A Model for the Quartz Crystal Microbalance Frequency Response to Wetting Characteristics of Corrugated Surfaces

We consider the effect of surface roughness, and its unique wetting behavior, on the response of a quartz crystal microbalance (QCM) resonator operating in contact with a fluid. The rough surface is modeled as sinusoidally corrugated particular to the case of a fixed relationship between amplitude and periodicity, as would arise from polishing with monodisperse spherical particles. The penetration of fluid into the troughs of the corrugations and the resulting meniscus are determined as a competition between surface tension and compression of the trapped gas. Liquid contained below the corrugation peaks, but above the gas/liquid meniscus, is trapped and behaves as an ideal mass layer, contributing a frequency shift that adds to that arising from liquid entrainment. This model allows QCM responses on rough surfaces to be described as a function of liquid properties and contact angle. This permits responses on hydrophobic surfaces to be understood in terms of incomplete surface wetting.