Chapter

The Quartz Crystal Microbalance in Soft Matter Research

Part of the series Soft and Biological Matter pp 287-311

Date:

Heterogeneous Samples

  • Diethelm JohannsmannAffiliated withInstitute of Physical Chemistry, Clausthal University of Technology Email author 

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Abstract

When the sample is structured in the plane of the resonator with a characteristic scale comparable to the wavelength of sound, analytical predictions of the displacement field and the frequency shift are difficult. Among the samples that are heterogeneous in this sense are nanobubbles, nanodroplets, nanoparticles, vesicles, and biological cells. In analyzing such samples, one can rely on common sense and empirical correlations. If one wants to go beyond those more qualitative pictures, one can calculate the area-averaged periodic stress at the resonator surface numerically. An example of a numerical method is discussed in detail. The finite element method (FEM) is employed to solve the incompressible Stokes problem and to predict the periodic interfacial stress. The frequency shift follows from the area-averaged stress and the SLA.