A Hamaker-type integration of the pairwise en vacuo intermolecular forces is performed for a homogeneous triaxial ellipsoidal particle in proximity to a homogeneous semi-infinite slab bounded by a plane wall. The orientation of the ellipsoid relative to the plane is taken to be arbitrary, as too is its distance from the plane. The integrated potential energy function of the ellipsoid with respect to the slab is found to possess nonadditive positional and orientational contributions. This macroscopic potential is employed to compute the force and torque on the ellipsoid as functions of both its position and orientation relative to the plane.The novel integration scheme pertains to centrally-symmetric pairwise intermolecular potentials of arbitrary functional form. Specific results are derived for classical inverse-power intermolecular potentials possessing both attractive (r−n) and repulsive (−r−m) additive components (with n > m). In stable equilibrium the ellipsoid aligns itself with the shortest of its three principal axes perpendicular to the bounding wall, and at a separation distance comparable to the length scale of the intermolecular potential itself.
Boundary behavior of positive solutions of the heat equation on a semi-infinite slab