An analysis of the surface menisci in a mixture of liquid and deformable grains

The capillary force due to liquid menisci at the surface of a mixture of deformable grains and a limited amount of liquid (exemplified by liquid phase sintered alloys) is analyzed. Geometrical models for the grains and the menisci at the specimen surface are described. The menisci curvature required to keep the grains in the anhedral (contact flattened) shape with limited liquid content is calculated from the condition that the capillary force is counterbalanced by the sphering force of the grains. The radius of the menisci at equilibrium increases with liquid content. Its dependence on the dihedral angle, on the wetting angle, and on the ratio of the interfacial energies between the liquid-vapor and solid-liquid phases is also described. The grain-meniscus system maintains a shape geometrically similar with respect to change of grain size; hence, the meniscus radius increases in proportion to the grain radius. It is proposed that the difference between the capillary force and the sphering force is the meaningful driving force for grain shape accommodation during liquid phase sintering. Finally, some experimental evidence supporting the results of these analyses is discussed.