  We investigate the effective interactions between two nanoparticles (or
colloids) immersed in a solvent exhibiting two-phase separation. Using a
non-local density functional theory, we determine the dependence of the
effective potential on the separation of the nanoparticles when the solvent is
near bulk two-phase coexistence. If identical nanoparticles preferentially
adsorbing phase $\alpha$ are inserted into phase $\beta$, thick wetting layers
of the preferable phase $\alpha$ develop at their surfaces. At some particular
separation $h_b$ of the nanoparticles, the wetting layers connect to form a
single bridge, and the induced effective potential becomes strongly attractive
for all distances $h<h_b$. The bridging is a first order capillary condensation
like transition for all radii of the nanoparticles greater than the critical
radius $R_c$, the value of which was estimated to be approximately
$R_c\approx20\sigma$ for a temperature $T/T_c\approx0.9$, where $\sigma$ is the
size of the solvent (square-well) particles. For radii $R<R_c$ the process of
bridging is continuous. If the same particles are inserted into the preferable
phase $\alpha$, the only effective interaction between them is induced by the
short-ranged depletion potential. If the nanoparticles have opposite adsorption
preferences, only a single wetting layer forms around one of the nanoparticles
and the effective interaction is strongly repulsive in both phases. The
repulsion, induced by a disruption of the wetting film by the presence of the
second particle, is larger and slightly longer-ranged in a low density state.
