Figure 46.

The contrast functions from Equation (58) and Equation (117) are similar, algebraically. The difference is in the numerical values. In optics, the refractive index varies by a few percent. The denominator is nearly constant. Because the change in $n_{\mathrm{r}}^2$ is about proportional to concentration, the integral of the contrast function is roughly proportional to the adsorbed amount. In the case of the QCM, the viscosity of an adsorbate layer easily exceeds the viscosity of the bulk by a factor of 10 or more. The contrast function saturates to unity and the integral of the contrast function is about proportional the acoustic thickness, $d_{\mathrm{ac}}$. $d_{\mathrm{ac}}$ is the distance, at which the sample’s viscosity has decreased to about twice the viscosity of the bulk.