frequency shift is usually determined with respect to a reference state, where the quartz is aheady immersed in hquid. When the fihn is absent, one has Zl = Zliq. Referencing the measurement to the bare quartz in liquid by means of subtraction of Eq. 61 from Eq. 76, one obtains [94-96]  

Because Eq. 77 is linear in mass, it also holds in an integral sense [97]  

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