  We present numerical studies of complete, first-order and critical wedge
filling transitions, at a right angle corner, using a microscopic fundamental
measure density functional theory. We consider systems with short-ranged,
cut-off Lennard-Jones, fluid-fluid forces and two types of wall-fluid
potential: a purely repulsive hard wall and also a long-ranged potential with
three different strengths. For each of these systems we first determine the
wetting properties occurring at a planar wall including any wetting transition
and the dependence of the contact angle on temperature. The hard wall corner is
completely filled by vapour on approaching bulk coexistence and the numerical
results for the growth of the meniscus thickness are in excellent agreement
with effective Hamiltonian predictions for the critical exponents and
amplitudes, at leading and next-to-leading order. In the presence of the
attractive wall-fluid interaction, the corresponding planar wall-fluid
interface exhibits a first-order wetting transition for each of the interaction
strengths considered. In the right angle wedge geometry the two strongest
interactions produce first-order filling transitions while for the weakest
interaction strength, for which wetting and filling occur closest to the bulk
critical point, the filling transition is second-order. For this continuous
transition the critical exponent describing the divergence of the meniscus
thickness is found to be in good agreement with effective Hamiltonian
predictions.
