Particle-surface interactions due to capillary effects between spherical, paraboloidal, and conical particles and a flat substrate are considered. A recent approach given in a previous issue of Langmuir (Marmur, A. Langmuir 1993, 9, 1922 to obtain analytical estimates of the resulting capillary forces is discussed. Because Marmur's analytic approximation includes unnecessary simplifications, an improved formula for the approximation is given. Furthermore, the contribution of the surface tension forces acting along the contact line to the total adhesion force, which was deliberately omitted in the above cited work, is shown to be, in some cases, of similar order of magnitude as the capillary forces or even to exceed the latter. The range of applicability of the improved approach is verified by comparison with numerical solutions of the capillary equation for the liquid thread joining particle and substrate. The improved analytic approach is shown to be within (5% of the exact solution for spherical and paraboloidal probes over a wide range of contact angles and contact line positions of the liquid bridge. However, for extreme configurations such as comparatively long and thin liquid bridges or when the absolute slopes of the interface at the contact lines on probe and surface differ greatly, large deviations might occur between approximation and the numerical solution. In such cases the numerical solution should be preferred to any approximation.

No abstract

The shape of liquid surfaces in regular N-pods in the absence of gravity is considered. A liquid volume in the vertex of a regular N-pod wets the adjacent faces if the sum of the liquid's contact angle γ with the faces and half the dihedral angle α between adjacent faces is smaller than π/2. A suggestion for why the surface shape in the wedge approaches its cylindrical shape at infinity exponentially is given. The range of this exponential decrease is related to the curvature of the meniscus and the angles α and γ: The decrement of the decrease generally shows a weak dependence on α+γ, predominantly depending on the liquid volume. Extremely close to the wetting limit, when α+γ approaches π/2, the decrement vanishes. The exponential meniscus shape leads to a similarity relation and allows small relative liquid volumes in polyhedrons to be split up into partial volumes ascribed to the corners and others ascribed to the wedges. The respective relations among volume, curvature, contact angle and corner geometry are obtained by numerical simulation and the limits of applicability are discussed. This greatly simplifies the calculation of liquid surfaces in the limit of small liquid volumes. The results obtained apply to liquid surfaces in a Space environment, e.g. to metallic melts in crucibles and to propellants and other technical fluids in tanks and reservoirs, as well as to liquid surfaces on Earth, e.g. to liquids trapped in polyhedral pores and to liquid foams, provided their characteristic length is sufficiently small compared to the capillary length.