Thermal fluctuations of a liquid film on a heterogeneous solid substrate.

The dynamics of the fluctuations of a liquid film on a heterogeneous substrate is analyzed. We consider the case of a viscous liquid in the Stokes limit, with small variations of substrate height and a small varying slip length. We discuss the possibility of extracting the topographic profile or the slip length profile at the liquid-solid interface from the measurement of the fluctuations of the free liquid surface. Our results, therefore, explore the theoretical basis of a strategy for a fluctuation-induced microscopy of immersed solids at the micrometer scale.