We investigate Monte Carlo simulation strategies for determining the effective (depletion) potential between a pair of hard spheres immersed in a dense sea of much smaller hard spheres. Two routes to the depletion potential are considered. The first
is based on estimates of the insertion probability of one big sphere in the presence of the other; we describe and compare three such methods. The second route exploits collective (cluster) updating to sample the depletion potential as a function of the separation of the big particles; we describe two such methods. For both routes we find that the sampling efficiency at high densities of small particles can be enhanced considerably by exploiting `geometrical shortcuts that focus the computational effort on a subset of small particles. All the methods we describe are readily extendable to particles interacting via arbitrary potentials.
We show that condensation in a capped capillary slit is a continuous interfacial critical phenomenon, related intimately to several other surface phase transitions. In three dimensions (3d), the adsorption and desorption branches correspond to the un
binding of the meniscus from the cap and opening, respectively and are equivalent to 2d-like complete-wetting transitions. For dispersion forces, the singularities on the two branches are distinct, owing to the different interplay of geometry and intermolecular forces. In 2d we establish precise connection, or covariance, with 2d critical-wetting and wedge-filling transitions, i.e. we establish that certain interfacial properties in very different geometries are identical. Our predictions of universal scaling and covariance in finite capillaries are supported by extensive Ising model simulation studies in 2d and 3d.
