problem to a continuous layer with an effective dielectric function. If $\varepsilon_1$ is the dielectric function of water in its homogeneous form, then the effective dielectric function $\tilde{\varepsilon}_1$ of the material containing a volume fraction of voids $f$ can be found from the equation $$\frac{\tilde{\varepsilon}_1 -\varepsilon _{H}}{
\tilde{\varepsilon}_1 +2\varepsilon _{H}}=f\frac{1-\varepsilon _{H}}{%
1+2\varepsilon _{H}}+(1-f)\frac{\varepsilon_1 -\varepsilon _{H}}{%
\varepsilon_1 +2\varepsilon _{H}},  \label{EMA}$$ where $\varepsilon _{H}$ is the dielectric function of the ”host” material. In the Bruggman approximation it is assumed that the host material coincides with the effective medium, $\varepsilon
_{H}=\tilde{\varepsilon}_1 $, so it treats both void and material phases on an equal basis. At the imaginary frequencies $\tilde{\varepsilon}_1$ with 50% of voids ($f=0.5$) is shown in Fig. \[fig4\] as the red line.

We can calculate the force between flat surfaces using the formulas (\[E\_conv\]) and (\[F-E\]). Now for the reflection coefficients we have to use Eqs. (\[r\_multi\]) and (\[rij\]) taken at imaginary frequencies.

Figure \[fig5\] shows the force at small distances between $Au$ surfaces when both of them are covered with a continuous water layer of thickness $h=0,\;1,\;{\rm and}\;1.5\;nm$. Indeed, the force versus distance between $Au$ surfaces increases with the water layer. This is because the external boundaries of the bodies (water 