Operation of the quartz crystal microbalance in liquids: Derivation of the elastic compliance of a film from the ratio of bandwidth shift and frequency shift

For a thin viscoelastic film deposited on a quartz crystal microbalance in a liquid environment, the change in dissipation induced by the presence of a film is proportional to the film's elastic compliance, J(f)'. This surprising result is a consequence of the fact that the film is clamped by a viscous fluid.