  Using classical density functional theory (DFT) we calculate the density
profile $\rho({\mathbf r})$ and local compressibility $\chi({\mathbf r})$ of a
simple liquid solvent in which a pair of blocks with (microscopic) rectangular
cross-section are immersed. We consider blocks that are solvophobic,
solvophilic and also ones that have both solvophobic and solvophilic patches.
Large values of $\chi({\mathbf r})$ correspond to regions in space where the
liquid density is fluctuating most strongly. We seek to elucidate how enhanced
density fluctuations correlate with the solvent mediated force between the
blocks, as the distance between the blocks and the chemical potential of the
liquid reservoir vary. For sufficiently solvophobic blocks, at small block
separations and small deviations from bulk gas-liquid coexistence, we observe a
strongly attractive (near constant) force, stemming from capillary evaporation
to form a low density gas-like intrusion between the blocks. The accompanying
$\chi({\mathbf r})$ exhibits structure which reflects the incipient gas-liquid
interfaces that develop. We argue that our model system provides a means to
understanding the basic physics of solvent mediated interactions between
nanostructures, and between objects such as proteins in water, that possess
hydrophobic and hydrophilic patches.
